A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants

ERIC Educational Resources Information Center

Cooper, Paul D.

2010-01-01

A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…

Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.

PubMed

Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo

2015-08-01

Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

PubMed

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

Structure-function relationships using spectral-domain optical coherence tomography: comparison with scanning laser polarimetry.

PubMed

Aptel, Florent; Sayous, Romain; Fortoul, Vincent; Beccat, Sylvain; Denis, Philippe

2010-12-01

To evaluate and compare the regional relationships between visual field sensitivity and retinal nerve fiber layer (RNFL) thickness as measured by spectral-domain optical coherence tomography (OCT) and scanning laser polarimetry. Prospective cross-sectional study. One hundred and twenty eyes of 120 patients (40 with healthy eyes, 40 with suspected glaucoma, and 40 with glaucoma) were tested on Cirrus-OCT, GDx VCC, and standard automated perimetry. Raw data on RNFL thickness were extracted for 256 peripapillary sectors of 1.40625 degrees each for the OCT measurement ellipse and 64 peripapillary sectors of 5.625 degrees each for the GDx VCC measurement ellipse. Correlations between peripapillary RNFL thickness in 6 sectors and visual field sensitivity in the 6 corresponding areas were evaluated using linear and logarithmic regression analysis. Receiver operating curve areas were calculated for each instrument. With spectral-domain OCT, the correlations (r(2)) between RNFL thickness and visual field sensitivity ranged from 0.082 (nasal RNFL and corresponding visual field area, linear regression) to 0.726 (supratemporal RNFL and corresponding visual field area, logarithmic regression). By comparison, with GDx-VCC, the correlations ranged from 0.062 (temporal RNFL and corresponding visual field area, linear regression) to 0.362 (supratemporal RNFL and corresponding visual field area, logarithmic regression). In pairwise comparisons, these structure-function correlations were generally stronger with spectral-domain OCT than with GDx VCC and with logarithmic regression than with linear regression. The largest areas under the receiver operating curve were seen for OCT superior thickness (0.963 ± 0.022; P < .001) in eyes with glaucoma and for OCT average thickness (0.888 ± 0.072; P < .001) in eyes with suspected glaucoma. The structure-function relationship was significantly stronger with spectral-domain OCT than with scanning laser polarimetry, and was better expressed logarithmically than linearly. Measurements with these 2 instruments should not be considered to be interchangeable. Copyright © 2010 Elsevier Inc. All rights reserved.

Linear and nonlinear regression techniques for simultaneous and proportional myoelectric control.

PubMed

Hahne, J M; Biessmann, F; Jiang, N; Rehbaum, H; Farina, D; Meinecke, F C; Muller, K-R; Parra, L C

2014-03-01

In recent years the number of active controllable joints in electrically powered hand-prostheses has increased significantly. However, the control strategies for these devices in current clinical use are inadequate as they require separate and sequential control of each degree-of-freedom (DoF). In this study we systematically compare linear and nonlinear regression techniques for an independent, simultaneous and proportional myoelectric control of wrist movements with two DoF. These techniques include linear regression, mixture of linear experts (ME), multilayer-perceptron, and kernel ridge regression (KRR). They are investigated offline with electro-myographic signals acquired from ten able-bodied subjects and one person with congenital upper limb deficiency. The control accuracy is reported as a function of the number of electrodes and the amount and diversity of training data providing guidance for the requirements in clinical practice. The results showed that KRR, a nonparametric statistical learning method, outperformed the other methods. However, simple transformations in the feature space could linearize the problem, so that linear models could achieve similar performance as KRR at much lower computational costs. Especially ME, a physiologically inspired extension of linear regression represents a promising candidate for the next generation of prosthetic devices.

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Quality of life in breast cancer patients--a quantile regression analysis.

PubMed

Pourhoseingholi, Mohamad Amin; Safaee, Azadeh; Moghimi-Dehkordi, Bijan; Zeighami, Bahram; Faghihzadeh, Soghrat; Tabatabaee, Hamid Reza; Pourhoseingholi, Asma

2008-01-01

Quality of life study has an important role in health care especially in chronic diseases, in clinical judgment and in medical resources supplying. Statistical tools like linear regression are widely used to assess the predictors of quality of life. But when the response is not normal the results are misleading. The aim of this study is to determine the predictors of quality of life in breast cancer patients, using quantile regression model and compare to linear regression. A cross-sectional study conducted on 119 breast cancer patients that admitted and treated in chemotherapy ward of Namazi hospital in Shiraz. We used QLQ-C30 questionnaire to assessment quality of life in these patients. A quantile regression was employed to assess the assocciated factors and the results were compared to linear regression. All analysis carried out using SAS. The mean score for the global health status for breast cancer patients was 64.92+/-11.42. Linear regression showed that only grade of tumor, occupational status, menopausal status, financial difficulties and dyspnea were statistically significant. In spite of linear regression, financial difficulties were not significant in quantile regression analysis and dyspnea was only significant for first quartile. Also emotion functioning and duration of disease statistically predicted the QOL score in the third quartile. The results have demonstrated that using quantile regression leads to better interpretation and richer inference about predictors of the breast cancer patient quality of life.

Naval Research Logistics Quarterly. Volume 28. Number 3,

DTIC Science & Technology

1981-09-01

denotes component-wise maximum. f has antone (isotone) differences on C x D if for cl < c2 and d, < d2, NAVAL RESEARCH LOGISTICS QUARTERLY VOL. 28...or negative correlations and linear or nonlinear regressions. Given are the mo- ments to order two and, for special cases, (he regression function and...data sets. We designate this bnb distribution as G - B - N(a, 0, v). The distribution admits only of positive correlation and linear regressions

RBF kernel based support vector regression to estimate the blood volume and heart rate responses during hemodialysis.

PubMed

Javed, Faizan; Chan, Gregory S H; Savkin, Andrey V; Middleton, Paul M; Malouf, Philip; Steel, Elizabeth; Mackie, James; Lovell, Nigel H

2009-01-01

This paper uses non-linear support vector regression (SVR) to model the blood volume and heart rate (HR) responses in 9 hemodynamically stable kidney failure patients during hemodialysis. Using radial bias function (RBF) kernels the non-parametric models of relative blood volume (RBV) change with time as well as percentage change in HR with respect to RBV were obtained. The e-insensitivity based loss function was used for SVR modeling. Selection of the design parameters which includes capacity (C), insensitivity region (e) and the RBF kernel parameter (sigma) was made based on a grid search approach and the selected models were cross-validated using the average mean square error (AMSE) calculated from testing data based on a k-fold cross-validation technique. Linear regression was also applied to fit the curves and the AMSE was calculated for comparison with SVR. For the model based on RBV with time, SVR gave a lower AMSE for both training (AMSE=1.5) as well as testing data (AMSE=1.4) compared to linear regression (AMSE=1.8 and 1.5). SVR also provided a better fit for HR with RBV for both training as well as testing data (AMSE=15.8 and 16.4) compared to linear regression (AMSE=25.2 and 20.1).

Adding a Parameter Increases the Variance of an Estimated Regression Function

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2011-01-01

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Penalized nonparametric scalar-on-function regression via principal coordinates

PubMed Central

Reiss, Philip T.; Miller, David L.; Wu, Pei-Shien; Hua, Wen-Yu

2016-01-01

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. PMID:29217963

Mental chronometry with simple linear regression.

PubMed

Chen, J Y

1997-10-01

Typically, mental chronometry is performed by means of introducing an independent variable postulated to affect selectively some stage of a presumed multistage process. However, the effect could be a global one that spreads proportionally over all stages of the process. Currently, there is no method to test this possibility although simple linear regression might serve the purpose. In the present study, the regression approach was tested with tasks (memory scanning and mental rotation) that involved a selective effect and with a task (word superiority effect) that involved a global effect, by the dominant theories. The results indicate (1) the manipulation of the size of a memory set or of angular disparity affects the intercept of the regression function that relates the times for memory scanning with different set sizes or for mental rotation with different angular disparities and (2) the manipulation of context affects the slope of the regression function that relates the times for detecting a target character under word and nonword conditions. These ratify the regression approach as a useful method for doing mental chronometry.

Structured functional additive regression in reproducing kernel Hilbert spaces.

PubMed

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2014-06-01

Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.

Generating linear regression model to predict motor functions by use of laser range finder during TUG.

PubMed

Adachi, Daiki; Nishiguchi, Shu; Fukutani, Naoto; Hotta, Takayuki; Tashiro, Yuto; Morino, Saori; Shirooka, Hidehiko; Nozaki, Yuma; Hirata, Hinako; Yamaguchi, Moe; Yorozu, Ayanori; Takahashi, Masaki; Aoyama, Tomoki

2017-05-01

The purpose of this study was to investigate which spatial and temporal parameters of the Timed Up and Go (TUG) test are associated with motor function in elderly individuals. This study included 99 community-dwelling women aged 72.9 ± 6.3 years. Step length, step width, single support time, variability of the aforementioned parameters, gait velocity, cadence, reaction time from starting signal to first step, and minimum distance between the foot and a marker placed to 3 in front of the chair were measured using our analysis system. The 10-m walk test, five times sit-to-stand (FTSTS) test, and one-leg standing (OLS) test were used to assess motor function. Stepwise multivariate linear regression analysis was used to determine which TUG test parameters were associated with each motor function test. Finally, we calculated a predictive model for each motor function test using each regression coefficient. In stepwise linear regression analysis, step length and cadence were significantly associated with the 10-m walk test, FTSTS and OLS test. Reaction time was associated with the FTSTS test, and step width was associated with the OLS test. Each predictive model showed a strong correlation with the 10-m walk test and OLS test (P < 0.01), which was not significant higher correlation than TUG test time. We showed which TUG test parameters were associated with each motor function test. Moreover, the TUG test time regarded as the lower extremity function and mobility has strong predictive ability in each motor function test. Copyright © 2017 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.

Pointwise influence matrices for functional-response regression.

PubMed

Reiss, Philip T; Huang, Lei; Wu, Pei-Shien; Chen, Huaihou; Colcombe, Stan

2017-12-01

We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise influence matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor. This procedure adapts to varying complexity of the nonlinear model at different locations along the function, and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain. © 2017, The International Biometric Society.

Weighted functional linear regression models for gene-based association analysis.

PubMed

Belonogova, Nadezhda M; Svishcheva, Gulnara R; Wilson, James F; Campbell, Harry; Axenovich, Tatiana I

2018-01-01

Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P < 0.1 in at least one analysis had lower P values with weighted models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.

Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi; Balasiddamuni, P.

2017-11-01

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work “Tutorial on maximum likelihood estimation

High-frequency toneburst-evoked ABR latency-intensity functions in sensorineural hearing-impaired humans.

PubMed

Fausti, S A; Olson, D J; Frey, R H; Henry, J A; Schaffer, H I; Phillips, D S

1995-01-01

The latency-intensity functions (LIFs) of ABRs elicited by high-frequency (8, 10, 12, and 14 kHz) toneburst stimuli were evaluated in 20 subjects with confirmed 'moderate' high-frequency sensorineural hearing loss. Wave V results from clicks and tonebursts revealed all intra- and intersession data to be reliable (p > 0.05). Linear regression curves were highly significant (p < or = 0.0001), indicating linear relationships for all stimuli analyzed. Comparisons between the linear regression curves from a previously reported normal-hearing subject group and this sensorineural hearing-impaired group showed no significant differences. This study demonstrated that tonebursts at 8, 10, and 12 kHz evoked ABRs which decreased in latency as a function of increasing intensity and that these LIFs were consistent and orderly (14 kHz was not determinable). These results will contribute information to facilitate the establishment of change criteria used to predict change in hearing during treatment with ototoxic medications.

Electricity Consumption in the Industrial Sector of Jordan: Application of Multivariate Linear Regression and Adaptive Neuro-Fuzzy Techniques

NASA Astrophysics Data System (ADS)

Samhouri, M.; Al-Ghandoor, A.; Fouad, R. H.

2009-08-01

In this study two techniques, for modeling electricity consumption of the Jordanian industrial sector, are presented: (i) multivariate linear regression and (ii) neuro-fuzzy models. Electricity consumption is modeled as function of different variables such as number of establishments, number of employees, electricity tariff, prevailing fuel prices, production outputs, capacity utilizations, and structural effects. It was found that industrial production and capacity utilization are the most important variables that have significant effect on future electrical power demand. The results showed that both the multivariate linear regression and neuro-fuzzy models are generally comparable and can be used adequately to simulate industrial electricity consumption. However, comparison that is based on the square root average squared error of data suggests that the neuro-fuzzy model performs slightly better for future prediction of electricity consumption than the multivariate linear regression model. Such results are in full agreement with similar work, using different methods, for other countries.

Improving Prediction Accuracy for WSN Data Reduction by Applying Multivariate Spatio-Temporal Correlation

PubMed Central

Carvalho, Carlos; Gomes, Danielo G.; Agoulmine, Nazim; de Souza, José Neuman

2011-01-01

This paper proposes a method based on multivariate spatial and temporal correlation to improve prediction accuracy in data reduction for Wireless Sensor Networks (WSN). Prediction of data not sent to the sink node is a technique used to save energy in WSNs by reducing the amount of data traffic. However, it may not be very accurate. Simulations were made involving simple linear regression and multiple linear regression functions to assess the performance of the proposed method. The results show a higher correlation between gathered inputs when compared to time, which is an independent variable widely used for prediction and forecasting. Prediction accuracy is lower when simple linear regression is used, whereas multiple linear regression is the most accurate one. In addition to that, our proposal outperforms some current solutions by about 50% in humidity prediction and 21% in light prediction. To the best of our knowledge, we believe that we are probably the first to address prediction based on multivariate correlation for WSN data reduction. PMID:22346626

Regression Model Term Selection for the Analysis of Strain-Gage Balance Calibration Data

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred; Volden, Thomas R.

2010-01-01

The paper discusses the selection of regression model terms for the analysis of wind tunnel strain-gage balance calibration data. Different function class combinations are presented that may be used to analyze calibration data using either a non-iterative or an iterative method. The role of the intercept term in a regression model of calibration data is reviewed. In addition, useful algorithms and metrics originating from linear algebra and statistics are recommended that will help an analyst (i) to identify and avoid both linear and near-linear dependencies between regression model terms and (ii) to make sure that the selected regression model of the calibration data uses only statistically significant terms. Three different tests are suggested that may be used to objectively assess the predictive capability of the final regression model of the calibration data. These tests use both the original data points and regression model independent confirmation points. Finally, data from a simplified manual calibration of the Ames MK40 balance is used to illustrate the application of some of the metrics and tests to a realistic calibration data set.

Structured functional additive regression in reproducing kernel Hilbert spaces

PubMed Central

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2013-01-01

Summary Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application. PMID:25013362

Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy.

PubMed

Huppert, Theodore J

2016-01-01

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

Identification of International Classification of Functioning, Disability and Health categories for patients with peripheral arterial disease.

PubMed

Vyskocil, Erich; Gruther, Wolfgang; Steiner, Irene; Schuhfried, Othmar

2014-07-01

Disease-specific categories of the International Classification of Functioning, Disability and Health have not yet been described for patients with chronic peripheral arterial obstructive disease (PAD). The authors examined the relationship between the categories of the Brief Core Sets for ischemic heart diseases with the Peripheral Artery Questionnaire and the ankle-brachial index to determine which International Classification of Functioning, Disability and Health categories are most relevant for patients with PAD. This is a retrospective cohort study including 77 patients with verified PAD. Statistical analyses of the relationship between International Classification of Functioning, Disability and Health categories as independent variables and the endpoints Peripheral Artery Questionnaire or ankle-brachial index were carried out by simple and stepwise linear regression models adjusting for age, sex, and leg (left vs. right). The stepwise linear regression model with the ankle-brachial index as dependent variable revealed a significant effect of the variables blood vessel functions and muscle endurance functions. Calculating a stepwise linear regression model with the Peripheral Artery Questionnaire as dependent variable, a significant effect of age, emotional functions, energy and drive functions, carrying out daily routine, as well as walking could be observed. This study identifies International Classification of Functioning, Disability and Health categories in the Brief Core Sets for ischemic heart diseases that show a significant effect on the ankle-brachial index and the Peripheral Artery Questionnaire score in patients with PAD. These categories provide fundamental information on functioning of patients with PAD and patient-centered outcomes for rehabilitation interventions.

Functional mixture regression.

PubMed

Yao, Fang; Fu, Yuejiao; Lee, Thomas C M

2011-04-01

In functional linear models (FLMs), the relationship between the scalar response and the functional predictor process is often assumed to be identical for all subjects. Motivated by both practical and methodological considerations, we relax this assumption and propose a new class of functional regression models that allow the regression structure to vary for different groups of subjects. By projecting the predictor process onto its eigenspace, the new functional regression model is simplified to a framework that is similar to classical mixture regression models. This leads to the proposed approach named as functional mixture regression (FMR). The estimation of FMR can be readily carried out using existing software implemented for functional principal component analysis and mixture regression. The practical necessity and performance of FMR are illustrated through applications to a longevity analysis of female medflies and a human growth study. Theoretical investigations concerning the consistent estimation and prediction properties of FMR along with simulation experiments illustrating its empirical properties are presented in the supplementary material available at Biostatistics online. Corresponding results demonstrate that the proposed approach could potentially achieve substantial gains over traditional FLMs.

A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models.

PubMed

Casero-Alonso, V; López-Fidalgo, J; Torsney, B

2017-01-01

Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions. The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

New method for calculating a mathematical expression for streamflow recession

USGS Publications Warehouse

Rutledge, Albert T.

1991-01-01

An empirical method has been devised to calculate the master recession curve, which is a mathematical expression for streamflow recession during times of negligible direct runoff. The method is based on the assumption that the storage-delay factor, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of streamflow. The resulting master recession curve can be nonlinear. The method can be executed by a computer program that reads a data file of daily mean streamflow, then allows the user to select several near-linear segments of streamflow recession. The storage-delay factor for each segment is one of the coefficients of the equation that results from linear least-squares regression. Using results for each recession segment, a mathematical expression of the storage-delay factor as a function of the log of streamflow is determined by linear least-squares regression. The master recession curve, which is a second-order polynomial expression for time as a function of log of streamflow, is then derived using the coefficients of this function.

Structured penalties for functional linear models-partially empirical eigenvectors for regression.

PubMed

Randolph, Timothy W; Harezlak, Jaroslaw; Feng, Ziding

2012-01-01

One of the challenges with functional data is incorporating geometric structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear model is often used to estimate the relationship between the predictor functions and scalar responses. Common approaches to the problem of estimating a coefficient function typically involve two stages: regularization and estimation. Regularization is usually done via dimension reduction, projecting onto a predefined span of basis functions or a reduced set of eigenvectors (principal components). In contrast, we present a unified approach that directly incorporates geometric structure into the estimation process by exploiting the joint eigenproperties of the predictors and a linear penalty operator. In this sense, the components in the regression are 'partially empirical' and the framework is provided by the generalized singular value decomposition (GSVD). The form of the penalized estimation is not new, but the GSVD clarifies the process and informs the choice of penalty by making explicit the joint influence of the penalty and predictors on the bias, variance and performance of the estimated coefficient function. Laboratory spectroscopy data and simulations are used to illustrate the concepts.

Deriving the Regression Equation without Using Calculus

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

A primer for biomedical scientists on how to execute model II linear regression analysis.

PubMed

Ludbrook, John

2012-04-01

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.

Methods for scalar-on-function regression.

PubMed

Reiss, Philip T; Goldsmith, Jeff; Shang, Han Lin; Ogden, R Todd

2017-08-01

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

Macrocell path loss prediction using artificial intelligence techniques

NASA Astrophysics Data System (ADS)

Usman, Abraham U.; Okereke, Okpo U.; Omizegba, Elijah E.

2014-04-01

The prediction of propagation loss is a practical non-linear function approximation problem which linear regression or auto-regression models are limited in their ability to handle. However, some computational Intelligence techniques such as artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs) have been shown to have great ability to handle non-linear function approximation and prediction problems. In this study, the multiple layer perceptron neural network (MLP-NN), radial basis function neural network (RBF-NN) and an ANFIS network were trained using actual signal strength measurement taken at certain suburban areas of Bauchi metropolis, Nigeria. The trained networks were then used to predict propagation losses at the stated areas under differing conditions. The predictions were compared with the prediction accuracy of the popular Hata model. It was observed that ANFIS model gave a better fit in all cases having higher R2 values in each case and on average is more robust than MLP and RBF models as it generalises better to a different data.

Simultaneous multiple non-crossing quantile regression estimation using kernel constraints

PubMed Central

Liu, Yufeng; Wu, Yichao

2011-01-01

Quantile regression (QR) is a very useful statistical tool for learning the relationship between the response variable and covariates. For many applications, one often needs to estimate multiple conditional quantile functions of the response variable given covariates. Although one can estimate multiple quantiles separately, it is of great interest to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain better estimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility of incorporating simultaneous non-crossing constraints of QR functions. In this paper, we propose a new kernel-based multiple QR estimation technique, namely simultaneous non-crossing quantile regression (SNQR). We use kernel representations for QR functions and apply constraints on the kernel coefficients to avoid crossing. Both unregularised and regularised SNQR techniques are considered. Asymptotic properties such as asymptotic normality of linear SNQR and oracle properties of the sparse linear SNQR are developed. Our numerical results demonstrate the competitive performance of our SNQR over the original individual QR estimation. PMID:22190842

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Prediction of clinical depression scores and detection of changes in whole-brain using resting-state functional MRI data with partial least squares regression

PubMed Central

Shimizu, Yu; Yoshimoto, Junichiro; Takamura, Masahiro; Okada, Go; Okamoto, Yasumasa; Yamawaki, Shigeto; Doya, Kenji

2017-01-01

In diagnostic applications of statistical machine learning methods to brain imaging data, common problems include data high-dimensionality and co-linearity, which often cause over-fitting and instability. To overcome these problems, we applied partial least squares (PLS) regression to resting-state functional magnetic resonance imaging (rs-fMRI) data, creating a low-dimensional representation that relates symptoms to brain activity and that predicts clinical measures. Our experimental results, based upon data from clinically depressed patients and healthy controls, demonstrated that PLS and its kernel variants provided significantly better prediction of clinical measures than ordinary linear regression. Subsequent classification using predicted clinical scores distinguished depressed patients from healthy controls with 80% accuracy. Moreover, loading vectors for latent variables enabled us to identify brain regions relevant to depression, including the default mode network, the right superior frontal gyrus, and the superior motor area. PMID:28700672

Lifespan development of pro- and anti-saccades: multiple regression models for point estimates.

PubMed

Klein, Christoph; Foerster, Friedrich; Hartnegg, Klaus; Fischer, Burkhart

2005-12-07

The comparative study of anti- and pro-saccade task performance contributes to our functional understanding of the frontal lobes, their alterations in psychiatric or neurological populations, and their changes during the life span. In the present study, we apply regression analysis to model life span developmental effects on various pro- and anti-saccade task parameters, using data of a non-representative sample of 327 participants aged 9 to 88 years. Development up to the age of about 27 years was dominated by curvilinear rather than linear effects of age. Furthermore, the largest developmental differences were found for intra-subject variability measures and the anti-saccade task parameters. Ageing, by contrast, had the shape of a global linear decline of the investigated saccade functions, lacking the differential effects of age observed during development. While these results do support the assumption that frontal lobe functions can be distinguished from other functions by their strong and protracted development, they do not confirm the assumption of disproportionate deterioration of frontal lobe functions with ageing. We finally show that the regression models applied here to quantify life span developmental effects can also be used for individual predictions in applied research contexts or clinical practice.

Estimating effects of limiting factors with regression quantiles

USGS Publications Warehouse

Cade, B.S.; Terrell, J.W.; Schroeder, R.L.

1999-01-01

In a recent Concepts paper in Ecology, Thomson et al. emphasized that assumptions of conventional correlation and regression analyses fundamentally conflict with the ecological concept of limiting factors, and they called for new statistical procedures to address this problem. The analytical issue is that unmeasured factors may be the active limiting constraint and may induce a pattern of unequal variation in the biological response variable through an interaction with the measured factors. Consequently, changes near the maxima, rather than at the center of response distributions, are better estimates of the effects expected when the observed factor is the active limiting constraint. Regression quantiles provide estimates for linear models fit to any part of a response distribution, including near the upper bounds, and require minimal assumptions about the form of the error distribution. Regression quantiles extend the concept of one-sample quantiles to the linear model by solving an optimization problem of minimizing an asymmetric function of absolute errors. Rank-score tests for regression quantiles provide tests of hypotheses and confidence intervals for parameters in linear models with heteroscedastic errors, conditions likely to occur in models of limiting ecological relations. We used selected regression quantiles (e.g., 5th, 10th, ..., 95th) and confidence intervals to test hypotheses that parameters equal zero for estimated changes in average annual acorn biomass due to forest canopy cover of oak (Quercus spp.) and oak species diversity. Regression quantiles also were used to estimate changes in glacier lily (Erythronium grandiflorum) seedling numbers as a function of lily flower numbers, rockiness, and pocket gopher (Thomomys talpoides fossor) activity, data that motivated the query by Thomson et al. for new statistical procedures. Both example applications showed that effects of limiting factors estimated by changes in some upper regression quantile (e.g., 90-95th) were greater than if effects were estimated by changes in the means from standard linear model procedures. Estimating a range of regression quantiles (e.g., 5-95th) provides a comprehensive description of biological response patterns for exploratory and inferential analyses in observational studies of limiting factors, especially when sampling large spatial and temporal scales.

Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

NASA Astrophysics Data System (ADS)

Caimmi, R.

2011-08-01

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in the presence of large dispersion data. An extension of the formalism to structural models is left to a forthcoming paper.

Enhancement of partial robust M-regression (PRM) performance using Bisquare weight function

NASA Astrophysics Data System (ADS)

Mohamad, Mazni; Ramli, Norazan Mohamed; Ghani@Mamat, Nor Azura Md; Ahmad, Sanizah

2014-09-01

Partial Least Squares (PLS) regression is a popular regression technique for handling multicollinearity in low and high dimensional data which fits a linear relationship between sets of explanatory and response variables. Several robust PLS methods are proposed to accommodate the classical PLS algorithms which are easily affected with the presence of outliers. The recent one was called partial robust M-regression (PRM). Unfortunately, the use of monotonous weighting function in the PRM algorithm fails to assign appropriate and proper weights to large outliers according to their severity. Thus, in this paper, a modified partial robust M-regression is introduced to enhance the performance of the original PRM. A re-descending weight function, known as Bisquare weight function is recommended to replace the fair function in the PRM. A simulation study is done to assess the performance of the modified PRM and its efficiency is also tested in both contaminated and uncontaminated simulated data under various percentages of outliers, sample sizes and number of predictors.

A land use regression model for ambient ultrafine particles in Montreal, Canada: A comparison of linear regression and a machine learning approach.

PubMed

Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne

2016-04-01

Existing evidence suggests that ambient ultrafine particles (UFPs) (<0.1µm) may contribute to acute cardiorespiratory morbidity. However, few studies have examined the long-term health effects of these pollutants owing in part to a need for exposure surfaces that can be applied in large population-based studies. To address this need, we developed a land use regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

Spatio-temporal water quality mapping from satellite images using geographically and temporally weighted regression

NASA Astrophysics Data System (ADS)

Chu, Hone-Jay; Kong, Shish-Jeng; Chang, Chih-Hua

2018-03-01

The turbidity (TB) of a water body varies with time and space. Water quality is traditionally estimated via linear regression based on satellite images. However, estimating and mapping water quality require a spatio-temporal nonstationary model, while TB mapping necessitates the use of geographically and temporally weighted regression (GTWR) and geographically weighted regression (GWR) models, both of which are more precise than linear regression. Given the temporal nonstationary models for mapping water quality, GTWR offers the best option for estimating regional water quality. Compared with GWR, GTWR provides highly reliable information for water quality mapping, boasts a relatively high goodness of fit, improves the explanation of variance from 44% to 87%, and shows a sufficient space-time explanatory power. The seasonal patterns of TB and the main spatial patterns of TB variability can be identified using the estimated TB maps from GTWR and by conducting an empirical orthogonal function (EOF) analysis.

A comparative study between nonlinear regression and artificial neural network approaches for modelling wild oat (Avena fatua) field emergence

USDA-ARS?s Scientific Manuscript database

Non-linear regression techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks present interesting and alternative features for such modeling purposes. In this work, a univariate hydrothermal-time based Weibull m...

Survival Data and Regression Models

NASA Astrophysics Data System (ADS)

Grégoire, G.

2014-12-01

We start this chapter by introducing some basic elements for the analysis of censored survival data. Then we focus on right censored data and develop two types of regression models. The first one concerns the so-called accelerated failure time models (AFT), which are parametric models where a function of a parameter depends linearly on the covariables. The second one is a semiparametric model, where the covariables enter in a multiplicative form in the expression of the hazard rate function. The main statistical tool for analysing these regression models is the maximum likelihood methodology and, in spite we recall some essential results about the ML theory, we refer to the chapter "Logistic Regression" for a more detailed presentation.

Double-time correlation functions of two quantum operations in open systems

NASA Astrophysics Data System (ADS)

Ban, Masashi

2017-10-01

A double-time correlation function of arbitrary two quantum operations is studied for a nonstationary open quantum system which is in contact with a thermal reservoir. It includes a usual correlation function, a linear response function, and a weak value of an observable. Time evolution of the correlation function can be derived by means of the time-convolution and time-convolutionless projection operator techniques. For this purpose, a quasidensity operator accompanied by a fictitious field is introduced, which makes it possible to derive explicit formulas for calculating a double-time correlation function in the second-order approximation with respect to a system-reservoir interaction. The derived formula explicitly shows that the quantum regression theorem for calculating the double-time correlation function cannot be used if a thermal reservoir has a finite correlation time. Furthermore, the formula is applied for a pure dephasing process and a linear dissipative process. The quantum regression theorem and the the Leggett-Garg inequality are investigated for an open two-level system. The results are compared with those obtained by exact calculation to examine whether the formula is a good approximation.

Optimizing Support Vector Machine Parameters with Genetic Algorithm for Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Manurung, Jonson; Mawengkang, Herman; Zamzami, Elviawaty

2017-12-01

Support vector machine (SVM) is a popular classification method known to have strong generalization capabilities. SVM can solve the problem of classification and linear regression or nonlinear kernel which can be a learning algorithm for the ability of classification and regression. However, SVM also has a weakness that is difficult to determine the optimal parameter value. SVM calculates the best linear separator on the input feature space according to the training data. To classify data which are non-linearly separable, SVM uses kernel tricks to transform the data into a linearly separable data on a higher dimension feature space. The kernel trick using various kinds of kernel functions, such as : linear kernel, polynomial, radial base function (RBF) and sigmoid. Each function has parameters which affect the accuracy of SVM classification. To solve the problem genetic algorithms are proposed to be applied as the optimal parameter value search algorithm thus increasing the best classification accuracy on SVM. Data taken from UCI repository of machine learning database: Australian Credit Approval. The results show that the combination of SVM and genetic algorithms is effective in improving classification accuracy. Genetic algorithms has been shown to be effective in systematically finding optimal kernel parameters for SVM, instead of randomly selected kernel parameters. The best accuracy for data has been upgraded from kernel Linear: 85.12%, polynomial: 81.76%, RBF: 77.22% Sigmoid: 78.70%. However, for bigger data sizes, this method is not practical because it takes a lot of time.

Image interpolation via regularized local linear regression.

PubMed

Liu, Xianming; Zhao, Debin; Xiong, Ruiqin; Ma, Siwei; Gao, Wen; Sun, Huifang

2011-12-01

The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the l(2)-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation. © 2011 IEEE

Comparing Linear Discriminant Function with Logistic Regression for the Two-Group Classification Problem.

ERIC Educational Resources Information Center

Fan, Xitao; Wang, Lin

The Monte Carlo study compared the performance of predictive discriminant analysis (PDA) and that of logistic regression (LR) for the two-group classification problem. Prior probabilities were used for classification, but the cost of misclassification was assumed to be equal. The study used a fully crossed three-factor experimental design (with…

Interaction Models for Functional Regression.

PubMed

Usset, Joseph; Staicu, Ana-Maria; Maity, Arnab

2016-02-01

A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized linear models and data observed on sparse grids or with measurement error are presented. A hypothesis testing procedure for the functional interaction effect is described. The proposed method can be easily implemented through existing software. Numerical studies show that fitting an additive model in the presence of interaction leads to both poor estimation performance and lost prediction power, while fitting an interaction model where there is in fact no interaction leads to negligible losses. The methodology is illustrated on the AneuRisk65 study data.

Precision Interval Estimation of the Response Surface by Means of an Integrated Algorithm of Neural Network and Linear Regression

NASA Technical Reports Server (NTRS)

Lo, Ching F.

1999-01-01

The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.

Estimation and Selection via Absolute Penalized Convex Minimization And Its Multistage Adaptive Applications

PubMed Central

Huang, Jian; Zhang, Cun-Hui

2013-01-01

The ℓ1-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of high-dimensional statistical problems. In this article, we consider a class of weighted ℓ1-penalized estimators for convex loss functions of a general form, including the generalized linear models. We study the estimation, prediction, selection and sparsity properties of the weighted ℓ1-penalized estimator in sparse, high-dimensional settings where the number of predictors p can be much larger than the sample size n. Adaptive Lasso is considered as a special case. A multistage method is developed to approximate concave regularized estimation by applying an adaptive Lasso recursively. We provide prediction and estimation oracle inequalities for single- and multi-stage estimators, a general selection consistency theorem, and an upper bound for the dimension of the Lasso estimator. Important models including the linear regression, logistic regression and log-linear models are used throughout to illustrate the applications of the general results. PMID:24348100

Modeling Pan Evaporation for Kuwait by Multiple Linear Regression

PubMed Central

Almedeij, Jaber

2012-01-01

Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984

Advanced statistics: linear regression, part I: simple linear regression.

PubMed

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Age and mortality after injury: is the association linear?

PubMed

Friese, R S; Wynne, J; Joseph, B; Hashmi, A; Diven, C; Pandit, V; O'Keeffe, T; Zangbar, B; Kulvatunyou, N; Rhee, P

2014-10-01

Multiple studies have demonstrated a linear association between advancing age and mortality after injury. An inflection point, or an age at which outcomes begin to differ, has not been previously described. We hypothesized that the relationship between age and mortality after injury is non-linear and an inflection point exists. We performed a retrospective cohort analysis at our urban level I center from 2007 through 2009. All patients aged 65 years and older with the admission diagnosis of injury were included. Non-parametric logistic regression was used to identify the functional form between mortality and age. Multivariate logistic regression was utilized to explore the association between age and mortality. Age 65 years was used as the reference. Significance was defined as p < 0.05. A total of 1,107 patients were included in the analysis. One-third required intensive care unit (ICU) admission and 48 % had traumatic brain injury. 229 patients (20.6 %) were 84 years of age or older. The overall mortality was 7.2 %. Our model indicates that mortality is a quadratic function of age. After controlling for confounders, age is associated with mortality with a regression coefficient of 1.08 for the linear term (p = 0.02) and a regression coefficient of -0.006 for the quadratic term (p = 0.03). The model identified 84.4 years of age as the inflection point at which mortality rates begin to decline. The risk of death after injury varies linearly with age until 84 years. After 84 years of age, the mortality rates decline. These findings may reflect the varying severity of comorbidities and differences in baseline functional status in elderly trauma patients. Specifically, a proportion of our injured patient population less than 84 years old may be more frail, contributing to increased mortality after trauma, whereas a larger proportion of our injured patients over 84 years old, by virtue of reaching this advanced age, may, in fact, be less frail, contributing to less risk of death.

Optimized multiple linear mappings for single image super-resolution

NASA Astrophysics Data System (ADS)

Zhang, Kaibing; Li, Jie; Xiong, Zenggang; Liu, Xiuping; Gao, Xinbo

2017-12-01

Learning piecewise linear regression has been recognized as an effective way for example learning-based single image super-resolution (SR) in literature. In this paper, we employ an expectation-maximization (EM) algorithm to further improve the SR performance of our previous multiple linear mappings (MLM) based SR method. In the training stage, the proposed method starts with a set of linear regressors obtained by the MLM-based method, and then jointly optimizes the clustering results and the low- and high-resolution subdictionary pairs for regression functions by using the metric of the reconstruction errors. In the test stage, we select the optimal regressor for SR reconstruction by accumulating the reconstruction errors of m-nearest neighbors in the training set. Thorough experimental results carried on six publicly available datasets demonstrate that the proposed SR method can yield high-quality images with finer details and sharper edges in terms of both quantitative and perceptual image quality assessments.

Connectome-based predictive modeling of attention: Comparing different functional connectivity features and prediction methods across datasets.

PubMed

Yoo, Kwangsun; Rosenberg, Monica D; Hsu, Wei-Ting; Zhang, Sheng; Li, Chiang-Shan R; Scheinost, Dustin; Constable, R Todd; Chun, Marvin M

2018-02-15

Connectome-based predictive modeling (CPM; Finn et al., 2015; Shen et al., 2017) was recently developed to predict individual differences in traits and behaviors, including fluid intelligence (Finn et al., 2015) and sustained attention (Rosenberg et al., 2016a), from functional brain connectivity (FC) measured with fMRI. Here, using the CPM framework, we compared the predictive power of three different measures of FC (Pearson's correlation, accordance, and discordance) and two different prediction algorithms (linear and partial least square [PLS] regression) for attention function. Accordance and discordance are recently proposed FC measures that respectively track in-phase synchronization and out-of-phase anti-correlation (Meskaldji et al., 2015). We defined connectome-based models using task-based or resting-state FC data, and tested the effects of (1) functional connectivity measure and (2) feature-selection/prediction algorithm on individualized attention predictions. Models were internally validated in a training dataset using leave-one-subject-out cross-validation, and externally validated with three independent datasets. The training dataset included fMRI data collected while participants performed a sustained attention task and rested (N = 25; Rosenberg et al., 2016a). The validation datasets included: 1) data collected during performance of a stop-signal task and at rest (N = 83, including 19 participants who were administered methylphenidate prior to scanning; Farr et al., 2014a; Rosenberg et al., 2016b), 2) data collected during Attention Network Task performance and rest (N = 41, Rosenberg et al., in press), and 3) resting-state data and ADHD symptom severity from the ADHD-200 Consortium (N = 113; Rosenberg et al., 2016a). Models defined using all combinations of functional connectivity measure (Pearson's correlation, accordance, and discordance) and prediction algorithm (linear and PLS regression) predicted attentional abilities, with correlations between predicted and observed measures of attention as high as 0.9 for internal validation, and 0.6 for external validation (all p's < 0.05). Models trained on task data outperformed models trained on rest data. Pearson's correlation and accordance features generally showed a small numerical advantage over discordance features, while PLS regression models were usually better than linear regression models. Overall, in addition to correlation features combined with linear models (Rosenberg et al., 2016a), it is useful to consider accordance features and PLS regression for CPM. Copyright © 2017 Elsevier Inc. All rights reserved.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-11-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Profile local linear estimation of generalized semiparametric regression model for longitudinal data.

PubMed

Sun, Yanqing; Sun, Liuquan; Zhou, Jie

2013-07-01

This paper studies the generalized semiparametric regression model for longitudinal data where the covariate effects are constant for some and time-varying for others. Different link functions can be used to allow more flexible modelling of longitudinal data. The nonparametric components of the model are estimated using a local linear estimating equation and the parametric components are estimated through a profile estimating function. The method automatically adjusts for heterogeneity of sampling times, allowing the sampling strategy to depend on the past sampling history as well as possibly time-dependent covariates without specifically model such dependence. A [Formula: see text]-fold cross-validation bandwidth selection is proposed as a working tool for locating an appropriate bandwidth. A criteria for selecting the link function is proposed to provide better fit of the data. Large sample properties of the proposed estimators are investigated. Large sample pointwise and simultaneous confidence intervals for the regression coefficients are constructed. Formal hypothesis testing procedures are proposed to check for the covariate effects and whether the effects are time-varying. A simulation study is conducted to examine the finite sample performances of the proposed estimation and hypothesis testing procedures. The methods are illustrated with a data example.

On the equivalence of case-crossover and time series methods in environmental epidemiology.

PubMed

Lu, Yun; Zeger, Scott L

2007-04-01

The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.

Neural network and multiple linear regression to predict school children dimensions for ergonomic school furniture design.

PubMed

Agha, Salah R; Alnahhal, Mohammed J

2012-11-01

The current study investigates the possibility of obtaining the anthropometric dimensions, critical to school furniture design, without measuring all of them. The study first selects some anthropometric dimensions that are easy to measure. Two methods are then used to check if these easy-to-measure dimensions can predict the dimensions critical to the furniture design. These methods are multiple linear regression and neural networks. Each dimension that is deemed necessary to ergonomically design school furniture is expressed as a function of some other measured anthropometric dimensions. Results show that out of the five dimensions needed for chair design, four can be related to other dimensions that can be measured while children are standing. Therefore, the method suggested here would definitely save time and effort and avoid the difficulty of dealing with students while measuring these dimensions. In general, it was found that neural networks perform better than multiple linear regression in the current study. Copyright © 2012 Elsevier Ltd and The Ergonomics Society. All rights reserved.

USE OF WEIBULL FUNCTION FOR NON-LINEAR ANALYSIS OF EFFECTS OF LOW LEVELS OF SIMULATED HERBICIDE DRIFT ON PLANTS

EPA Science Inventory

We compared two regression models, which are based on the Weibull and probit functions, for the analysis of pesticide toxicity data from laboratory studies on Illinois crop and native plant species. Both mathematical models are continuous, differentiable, strictly positive, and...

Association of sleep disturbances with cognitive impairment and depression in maintenance memodialysis patients

USDA-ARS?s Scientific Manuscript database

There are few data on the relationship of sleep with measures of cognitive function and symptoms of depression in dialysis patients. We evaluated the relationship of sleep with cognitive function and symptoms of depression in 168 hemodialysis patients, using multivariable linear and logistic regress...

Multiresponse semiparametric regression for modelling the effect of regional socio-economic variables on the use of information technology

NASA Astrophysics Data System (ADS)

Wibowo, Wahyu; Wene, Chatrien; Budiantara, I. Nyoman; Permatasari, Erma Oktania

2017-03-01

Multiresponse semiparametric regression is simultaneous equation regression model and fusion of parametric and nonparametric model. The regression model comprise several models and each model has two components, parametric and nonparametric. The used model has linear function as parametric and polynomial truncated spline as nonparametric component. The model can handle both linearity and nonlinearity relationship between response and the sets of predictor variables. The aim of this paper is to demonstrate the application of the regression model for modeling of effect of regional socio-economic on use of information technology. More specific, the response variables are percentage of households has access to internet and percentage of households has personal computer. Then, predictor variables are percentage of literacy people, percentage of electrification and percentage of economic growth. Based on identification of the relationship between response and predictor variable, economic growth is treated as nonparametric predictor and the others are parametric predictors. The result shows that the multiresponse semiparametric regression can be applied well as indicate by the high coefficient determination, 90 percent.

Parameterizing sorption isotherms using a hybrid global-local fitting procedure.

PubMed

Matott, L Shawn; Singh, Anshuman; Rabideau, Alan J

2017-05-01

Predictive modeling of the transport and remediation of groundwater contaminants requires an accurate description of the sorption process, which is usually provided by fitting an isotherm model to site-specific laboratory data. Commonly used calibration procedures, listed in order of increasing sophistication, include: trial-and-error, linearization, non-linear regression, global search, and hybrid global-local search. Given the considerable variability in fitting procedures applied in published isotherm studies, we investigated the importance of algorithm selection through a series of numerical experiments involving 13 previously published sorption datasets. These datasets, considered representative of state-of-the-art for isotherm experiments, had been previously analyzed using trial-and-error, linearization, or non-linear regression methods. The isotherm expressions were re-fit using a 3-stage hybrid global-local search procedure (i.e. global search using particle swarm optimization followed by Powell's derivative free local search method and Gauss-Marquardt-Levenberg non-linear regression). The re-fitted expressions were then compared to previously published fits in terms of the optimized weighted sum of squared residuals (WSSR) fitness function, the final estimated parameters, and the influence on contaminant transport predictions - where easily computed concentration-dependent contaminant retardation factors served as a surrogate measure of likely transport behavior. Results suggest that many of the previously published calibrated isotherm parameter sets were local minima. In some cases, the updated hybrid global-local search yielded order-of-magnitude reductions in the fitness function. In particular, of the candidate isotherms, the Polanyi-type models were most likely to benefit from the use of the hybrid fitting procedure. In some cases, improvements in fitness function were associated with slight (<10%) changes in parameter values, but in other cases significant (>50%) changes in parameter values were noted. Despite these differences, the influence of isotherm misspecification on contaminant transport predictions was quite variable and difficult to predict from inspection of the isotherms. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

PubMed

Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P

2006-04-01

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Stochastic search, optimization and regression with energy applications

NASA Astrophysics Data System (ADS)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings. Finally, we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel-based weights and Dirichlet process-based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour-ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

A new approach to assess COPD by identifying lung function break-points

PubMed Central

Eriksson, Göran; Jarenbäck, Linnea; Peterson, Stefan; Ankerst, Jaro; Bjermer, Leif; Tufvesson, Ellen

2015-01-01

Purpose COPD is a progressive disease, which can take different routes, leading to great heterogeneity. The aim of the post-hoc analysis reported here was to perform continuous analyses of advanced lung function measurements, using linear and nonlinear regressions. Patients and methods Fifty-one COPD patients with mild to very severe disease (Global Initiative for Chronic Obstructive Lung Disease [GOLD] Stages I–IV) and 41 healthy smokers were investigated post-bronchodilation by flow-volume spirometry, body plethysmography, diffusion capacity testing, and impulse oscillometry. The relationship between COPD severity, based on forced expiratory volume in 1 second (FEV1), and different lung function parameters was analyzed by flexible nonparametric method, linear regression, and segmented linear regression with break-points. Results Most lung function parameters were nonlinear in relation to spirometric severity. Parameters related to volume (residual volume, functional residual capacity, total lung capacity, diffusion capacity [diffusion capacity of the lung for carbon monoxide], diffusion capacity of the lung for carbon monoxide/alveolar volume) and reactance (reactance area and reactance at 5Hz) were segmented with break-points at 60%–70% of FEV1. FEV1/forced vital capacity (FVC) and resonance frequency had break-points around 80% of FEV1, while many resistance parameters had break-points below 40%. The slopes in percent predicted differed; resistance at 5 Hz minus resistance at 20 Hz had a linear slope change of −5.3 per unit FEV1, while residual volume had no slope change above and −3.3 change per unit FEV1 below its break-point of 61%. Conclusion Continuous analyses of different lung function parameters over the spirometric COPD severity range gave valuable information additional to categorical analyses. Parameters related to volume, diffusion capacity, and reactance showed break-points around 65% of FEV1, indicating that air trapping starts to dominate in moderate COPD (FEV1 =50%–80%). This may have an impact on the patient’s management plan and selection of patients and/or outcomes in clinical research. PMID:26508849

Impact of Trichiasis Surgery on Physical Functioning in Ethiopian Patients: STAR Trial

PubMed Central

Wolle, Meraf A.; Cassard, Sandra D.; Gower, Emily W.; Munoz, Beatriz E.; Wang, Jiangxia; Alemayehu, Wondu; West, Sheila K.

2010-01-01

Purpose To evaluate the physical functioning of Ethiopian trichiasis surgery patients before and six months after surgery. Design Nested Cohort Study Methods This study was nested within the Surgery for Trichiasis, Antibiotics to Prevent Recurrence (STAR) clinical trial conducted in Ethiopia. Demographic information, ocular examinations, and physical functioning assessments were collected before and 6 months after surgery. A single score for patients’ physical functioning was constructed using Rasch analysis. A multivariate linear regression model was used to determine if change in physical functioning was associated with change in visual acuity. Results Of the 438 participants, 411 (93.8%) had both baseline and follow-up questionnaires. Physical functioning scores at baseline ranged from −6.32 (great difficulty) to +6.01 (no difficulty). The percent of participants reporting no difficulty in physical functioning increased by 32.6%; the proportion of participants in the mild/no visual impairment category increased by 8.6%. A multivariate linear regression model showed that for every line of vision gained, physical functioning improves significantly (0.09 units; 95% CI: 0.02–0.16). Conclusions Surgery to correct trichiasis appears to improve patients’ physical functioning as measured at 6 months. More effort in promoting trichiasis surgery is essential, not only to prevent corneal blindness, but also to enable improved functioning in daily life. PMID:21333268

Conceptual model of consumer’s willingness to eat functional foods

PubMed

Babicz-Zielinska, Ewa; Jezewska-Zychowicz, Maria

The functional foods constitute the important segment of the food market. Among factors that determine the intentions to eat functional foods, the psychological factors play very important roles. Motives, attitudes and personality are key factors. The relationships between socio-demographic characteristics, attitudes and willingness to purchase functional foods were not fully confirmed. Consumers’ beliefs about health benefits from eaten foods seem to be a strong determinant of a choice of functional foods. The objective of this study was to determine relations between familiarity, attitudes, and beliefs in benefits and risks about functional foods and develop some conceptual models of willingness to eat. The sample of Polish consumers counted 1002 subjects at age 15+. The foods enriched with vitamins or minerals, and cholesterol-lowering margarine or drinks were considered. The questionnaire focused on familiarity with foods, attitudes, beliefs about benefits and risks of their consumption was constructed. The Pearson’s correlations and linear regression equations were calculated. The strongest relations appeared between attitudes, high health value and high benefits, (r = 0.722 and 0.712 for enriched foods, and 0.664 and 0.693 for cholesterol-lowering foods), and between high health value and high benefits (0.814 for enriched foods and 0.758 for cholesterol-lowering foods). The conceptual models based on linear regression of relations between attitudes and all other variables, considering or not the familiarity with the foods, were developed. The positive attitudes and declared consumption are more important for enriched foods. The beliefs on high health value and high benefits play the most important role in the purchase. The interrelations between different variables may be described by new linear regression models, with the beliefs in high benefits, positive attitudes and familiarity being most significant predictors. Health expectations and trust to functional foods are the key factors in their choice.

Can Functional Cardiac Age be Predicted from ECG in a Normal Healthy Population

NASA Technical Reports Server (NTRS)

Schlegel, Todd; Starc, Vito; Leban, Manja; Sinigoj, Petra; Vrhovec, Milos

2011-01-01

In a normal healthy population, we desired to determine the most age-dependent conventional and advanced ECG parameters. We hypothesized that changes in several ECG parameters might correlate with age and together reliably characterize the functional age of the heart. Methods: An initial study population of 313 apparently healthy subjects was ultimately reduced to 148 subjects (74 men, 84 women, in the range from 10 to 75 years of age) after exclusion criteria. In all subjects, ECG recordings (resting 5-minute 12-lead high frequency ECG) were evaluated via custom software programs to calculate up to 85 different conventional and advanced ECG parameters including beat-to-beat QT and RR variability, waveform complexity, and signal-averaged, high-frequency and spatial/spatiotemporal ECG parameters. The prediction of functional age was evaluated by multiple linear regression analysis using the best 5 univariate predictors. Results: Ignoring what were ultimately small differences between males and females, the functional age was found to be predicted (R2= 0.69, P < 0.001) from a linear combination of 5 independent variables: QRS elevation in the frontal plane (p<0.001), a new repolarization parameter QTcorr (p<0.001), mean high frequency QRS amplitude (p=0.009), the variability parameter % VLF of RRV (p=0.021) and the P-wave width (p=0.10). Here, QTcorr represents the correlation between the calculated QT and the measured QT signal. Conclusions: In apparently healthy subjects with normal conventional ECGs, functional cardiac age can be estimated by multiple linear regression analysis of mostly advanced ECG results. Because some parameters in the regression formula, such as QTcorr, high frequency QRS amplitude and P-wave width also change with disease in the same direction as with increased age, increased functional age of the heart may reflect subtle age-related pathologies in cardiac electrical function that are usually hidden on conventional ECG.

Correlation and simple linear regression.

PubMed

Eberly, Lynn E

2007-01-01

This chapter highlights important steps in using correlation and simple linear regression to address scientific questions about the association of two continuous variables with each other. These steps include estimation and inference, assessing model fit, the connection between regression and ANOVA, and study design. Examples in microbiology are used throughout. This chapter provides a framework that is helpful in understanding more complex statistical techniques, such as multiple linear regression, linear mixed effects models, logistic regression, and proportional hazards regression.

Functional linear models to test for differences in prairie wetland hydraulic gradients

USGS Publications Warehouse

Greenwood, Mark C.; Sojda, Richard S.; Preston, Todd M.; Swayne, David A.; Yang, Wanhong; Voinov, A.A.; Rizzoli, A.; Filatova, T.

2010-01-01

Functional data analysis provides a framework for analyzing multiple time series measured frequently in time, treating each series as a continuous function of time. Functional linear models are used to test for effects on hydraulic gradient functional responses collected from three types of land use in Northeastern Montana at fourteen locations. Penalized regression-splines are used to estimate the underlying continuous functions based on the discretely recorded (over time) gradient measurements. Permutation methods are used to assess the statistical significance of effects. A method for accommodating missing observations in each time series is described. Hydraulic gradients may be an initial and fundamental ecosystem process that responds to climate change. We suggest other potential uses of these methods for detecting evidence of climate change.

Stature Estimation from Lower Limb Anthropometry using Linear Regression Analysis: A Study on the Malaysian Population.

PubMed

Abu Bakar, S N; Aspalilah, A; AbdelNasser, I; Nurliza, A; Hairuliza, M J; Swarhib, M; Das, S; Mohd Nor, F

2017-01-01

Stature is one of the characteristics that could be used to identify human, besides age, sex and racial affiliation. This is useful when the body found is either dismembered, mutilated or even decomposed, and helps in narrowing down the missing person's identity. The main aim of the present study was to construct regression functions for stature estimation by using lower limb bones in the Malaysian population. The sample comprised 87 adult individuals (81 males, 6 females) aged between 20 to 79 years. The parameters such as thigh length, lower leg length, leg length, foot length, foot height and foot breadth were measured. They were measured by a ruler and measuring tape. Statistical analysis involved independent t-test to analyse the difference between lower limbs in male and female. The Pearson's correlation test was used to analyse correlations between lower limb parameters and stature, and the linear regressions were used to form equations. The paired t-test was used to compare between actual stature and estimated stature by using the equations formed. Using independent t-test, there was a significant difference (p< 0.05) in the measurement between males and females with regard to leg length, thigh length, lower leg length, foot length and foot breadth. The thigh length, leg length and foot length were observed to have strong correlations with stature with p= 0.75, p= 0.81 and p= 0.69, respectively. Linear regressions were formulated for stature estimation. Paired t-test showed no significant difference between actual stature and estimated stature. It is concluded that regression functions can be used to estimate stature to identify skeletal remains in the Malaysia population.

Analytical framework for reconstructing heterogeneous environmental variables from mammal community structure.

PubMed

Louys, Julien; Meloro, Carlo; Elton, Sarah; Ditchfield, Peter; Bishop, Laura C

2015-01-01

We test the performance of two models that use mammalian communities to reconstruct multivariate palaeoenvironments. While both models exploit the correlation between mammal communities (defined in terms of functional groups) and arboreal heterogeneity, the first uses a multiple multivariate regression of community structure and arboreal heterogeneity, while the second uses a linear regression of the principal components of each ecospace. The success of these methods means the palaeoenvironment of a particular locality can be reconstructed in terms of the proportions of heavy, moderate, light, and absent tree canopy cover. The linear regression is less biased, and more precisely and accurately reconstructs heavy tree canopy cover than the multiple multivariate model. However, the multiple multivariate model performs better than the linear regression for all other canopy cover categories. Both models consistently perform better than randomly generated reconstructions. We apply both models to the palaeocommunity of the Upper Laetolil Beds, Tanzania. Our reconstructions indicate that there was very little heavy tree cover at this site (likely less than 10%), with the palaeo-landscape instead comprising a mixture of light and absent tree cover. These reconstructions help resolve the previous conflicting palaeoecological reconstructions made for this site. Copyright © 2014 Elsevier Ltd. All rights reserved.

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PubMed

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET d based models should be further evaluated in clinically realistic scenarios. © 2017 American Association of Physicists in Medicine.

Assessment of triglyceride and cholesterol in overweight people based on multiple linear regression and artificial intelligence model.

PubMed

Ma, Jing; Yu, Jiong; Hao, Guangshu; Wang, Dan; Sun, Yanni; Lu, Jianxin; Cao, Hongcui; Lin, Feiyan

2017-02-20

The prevalence of high hyperlipemia is increasing around the world. Our aims are to analyze the relationship of triglyceride (TG) and cholesterol (TC) with indexes of liver function and kidney function, and to develop a prediction model of TG, TC in overweight people. A total of 302 adult healthy subjects and 273 overweight subjects were enrolled in this study. The levels of fasting indexes of TG (fs-TG), TC (fs-TC), blood glucose, liver function, and kidney function were measured and analyzed by correlation analysis and multiple linear regression (MRL). The back propagation artificial neural network (BP-ANN) was applied to develop prediction models of fs-TG and fs-TC. The results showed there was significant difference in biochemical indexes between healthy people and overweight people. The correlation analysis showed fs-TG was related to weight, height, blood glucose, and indexes of liver and kidney function; while fs-TC was correlated with age, indexes of liver function (P < 0.01). The MRL analysis indicated regression equations of fs-TG and fs-TC both had statistic significant (P < 0.01) when included independent indexes. The BP-ANN model of fs-TG reached training goal at 59 epoch, while fs-TC model achieved high prediction accuracy after training 1000 epoch. In conclusions, there was high relationship of fs-TG and fs-TC with weight, height, age, blood glucose, indexes of liver function and kidney function. Based on related variables, the indexes of fs-TG and fs-TC can be predicted by BP-ANN models in overweight people.

Theory of mind and executive function: working-memory capacity and inhibitory control as predictors of false-belief task performance.

PubMed

Mutter, Brigitte; Alcorn, Mark B; Welsh, Marilyn

2006-06-01

This study of the relationship between theory of mind and executive function examined whether on the false-belief task age differences between 3 and 5 ears of age are related to development of working-memory capacity and inhibitory processes. 72 children completed tasks measuring false belief, working memory, and inhibition. Significant age effects were observed for false-belief and working-memory performance, as well as for the false-alarm and perseveration measures of inhibition. A simultaneous multiple linear regression specified the contribution of age, inhibition, and working memory to the prediction of false-belief performance. This model was significant, explaining a total of 36% of the variance. To examine the independent contributions of the working-memory and inhibition variables, after controlling for age, two hierarchical multiple linear regressions were conducted. These multiple regression analyses indicate that working memory and inhibition make small, overlapping contributions to false-belief performance after accounting for age, but that working memory, as measured in this study, is a somewhat better predictor of false-belief understanding than is inhibition.

Mapping diffuse photosynthetically active radiation from satellite data in Thailand

NASA Astrophysics Data System (ADS)

Choosri, P.; Janjai, S.; Nunez, M.; Buntoung, S.; Charuchittipan, D.

2017-12-01

In this paper, calculation of monthly average hourly diffuse photosynthetically active radiation (PAR) using satellite data is proposed. Diffuse PAR was analyzed at four stations in Thailand. A radiative transfer model was used for calculating the diffuse PAR for cloudless sky conditions. Differences between the diffuse PAR under all sky conditions obtained from the ground-based measurements and those from the model are representative of cloud effects. Two models are developed, one describing diffuse PAR only as a function of solar zenith angle, and the second one as a multiple linear regression with solar zenith angle and satellite reflectivity acting linearly and aerosol optical depth acting in logarithmic functions. When tested with an independent data set, the multiple regression model performed best with a higher coefficient of variance R2 (0.78 vs. 0.70), lower root mean square difference (RMSD) (12.92% vs. 13.05%) and the same mean bias difference (MBD) of -2.20%. Results from the multiple regression model are used to map diffuse PAR throughout the country as monthly averages of hourly data.

The impact of mental state disorder and personality on social functioning in patients engaged in community mental health care.

PubMed

Newton-Howes, Giles

2014-02-01

The aim of this study was to assess the degree to which mental state disorder and personality disorder impact on social functioning in patients engaged in secondary mental health care in New Zealand. Patients were interviewed using peer-reviewed instruments able to provide an indication of severity to assess their social functioning, personality status and diagnosis. Univariate correlations and linear regression was used to identify the association between social functioning, mental state disorder and personality. Using simple correlations all diagnostic categories associated with declines in social functioning. In the regression analysis depression and personality dysfunction accounted for 48% of the variance in social functioning. For patients engaged in secondary care, depression and personality dysfunction are significantly associated with poorer social functioning.

The Inverted Student Density and Test Scores.

ERIC Educational Resources Information Center

Boldt, Robert F.

The inverted density is one whose contour lines are spheroidal as in the normal distribution, but whose moments differ from those of the normal in that its conditional arrays are not homoscedastic, being quadratic functions of the values of the linear regression functions. It is also platykurtic, its measure of kurtosis ranging from that of the…

On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction.

PubMed

Crop, F; Van Rompaye, B; Paelinck, L; Vakaet, L; Thierens, H; De Wagter, C

2008-07-21

The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry.

A rational model of function learning.

PubMed

Lucas, Christopher G; Griffiths, Thomas L; Williams, Joseph J; Kalish, Michael L

2015-10-01

Theories of how people learn relationships between continuous variables have tended to focus on two possibilities: one, that people are estimating explicit functions, or two that they are performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian linear regression and Gaussian processes, which provide a probabilistic basis for similarity-based function learning, we show that learning explicit rules and using similarity can be seen as two views of one solution to this problem. We use this insight to define a rational model of human function learning that combines the strengths of both approaches and accounts for a wide variety of experimental results.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Quasi-likelihood generalized linear regression analysis of fatality risk data

DOT National Transportation Integrated Search

2009-01-01

Transportation-related fatality risks is a function of many interacting human, vehicle, and environmental factors. Statisitcally valid analysis of such data is challenged both by the complexity of plausable structural models relating fatality rates t...

RELATIONSHIP BETWEEN ISOMETRIC THIGH MUSCLE STRENGTH AND MINIMAL CLINICALLY IMPORTANT DIFFERENCES (MCIDS) IN KNEE FUNCTION IN OSTEOARTHRITIS – DATA FROM THE OSTEOARTHRITIS INITIATIVE

PubMed Central

Ruhdorfer, Anja; Wirth, Wolfgang; Eckstein, Felix

2014-01-01

Objective To determine the relationship between thigh muscle strength and clinically relevant differences in self-assessed lower limb function. Methods Isometric knee extensor and flexor strength of 4553 Osteoarthritis Initiative participants (2651 women/1902 men) was related to Western Ontario McMasters Universities (WOMAC) physical function scores by linear regression. Further, groups of Male and female participant strata with minimal clinically important differences (MCIDs) in WOMAC function scores (6/68) were compared across the full range of observed values, and to participants without functional deficits (WOMAC=0). The effect of WOMAC knee pain and body mass index on the above relationships was explored using stepwise regression. Results Per regression equations, a 3.7% reduction in extensor and a 4.0% reduction in flexor strength were associated with an MCID in WOMAC function in women, and a 3.6%/4.8% reduction in men. For strength divided by body weight, reductions were 5.2%/6.7% in women and 5.8%/6.7% in men. Comparing MCID strata across the full observed range of WOMAC function confirmed the above estimates and did not suggest non-linear relationships across the spectrum of observed values. WOMAC pain correlated strongly with WOMAC function, but extensor (and flexor) muscle strength contributed significant independent information. Conclusion Reductions of approximately 4% in isometric muscle strength and of 6% in strength/weight were related to a clinically relevant difference in WOMAC functional disability. Longitudinal studies will need to confirm these relationships within persons. Muscle extensor (and flexor) strength (per body weight) provided significant independent information in addition to pain in explaining variability in lower limb function. PMID:25303012

Glomerular structural-functional relationship models of diabetic nephropathy are robust in type 1 diabetic patients.

PubMed

Mauer, Michael; Caramori, Maria Luiza; Fioretto, Paola; Najafian, Behzad

2015-06-01

Studies of structural-functional relationships have improved understanding of the natural history of diabetic nephropathy (DN). However, in order to consider structural end points for clinical trials, the robustness of the resultant models needs to be verified. This study examined whether structural-functional relationship models derived from a large cohort of type 1 diabetic (T1D) patients with a wide range of renal function are robust. The predictability of models derived from multiple regression analysis and piecewise linear regression analysis was also compared. T1D patients (n = 161) with research renal biopsies were divided into two equal groups matched for albumin excretion rate (AER). Models to explain AER and glomerular filtration rate (GFR) by classical DN lesions in one group (T1D-model, or T1D-M) were applied to the other group (T1D-test, or T1D-T) and regression analyses were performed. T1D-M-derived models explained 70 and 63% of AER variance and 32 and 21% of GFR variance in T1D-M and T1D-T, respectively, supporting the substantial robustness of the models. Piecewise linear regression analyses substantially improved predictability of the models with 83% of AER variance and 66% of GFR variance explained by classical DN glomerular lesions alone. These studies demonstrate that DN structural-functional relationship models are robust, and if appropriate models are used, glomerular lesions alone explain a major proportion of AER and GFR variance in T1D patients. © The Author 2014. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Physical Function in Older Men With Hyperkyphosis

PubMed Central

Harrison, Stephanie L.; Fink, Howard A.; Marshall, Lynn M.; Orwoll, Eric; Barrett-Connor, Elizabeth; Cawthon, Peggy M.; Kado, Deborah M.

2015-01-01

Background. Age-related hyperkyphosis has been associated with poor physical function and is a well-established predictor of adverse health outcomes in older women, but its impact on health in older men is less well understood. Methods. We conducted a cross-sectional study to evaluate the association of hyperkyphosis and physical function in 2,363 men, aged 71–98 (M = 79) from the Osteoporotic Fractures in Men Study. Kyphosis was measured using the Rancho Bernardo Study block method. Measurements of grip strength and lower extremity function, including gait speed over 6 m, narrow walk (measure of dynamic balance), repeated chair stands ability and time, and lower extremity power (Nottingham Power Rig) were included separately as primary outcomes. We investigated associations of kyphosis and each outcome in age-adjusted and multivariable linear or logistic regression models, controlling for age, clinic, education, race, bone mineral density, height, weight, diabetes, and physical activity. Results. In multivariate linear regression, we observed a dose-related response of worse scores on each lower extremity physical function test as number of blocks increased, p for trend ≤.001. Using a cutoff of ≥4 blocks, 20% (N = 469) of men were characterized with hyperkyphosis. In multivariate logistic regression, men with hyperkyphosis had increased odds (range 1.5–1.8) of being in the worst quartile of performing lower extremity physical function tasks (p < .001 for each outcome). Kyphosis was not associated with grip strength in any multivariate analysis. Conclusions. Hyperkyphosis is associated with impaired lower extremity physical function in older men. Further studies are needed to determine the direction of causality. PMID:25431353

CO-occurring exposure to perchlorate, nitrate and thiocyanate alters thyroid function in healthy pregnant women.

PubMed

Horton, Megan K; Blount, Benjamin C; Valentin-Blasini, Liza; Wapner, Ronald; Whyatt, Robin; Gennings, Chris; Factor-Litvak, Pam

2015-11-01

Adequate maternal thyroid function during pregnancy is necessary for normal fetal brain development, making pregnancy a critical window of vulnerability to thyroid disrupting insults. Sodium/iodide symporter (NIS) inhibitors, namely perchlorate, nitrate, and thiocyanate, have been shown individually to competitively inhibit uptake of iodine by the thyroid. Several epidemiologic studies examined the association between these individual exposures and thyroid function. Few studies have examined the effect of this chemical mixture on thyroid function during pregnancy We examined the cross sectional association between urinary perchlorate, thiocyanate and nitrate concentrations and thyroid function among healthy pregnant women living in New York City using weighted quantile sum (WQS) regression. We measured thyroid stimulating hormone (TSH) and free thyroxine (FreeT4) in blood samples; perchlorate, thiocyanate, nitrate and iodide in urine samples collected from 284 pregnant women at 12 (±2.8) weeks gestation. We examined associations between urinary analyte concentrations and TSH or FreeT4 using linear regression or WQS adjusting for gestational age, urinary iodide and creatinine. Individual analyte concentrations in urine were significantly correlated (Spearman's r 0.4-0.5, p<0.001). Linear regression analyses did not suggest associations between individual concentrations and thyroid function. The WQS revealed a significant positive association between the weighted sum of urinary concentrations of the three analytes and increased TSH. Perchlorate had the largest weight in the index, indicating the largest contribution to the WQS. Co-exposure to perchlorate, nitrate and thiocyanate may alter maternal thyroid function, specifically TSH, during pregnancy. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Co-occurring exposure to perchlorate, nitrate and thiocyanate alters thyroid function in healthy pregnant women

PubMed Central

Horton, Megan K.; Blount, Benjamin C.; Valentin-Blasini, Liza; Wapner, Ronald; Whyatt, Robin; Gennings, Chris; Factor-Litvak, Pam

2015-01-01

Background Adequate maternal thyroid function during pregnancy is necessary for normal fetal brain development, making pregnancy a critical window of vulnerability to thyroid disrupting insults. Sodium/iodide symporter (NIS) inhibitors, namely perchlorate, nitrate, and thiocyanate, have been shown individually to competitively inhibit uptake of iodine by the thyroid. Several epidemiologic studies examined the association between these individual exposures and thyroid function. Few studies have examined the effect of this chemical mixture on thyroid function during pregnancy. Objectives We examined the cross sectional association between urinary perchlorate, thiocyanate and nitrate concentrations and thyroid function among healthy pregnant women living in New York City using weighted quantile sum (WQS) regression. Methods We measured thyroid stimulating hormone (TSH) and free thyroxine (FreeT4) in blood samples; perchlorate, thiocyanate, nitrate and iodide in urine samples collected from 284 pregnant women at 12 (± 2.8) weeks gestation. We examined associations between urinary analyte concentrations and TSH or FreeT4 using linear regression or WQS adjusting for gestational age, urinary iodide and creatinine. Results Individual analyte concentrations in urine were significantly correlated (Spearman’s r 0.4–0.5, p < 0.001). Linear regression analyses did not suggest associations between individual concentrations and thyroid function. The WQS revealed a significant positive association between the weighted sum of urinary concentrations of the three analytes and increased TSH. Perchlorate had the largest weight in the index, indicating the largest contribution to the WQS. Conclusions Co-exposure to perchlorate, nitrate and thiocyanate may alter maternal thyroid function, specifically TSH, during pregnancy. PMID:26408806

CO-occurring exposure to perchlorate, nitrate and thiocyanate alters thyroid function in healthy pregnant women

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horton, Megan K., E-mail: megan.horton@mssm.edu; Blount, Benjamin C.; Valentin-Blasini, Liza

Background: Adequate maternal thyroid function during pregnancy is necessary for normal fetal brain development, making pregnancy a critical window of vulnerability to thyroid disrupting insults. Sodium/iodide symporter (NIS) inhibitors, namely perchlorate, nitrate, and thiocyanate, have been shown individually to competitively inhibit uptake of iodine by the thyroid. Several epidemiologic studies examined the association between these individual exposures and thyroid function. Few studies have examined the effect of this chemical mixture on thyroid function during pregnancy Objectives: We examined the cross sectional association between urinary perchlorate, thiocyanate and nitrate concentrations and thyroid function among healthy pregnant women living in New Yorkmore » City using weighted quantile sum (WQS) regression. Methods: We measured thyroid stimulating hormone (TSH) and free thyroxine (FreeT4) in blood samples; perchlorate, thiocyanate, nitrate and iodide in urine samples collected from 284 pregnant women at 12 (±2.8) weeks gestation. We examined associations between urinary analyte concentrations and TSH or FreeT4 using linear regression or WQS adjusting for gestational age, urinary iodide and creatinine. Results: Individual analyte concentrations in urine were significantly correlated (Spearman's r 0.4–0.5, p<0.001). Linear regression analyses did not suggest associations between individual concentrations and thyroid function. The WQS revealed a significant positive association between the weighted sum of urinary concentrations of the three analytes and increased TSH. Perchlorate had the largest weight in the index, indicating the largest contribution to the WQS. Conclusions: Co-exposure to perchlorate, nitrate and thiocyanate may alter maternal thyroid function, specifically TSH, during pregnancy. - Highlights: • Perchlorate, nitrate, thiocyanate and iodide measured in maternal urine. • Thyroid function (TSH and Free T4) measured in maternal blood. • Weighted quantile sum (WQS) regression examined complex mixture effect. • WQS identified an inverse association between the exposure mixture and maternal TSH. • Perchlorate indicated as the ‘bad actor’ of the mixture.« less

Seeking maximum linearity of transfer functions

NASA Astrophysics Data System (ADS)

Silva, Filipi N.; Comin, Cesar H.; Costa, Luciano da F.

2016-12-01

Linearity is an important and frequently sought property in electronics and instrumentation. Here, we report a method capable of, given a transfer function (theoretical or derived from some real system), identifying the respective most linear region of operation with a fixed width. This methodology, which is based on least squares regression and systematic consideration of all possible regions, has been illustrated with respect to both an analytical (sigmoid transfer function) and a simple situation involving experimental data of a low-power, one-stage class A transistor current amplifier. Such an approach, which has been addressed in terms of transfer functions derived from experimentally obtained characteristic surface, also yielded contributions such as the estimation of local constants of the device, as opposed to typically considered average values. The reported method and results pave the way to several further applications in other types of devices and systems, intelligent control operation, and other areas such as identifying regions of power law behavior.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Convert a low-cost sensor to a colorimeter using an improved regression method

NASA Astrophysics Data System (ADS)

Wu, Yifeng

2008-01-01

Closed loop color calibration is a process to maintain consistent color reproduction for color printers. To perform closed loop color calibration, a pre-designed color target should be printed, and automatically measured by a color measuring instrument. A low cost sensor has been embedded to the printer to perform the color measurement. A series of sensor calibration and color conversion methods have been developed. The purpose is to get accurate colorimetric measurement from the data measured by the low cost sensor. In order to get high accuracy colorimetric measurement, we need carefully calibrate the sensor, and minimize all possible errors during the color conversion. After comparing several classical color conversion methods, a regression based color conversion method has been selected. The regression is a powerful method to estimate the color conversion functions. But the main difficulty to use this method is to find an appropriate function to describe the relationship between the input and the output data. In this paper, we propose to use 1D pre-linearization tables to improve the linearity between the input sensor measuring data and the output colorimetric data. Using this method, we can increase the accuracy of the regression method, so as to improve the accuracy of the color conversion.

Which Frail Older People Are Dehydrated? The UK DRIE Study

PubMed Central

Bunn, Diane K.; Downing, Alice; Jimoh, Florence O.; Groves, Joyce; Free, Carol; Cowap, Vicky; Potter, John F.; Hunter, Paul R.; Shepstone, Lee

2016-01-01

Background: Water-loss dehydration in older people is associated with increased mortality and disability. We aimed to assess the prevalence of dehydration in older people living in UK long-term care and associated cognitive, functional, and health characteristics. Methods: The Dehydration Recognition In our Elders (DRIE) cohort study included people aged 65 or older living in long-term care without heart or renal failure. In a cross-sectional baseline analysis, we assessed serum osmolality, previously suggested dehydration risk factors, general health, markers of continence, cognitive and functional health, nutrition status, and medications. Univariate linear regression was used to assess relationships between participant characteristics and serum osmolality, then associated characteristics entered into stepwise backwards multivariate linear regression. Results: DRIE included 188 residents (mean age 86 years, 66% women) of whom 20% were dehydrated (serum osmolality >300 mOsm/kg). Linear and logistic regression suggested that renal, cognitive, and diabetic status were consistently associated with serum osmolality and odds of dehydration, while potassium-sparing diuretics, sex, number of recent health contacts, and bladder incontinence were sometimes associated. Thirst was not associated with hydration status. Conclusions: DRIE found high prevalence of dehydration in older people living in UK long-term care, reinforcing the proposed association between cognitive and renal function and hydration. Dehydration is associated with increased mortality and disability in older people, but trials to assess effects of interventions to support healthy fluid intakes in older people living in residential care are needed to enable us to formally assess causal direction and any health benefits of increasing fluid intakes. PMID:26553658

Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

PubMed

Dinç, Erdal; Ozdemir, Abdil

2005-01-01

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.

Non-Linear Relationship between Economic Growth and CO2 Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models

PubMed Central

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-01-01

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO2 emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO2 emissions is significantly higher than those of GDPpc and Es on per capita CO2 emissions. PMID:29236083

Non-Linear Relationship between Economic Growth and CO₂ Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models.

PubMed

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-12-13

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO₂ emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO₂ emissions is significantly higher than those of GDPpc and Es on per capita CO₂ emissions.

Testing for gene-environment interaction under exposure misspecification.

PubMed

Sun, Ryan; Carroll, Raymond J; Christiani, David C; Lin, Xihong

2017-11-09

Complex interplay between genetic and environmental factors characterizes the etiology of many diseases. Modeling gene-environment (GxE) interactions is often challenged by the unknown functional form of the environment term in the true data-generating mechanism. We study the impact of misspecification of the environmental exposure effect on inference for the GxE interaction term in linear and logistic regression models. We first examine the asymptotic bias of the GxE interaction regression coefficient, allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects. For linear regression, we show that under gene-environment independence and some confounder-dependent conditions, when the environment effect is misspecified, the regression coefficient of the GxE interaction can be unbiased. However, inference on the GxE interaction is still often incorrect. In logistic regression, we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly. Further, we show that the standard robust sandwich variance estimator for the GxE interaction does not perform well in practical GxE studies, and we provide an alternative testing procedure that has better finite sample properties. © 2017, The International Biometric Society.

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

Does physical exposure throughout working life influence chair-rise performance in midlife? A retrospective cohort study of associations between work and physical function in Denmark

PubMed Central

Møller, Anne; Reventlow, Susanne; Hansen, Åse Marie; Andersen, Lars L; Siersma, Volkert; Lund, Rikke; Avlund, Kirsten; Andersen, Johan Hviid; Mortensen, Ole Steen

2015-01-01

Objectives Our aim was to study associations between physical exposures throughout working life and physical function measured as chair-rise performance in midlife. Methods The Copenhagen Aging and Midlife Biobank (CAMB) provided data about employment and measures of physical function. Individual job histories were assigned exposures from a job exposure matrix. Exposures were standardised to ton-years (lifting 1000 kg each day in 1 year), stand-years (standing/walking for 6 h each day in 1 year) and kneel-years (kneeling for 1 h each day in 1 year). The associations between exposure-years and chair-rise performance (number of chair-rises in 30 s) were analysed in multivariate linear and non-linear regression models adjusted for covariates. Results Mean age among the 5095 participants was 59 years in both genders, and, on average, men achieved 21.58 (SD=5.60) and women 20.38 (SD=5.33) chair-rises in 30 s. Physical exposures were associated with poorer chair-rise performance in both men and women, however, only associations between lifting and standing/walking and chair-rise remained statistically significant among men in the final model. Spline regression analyses showed non-linear associations and confirmed the findings. Conclusions Higher physical exposure throughout working life is associated with slightly poorer chair-rise performance. The associations between exposure and outcome were non-linear. PMID:26537502

TI-59 Programs for Multiple Regression.

DTIC Science & Technology

1980-05-01

general linear hypothesis model of full rank [ Graybill , 19611 can be written as Y = x 8 + C , s-N(O,o 2I) nxl nxk kxl nxl where Y is the vector of n...a "reduced model " solution, and confidence intervals for linear functions of the coefficients can be obtained using (x’x) and a2, based on the t...O107)l UA.LLL. Library ModuIe NASTER -Puter 0NTINA Cards 1 PROGRAM DESCRIPTION (s s 2 ror the general linear hypothesis model Y - XO + C’ calculates

Robust Multiple Linear Regression.

DTIC Science & Technology

1982-12-01

difficulty, but it might have more solutions corresponding to local minima. Influence Function of M-Estimates The influence function describes the effect...distributionn n function. In case of M-Estimates the influence function was found to be pro- portional to and given as T(X F)) " C(xpF,T) = .(X.T(F) F(dx...where the inverse of any distribution function F is defined in the usual way as F- (s) = inf{x IF(x) > s) 0<sə Influence Function of L-Estimates In a

Testing the dose-response specification in epidemiology: public health and policy consequences for lead.

PubMed

Rothenberg, Stephen J; Rothenberg, Jesse C

2005-09-01

Statistical evaluation of the dose-response function in lead epidemiology is rarely attempted. Economic evaluation of health benefits of lead reduction usually assumes a linear dose-response function, regardless of the outcome measure used. We reanalyzed a previously published study, an international pooled data set combining data from seven prospective lead studies examining contemporaneous blood lead effect on IQ (intelligence quotient) of 7-year-old children (n = 1,333). We constructed alternative linear multiple regression models with linear blood lead terms (linear-linear dose response) and natural-log-transformed blood lead terms (log-linear dose response). We tested the two lead specifications for nonlinearity in the models, compared the two lead specifications for significantly better fit to the data, and examined the effects of possible residual confounding on the functional form of the dose-response relationship. We found that a log-linear lead-IQ relationship was a significantly better fit than was a linear-linear relationship for IQ (p = 0.009), with little evidence of residual confounding of included model variables. We substituted the log-linear lead-IQ effect in a previously published health benefits model and found that the economic savings due to U.S. population lead decrease between 1976 and 1999 (from 17.1 microg/dL to 2.0 microg/dL) was 2.2 times (319 billion dollars) that calculated using a linear-linear dose-response function (149 billion dollars). The Centers for Disease Control and Prevention action limit of 10 microg/dL for children fails to protect against most damage and economic cost attributable to lead exposure.

Analysis of reciprocal creatinine plots by two-phase linear regression.

PubMed

Rowe, P A; Richardson, R E; Burton, P R; Morgan, A G; Burden, R P

1989-01-01

The progression of renal diseases is often monitored by the serial measurement of plasma creatinine. The slope of the linear relation that is frequently found between the reciprocal of creatinine concentration and time delineates the rate of change in renal function. Minor changes in slope, perhaps indicating response to therapeutic intervention, can be difficult to identify and yet be of clinical importance. We describe the application of two-phase linear regression to identify and characterise changes in slope using a microcomputer. The method fits two intersecting lines to the data by computing a least-squares estimate of the position of the slope change and its 95% confidence limits. This avoids the potential bias of fixing the change at a preconceived time corresponding with an alteration in treatment. The program then evaluates the statistical and clinical significance of the slope change and produces a graphical output to aid interpretation.

A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield

NASA Astrophysics Data System (ADS)

Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan

2018-04-01

In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

PubMed

Anderson, Carl A; McRae, Allan F; Visscher, Peter M

2006-07-01

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

Wavelet-based functional linear mixed models: an application to measurement error-corrected distributed lag models.

PubMed

Malloy, Elizabeth J; Morris, Jeffrey S; Adar, Sara D; Suh, Helen; Gold, Diane R; Coull, Brent A

2010-07-01

Frequently, exposure data are measured over time on a grid of discrete values that collectively define a functional observation. In many applications, researchers are interested in using these measurements as covariates to predict a scalar response in a regression setting, with interest focusing on the most biologically relevant time window of exposure. One example is in panel studies of the health effects of particulate matter (PM), where particle levels are measured over time. In such studies, there are many more values of the functional data than observations in the data set so that regularization of the corresponding functional regression coefficient is necessary for estimation. Additional issues in this setting are the possibility of exposure measurement error and the need to incorporate additional potential confounders, such as meteorological or co-pollutant measures, that themselves may have effects that vary over time. To accommodate all these features, we develop wavelet-based linear mixed distributed lag models that incorporate repeated measures of functional data as covariates into a linear mixed model. A Bayesian approach to model fitting uses wavelet shrinkage to regularize functional coefficients. We show that, as long as the exposure error induces fine-scale variability in the functional exposure profile and the distributed lag function representing the exposure effect varies smoothly in time, the model corrects for the exposure measurement error without further adjustment. Both these conditions are likely to hold in the environmental applications we consider. We examine properties of the method using simulations and apply the method to data from a study examining the association between PM, measured as hourly averages for 1-7 days, and markers of acute systemic inflammation. We use the method to fully control for the effects of confounding by other time-varying predictors, such as temperature and co-pollutants.

Effect of removing the common mode errors on linear regression analysis of noise amplitudes in position time series of a regional GPS network & a case study of GPS stations in Southern California

NASA Astrophysics Data System (ADS)

Jiang, Weiping; Ma, Jun; Li, Zhao; Zhou, Xiaohui; Zhou, Boye

2018-05-01

The analysis of the correlations between the noise in different components of GPS stations has positive significance to those trying to obtain more accurate uncertainty of velocity with respect to station motion. Previous research into noise in GPS position time series focused mainly on single component evaluation, which affects the acquisition of precise station positions, the velocity field, and its uncertainty. In this study, before and after removing the common-mode error (CME), we performed one-dimensional linear regression analysis of the noise amplitude vectors in different components of 126 GPS stations with a combination of white noise, flicker noise, and random walking noise in Southern California. The results show that, on the one hand, there are above-moderate degrees of correlation between the white noise amplitude vectors in all components of the stations before and after removal of the CME, while the correlations between flicker noise amplitude vectors in horizontal and vertical components are enhanced from un-correlated to moderately correlated by removing the CME. On the other hand, the significance tests show that, all of the obtained linear regression equations, which represent a unique function of the noise amplitude in any two components, are of practical value after removing the CME. According to the noise amplitude estimates in two components and the linear regression equations, more accurate noise amplitudes can be acquired in the two components.

Predicting birth weight with conditionally linear transformation models.

PubMed

Möst, Lisa; Schmid, Matthias; Faschingbauer, Florian; Hothorn, Torsten

2016-12-01

Low and high birth weight (BW) are important risk factors for neonatal morbidity and mortality. Gynecologists must therefore accurately predict BW before delivery. Most prediction formulas for BW are based on prenatal ultrasound measurements carried out within one week prior to birth. Although successfully used in clinical practice, these formulas focus on point predictions of BW but do not systematically quantify uncertainty of the predictions, i.e. they result in estimates of the conditional mean of BW but do not deliver prediction intervals. To overcome this problem, we introduce conditionally linear transformation models (CLTMs) to predict BW. Instead of focusing only on the conditional mean, CLTMs model the whole conditional distribution function of BW given prenatal ultrasound parameters. Consequently, the CLTM approach delivers both point predictions of BW and fetus-specific prediction intervals. Prediction intervals constitute an easy-to-interpret measure of prediction accuracy and allow identification of fetuses subject to high prediction uncertainty. Using a data set of 8712 deliveries at the Perinatal Centre at the University Clinic Erlangen (Germany), we analyzed variants of CLTMs and compared them to standard linear regression estimation techniques used in the past and to quantile regression approaches. The best-performing CLTM variant was competitive with quantile regression and linear regression approaches in terms of conditional coverage and average length of the prediction intervals. We propose that CLTMs be used because they are able to account for possible heteroscedasticity, kurtosis, and skewness of the distribution of BWs. © The Author(s) 2014.

Estimating PM2.5 Concentrations in Xi'an City Using a Generalized Additive Model with Multi-Source Monitoring Data

PubMed Central

Song, Yong-Ze; Yang, Hong-Lei; Peng, Jun-Huan; Song, Yi-Rong; Sun, Qian; Li, Yuan

2015-01-01

Particulate matter with an aerodynamic diameter <2.5 μm (PM2.5) represents a severe environmental problem and is of negative impact on human health. Xi'an City, with a population of 6.5 million, is among the highest concentrations of PM2.5 in China. In 2013, in total, there were 191 days in Xi’an City on which PM2.5 concentrations were greater than 100 μg/m3. Recently, a few studies have explored the potential causes of high PM2.5 concentration using remote sensing data such as the MODIS aerosol optical thickness (AOT) product. Linear regression is a commonly used method to find statistical relationships among PM2.5 concentrations and other pollutants, including CO, NO2, SO2, and O3, which can be indicative of emission sources. The relationships of these variables, however, are usually complicated and non-linear. Therefore, a generalized additive model (GAM) is used to estimate the statistical relationships between potential variables and PM2.5 concentrations. This model contains linear functions of SO2 and CO, univariate smoothing non-linear functions of NO2, O3, AOT and temperature, and bivariate smoothing non-linear functions of location and wind variables. The model can explain 69.50% of PM2.5 concentrations, with R2 = 0.691, which improves the result of a stepwise linear regression (R2 = 0.582) by 18.73%. The two most significant variables, CO concentration and AOT, represent 20.65% and 19.54% of the deviance, respectively, while the three other gas-phase concentrations, SO2, NO2, and O3 account for 10.88% of the total deviance. These results show that in Xi'an City, the traffic and other industrial emissions are the primary source of PM2.5. Temperature, location, and wind variables also non-linearly related with PM2.5. PMID:26540446

Effects of Body Mass Index on Lung Function Index of Chinese Population

NASA Astrophysics Data System (ADS)

Guo, Qiao; Ye, Jun; Yang, Jian; Zhu, Changan; Sheng, Lei; Zhang, Yongliang

2018-01-01

To study the effect of body mass index (BMI) on lung function indexes in Chinese population. A cross-sectional study was performed on 10, 592 participants. The linear relationship between lung function and BMI was evaluated by multivariate linear regression analysis, and the correlation between BMI and lung function was assessed by Pearson correlation analysis. Correlation analysis showed that BMI was positively related with the decreasing of forced vital capacity (FVC), forced expiratory volume in one second (FEV1) and FEV1/FVC (P <0.05), the increasing of FVC% predicted value (FVC%pre) and FEV1% predicted value (FEV1%pre). These suggested that Chinese people can restrain the decline of lung function to prevent the occurrence and development of COPD by the control of BMI.

Association between the Type of Workplace and Lung Function in Copper Miners

PubMed Central

Gruszczyński, Leszek; Wojakowska, Anna; Ścieszka, Marek; Turczyn, Barbara; Schmidt, Edward

2016-01-01

The aim of the analysis was to retrospectively assess changes in lung function in copper miners depending on the type of workplace. In the groups of 225 operators, 188 welders, and 475 representatives of other jobs, spirometry was performed at the start of employment and subsequently after 10, 20, and 25 years of work. Spirometry Longitudinal Data Analysis software was used to estimate changes in group means for FEV1 and FVC. Multiple linear regression analysis was used to assess an association between workplace and lung function. Lung function assessed on the basis of calculation of longitudinal FEV1 (FVC) decline was similar in all studied groups. However, multiple linear regression model used in cross-sectional analysis revealed an association between workplace and lung function. In the group of welders, FEF75 was lower in comparison to operators and other miners as early as after 10 years of work. Simultaneously, in smoking welders, the FEV1/FVC ratio was lower than in nonsmokers (p < 0,05). The interactions between type of workplace and smoking (p < 0,05) in their effect on FVC, FEV1, PEF, and FEF50 were shown. Among underground working copper miners, the group of smoking welders is especially threatened by impairment of lung ventilatory function. PMID:27274987

Linear regression crash prediction models : issues and proposed solutions.

DOT National Transportation Integrated Search

2010-05-01

The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

A generalized partially linear mean-covariance regression model for longitudinal proportional data, with applications to the analysis of quality of life data from cancer clinical trials.

PubMed

Zheng, Xueying; Qin, Guoyou; Tu, Dongsheng

2017-05-30

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean-covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within-subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Use of multivariate linear regression and support vector regression to predict functional outcome after surgery for cervical spondylotic myelopathy.

PubMed

Hoffman, Haydn; Lee, Sunghoon I; Garst, Jordan H; Lu, Derek S; Li, Charles H; Nagasawa, Daniel T; Ghalehsari, Nima; Jahanforouz, Nima; Razaghy, Mehrdad; Espinal, Marie; Ghavamrezaii, Amir; Paak, Brian H; Wu, Irene; Sarrafzadeh, Majid; Lu, Daniel C

2015-09-01

This study introduces the use of multivariate linear regression (MLR) and support vector regression (SVR) models to predict postoperative outcomes in a cohort of patients who underwent surgery for cervical spondylotic myelopathy (CSM). Currently, predicting outcomes after surgery for CSM remains a challenge. We recruited patients who had a diagnosis of CSM and required decompressive surgery with or without fusion. Fine motor function was tested preoperatively and postoperatively with a handgrip-based tracking device that has been previously validated, yielding mean absolute accuracy (MAA) results for two tracking tasks (sinusoidal and step). All patients completed Oswestry disability index (ODI) and modified Japanese Orthopaedic Association questionnaires preoperatively and postoperatively. Preoperative data was utilized in MLR and SVR models to predict postoperative ODI. Predictions were compared to the actual ODI scores with the coefficient of determination (R(2)) and mean absolute difference (MAD). From this, 20 patients met the inclusion criteria and completed follow-up at least 3 months after surgery. With the MLR model, a combination of the preoperative ODI score, preoperative MAA (step function), and symptom duration yielded the best prediction of postoperative ODI (R(2)=0.452; MAD=0.0887; p=1.17 × 10(-3)). With the SVR model, a combination of preoperative ODI score, preoperative MAA (sinusoidal function), and symptom duration yielded the best prediction of postoperative ODI (R(2)=0.932; MAD=0.0283; p=5.73 × 10(-12)). The SVR model was more accurate than the MLR model. The SVR can be used preoperatively in risk/benefit analysis and the decision to operate. Copyright © 2015 Elsevier Ltd. All rights reserved.

Valuing the visual impact of wind farms: A calculus method for synthesizing choice experiments studies.

PubMed

Wen, Cheng; Dallimer, Martin; Carver, Steve; Ziv, Guy

2018-05-06

Despite the great potential of mitigating carbon emission, development of wind farms is often opposed by local communities due to the visual impact on landscape. A growing number of studies have applied nonmarket valuation methods like Choice Experiments (CE) to value the visual impact by eliciting respondents' willingness to pay (WTP) or willingness to accept (WTA) for hypothetical wind farms through survey questions. Several meta-analyses have been found in the literature to synthesize results from different valuation studies, but they have various limitations related to the use of the prevailing multivariate meta-regression analysis. In this paper, we propose a new meta-analysis method to establish general functions for the relationships between the estimated WTP or WTA and three wind farm attributes, namely the distance to residential/coastal areas, the number of turbines and turbine height. This method involves establishing WTA or WTP functions for individual studies, fitting the average derivative functions and deriving the general integral functions of WTP or WTA against wind farm attributes. Results indicate that respondents in different studies consistently showed increasing WTP for moving wind farms to greater distances, which can be fitted by non-linear (natural logarithm) functions. However, divergent preferences for the number of turbines and turbine height were found in different studies. We argue that the new analysis method proposed in this paper is an alternative to the mainstream multivariate meta-regression analysis for synthesizing CE studies and the general integral functions of WTP or WTA against wind farm attributes are useful for future spatial modelling and benefit transfer studies. We also suggest that future multivariate meta-analyses should include non-linear components in the regression functions. Copyright © 2018. Published by Elsevier B.V.

Physical function in older men with hyperkyphosis.

PubMed

Katzman, Wendy B; Harrison, Stephanie L; Fink, Howard A; Marshall, Lynn M; Orwoll, Eric; Barrett-Connor, Elizabeth; Cawthon, Peggy M; Kado, Deborah M

2015-05-01

Age-related hyperkyphosis has been associated with poor physical function and is a well-established predictor of adverse health outcomes in older women, but its impact on health in older men is less well understood. We conducted a cross-sectional study to evaluate the association of hyperkyphosis and physical function in 2,363 men, aged 71-98 (M = 79) from the Osteoporotic Fractures in Men Study. Kyphosis was measured using the Rancho Bernardo Study block method. Measurements of grip strength and lower extremity function, including gait speed over 6 m, narrow walk (measure of dynamic balance), repeated chair stands ability and time, and lower extremity power (Nottingham Power Rig) were included separately as primary outcomes. We investigated associations of kyphosis and each outcome in age-adjusted and multivariable linear or logistic regression models, controlling for age, clinic, education, race, bone mineral density, height, weight, diabetes, and physical activity. In multivariate linear regression, we observed a dose-related response of worse scores on each lower extremity physical function test as number of blocks increased, p for trend ≤.001. Using a cutoff of ≥4 blocks, 20% (N = 469) of men were characterized with hyperkyphosis. In multivariate logistic regression, men with hyperkyphosis had increased odds (range 1.5-1.8) of being in the worst quartile of performing lower extremity physical function tasks (p < .001 for each outcome). Kyphosis was not associated with grip strength in any multivariate analysis. Hyperkyphosis is associated with impaired lower extremity physical function in older men. Further studies are needed to determine the direction of causality. © The Author 2014. Published by Oxford University Press on behalf of The Gerontological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Modification of the USLE K factor for soil erodibility assessment on calcareous soils in Iran

NASA Astrophysics Data System (ADS)

Ostovari, Yaser; Ghorbani-Dashtaki, Shoja; Bahrami, Hossein-Ali; Naderi, Mehdi; Dematte, Jose Alexandre M.; Kerry, Ruth

2016-11-01

The measurement of soil erodibility (K) in the field is tedious, time-consuming and expensive; therefore, its prediction through pedotransfer functions (PTFs) could be far less costly and time-consuming. The aim of this study was to develop new PTFs to estimate the K factor using multiple linear regression, Mamdani fuzzy inference systems, and artificial neural networks. For this purpose, K was measured in 40 erosion plots with natural rainfall. Various soil properties including the soil particle size distribution, calcium carbonate equivalent, organic matter, permeability, and wet-aggregate stability were measured. The results showed that the mean measured K was 0.014 t h MJ- 1 mm- 1 and 2.08 times less than the estimated mean K (0.030 t h MJ- 1 mm- 1) using the USLE model. Permeability, wet-aggregate stability, very fine sand, and calcium carbonate were selected as independent variables by forward stepwise regression in order to assess the ability of multiple linear regression, Mamdani fuzzy inference systems and artificial neural networks to predict K. The calcium carbonate equivalent, which is not accounted for in the USLE model, had a significant impact on K in multiple linear regression due to its strong influence on the stability of aggregates and soil permeability. Statistical indices in validation and calibration datasets determined that the artificial neural networks method with the highest R2, lowest RMSE, and lowest ME was the best model for estimating the K factor. A strong correlation (R2 = 0.81, n = 40, p < 0.05) between the estimated K from multiple linear regression and measured K indicates that the use of calcium carbonate equivalent as a predictor variable gives a better estimation of K in areas with calcareous soils.

The Application of the Cumulative Logistic Regression Model to Automated Essay Scoring

ERIC Educational Resources Information Center

Haberman, Shelby J.; Sinharay, Sandip

2010-01-01

Most automated essay scoring programs use a linear regression model to predict an essay score from several essay features. This article applied a cumulative logit model instead of the linear regression model to automated essay scoring. Comparison of the performances of the linear regression model and the cumulative logit model was performed on a…

The Multiple Correspondence Analysis Method and Brain Functional Connectivity: Its Application to the Study of the Non-linear Relationships of Motor Cortex and Basal Ganglia.

PubMed

Rodriguez-Sabate, Clara; Morales, Ingrid; Sanchez, Alberto; Rodriguez, Manuel

2017-01-01

The complexity of basal ganglia (BG) interactions is often condensed into simple models mainly based on animal data and that present BG in closed-loop cortico-subcortical circuits of excitatory/inhibitory pathways which analyze the incoming cortical data and return the processed information to the cortex. This study was aimed at identifying functional relationships in the BG motor-loop of 24 healthy-subjects who provided written, informed consent and whose BOLD-activity was recorded by MRI methods. The analysis of the functional interaction between these centers by correlation techniques and multiple linear regression showed non-linear relationships which cannot be suitably addressed with these methods. The multiple correspondence analysis (MCA), an unsupervised multivariable procedure which can identify non-linear interactions, was used to study the functional connectivity of BG when subjects were at rest. Linear methods showed different functional interactions expected according to current BG models. MCA showed additional functional interactions which were not evident when using lineal methods. Seven functional configurations of BG were identified with MCA, two involving the primary motor and somatosensory cortex, one involving the deepest BG (external-internal globus pallidum, subthalamic nucleus and substantia nigral), one with the input-output BG centers (putamen and motor thalamus), two linking the input-output centers with other BG (external pallidum and subthalamic nucleus), and one linking the external pallidum and the substantia nigral. The results provide evidence that the non-linear MCA and linear methods are complementary and should be best used in conjunction to more fully understand the nature of functional connectivity of brain centers.

Which Frail Older People Are Dehydrated? The UK DRIE Study.

PubMed

Hooper, Lee; Bunn, Diane K; Downing, Alice; Jimoh, Florence O; Groves, Joyce; Free, Carol; Cowap, Vicky; Potter, John F; Hunter, Paul R; Shepstone, Lee

2016-10-01

Water-loss dehydration in older people is associated with increased mortality and disability. We aimed to assess the prevalence of dehydration in older people living in UK long-term care and associated cognitive, functional, and health characteristics. The Dehydration Recognition In our Elders (DRIE) cohort study included people aged 65 or older living in long-term care without heart or renal failure. In a cross-sectional baseline analysis, we assessed serum osmolality, previously suggested dehydration risk factors, general health, markers of continence, cognitive and functional health, nutrition status, and medications. Univariate linear regression was used to assess relationships between participant characteristics and serum osmolality, then associated characteristics entered into stepwise backwards multivariate linear regression. DRIE included 188 residents (mean age 86 years, 66% women) of whom 20% were dehydrated (serum osmolality >300 mOsm/kg). Linear and logistic regression suggested that renal, cognitive, and diabetic status were consistently associated with serum osmolality and odds of dehydration, while potassium-sparing diuretics, sex, number of recent health contacts, and bladder incontinence were sometimes associated. Thirst was not associated with hydration status. DRIE found high prevalence of dehydration in older people living in UK long-term care, reinforcing the proposed association between cognitive and renal function and hydration. Dehydration is associated with increased mortality and disability in older people, but trials to assess effects of interventions to support healthy fluid intakes in older people living in residential care are needed to enable us to formally assess causal direction and any health benefits of increasing fluid intakes. © The Author 2015. Published by Oxford University Press on behalf of The Gerontological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Sick of our loans: Student borrowing and the mental health of young adults in the United States.

PubMed

Walsemann, Katrina M; Gee, Gilbert C; Gentile, Danielle

2015-01-01

Student loans are increasingly important and commonplace, especially among recent cohorts of young adults in the United States. These loans facilitate the acquisition of human capital in the form of education, but may also lead to stress and worries related to repayment. This study investigated two questions: 1) what is the association between the cumulative amount of student loans borrowed over the course of schooling and psychological functioning when individuals are 25-31 years old; and 2) what is the association between annual student loan borrowing and psychological functioning among currently enrolled college students? We also examined whether these relationships varied by parental wealth, college enrollment history (e.g. 2-year versus 4-year college), and educational attainment (for cumulative student loans only). We analyzed data from the National Longitudinal Survey of Youth 1997 (NLSY97), a nationally representative sample of young adults in the United States. Analyses employed multivariate linear regression and within-person fixed-effects models. Student loans were associated with poorer psychological functioning, adjusting for covariates, in both the multivariate linear regression and the within-person fixed effects models. This association varied by level of parental wealth in the multivariate linear regression models only, and did not vary by college enrollment history or educational attainment. The present findings raise novel questions for further research regarding student loan debt and the possible spillover effects on other life circumstances, such as occupational trajectories and health inequities. The study of student loans is even more timely and significant given the ongoing rise in the costs of higher education. Copyright © 2014 Elsevier Ltd. All rights reserved.

Measurement of pediatric regional cerebral blood flow from 6 months to 15 years of age in a clinical population.

PubMed

Carsin-Vu, Aline; Corouge, Isabelle; Commowick, Olivier; Bouzillé, Guillaume; Barillot, Christian; Ferré, Jean-Christophe; Proisy, Maia

2018-04-01

To investigate changes in cerebral blood flow (CBF) in gray matter (GM) between 6 months and 15 years of age and to provide CBF values for the brain, GM, white matter (WM), hemispheres and lobes. Between 2013 and 2016, we retrospectively included all clinical MRI examinations with arterial spin labeling (ASL). We excluded subjects with a condition potentially affecting brain perfusion. For each subject, mean values of CBF in the brain, GM, WM, hemispheres and lobes were calculated. GM CBF was fitted using linear, quadratic and cubic polynomial regression against age. Regression models were compared with Akaike's information criterion (AIC), and Likelihood Ratio tests. 84 children were included (44 females/40 males). Mean CBF values were 64.2 ± 13.8 mL/100 g/min in GM, and 29.3 ± 10.0 mL/100 g/min in WM. The best-fit model of brain perfusion was the cubic polynomial function (AIC = 672.7, versus respectively AIC = 673.9 and AIC = 674.1 with the linear negative function and the quadratic polynomial function). A statistically significant difference between the tested models demonstrating the superiority of the quadratic (p = 0.18) or cubic polynomial model (p = 0.06), over the negative linear regression model was not found. No effect of general anesthesia (p = 0.34) or of gender (p = 0.16) was found. we provided values for ASL CBF in the brain, GM, WM, hemispheres, and lobes over a wide pediatric age range, approximately showing inverted U-shaped changes in GM perfusion over the course of childhood. Copyright © 2018 Elsevier B.V. All rights reserved.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle.

PubMed

Pereira, R J; Bignardi, A B; El Faro, L; Verneque, R S; Vercesi Filho, A E; Albuquerque, L G

2013-01-01

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Transmission of linear regression patterns between time series: From relationship in time series to complex networks

NASA Astrophysics Data System (ADS)

Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui

2014-07-01

The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.

Transmission of linear regression patterns between time series: from relationship in time series to complex networks.

PubMed

Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui

2014-07-01

The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.

Estimating the population size and colony boundary of subterranean termites by using the density functions of directionally averaged capture probability.

PubMed

Su, Nan-Yao; Lee, Sang-Hee

2008-04-01

Marked termites were released in a linear-connected foraging arena, and the spatial heterogeneity of their capture probabilities was averaged for both directions at distance r from release point to obtain a symmetrical distribution, from which the density function of directionally averaged capture probability P(x) was derived. We hypothesized that as marked termites move into the population and given sufficient time, the directionally averaged capture probability may reach an equilibrium P(e) over the distance r and thus satisfy the equal mixing assumption of the mark-recapture protocol. The equilibrium capture probability P(e) was used to estimate the population size N. The hypothesis was tested in a 50-m extended foraging arena to simulate the distance factor of field colonies of subterranean termites. Over the 42-d test period, the density functions of directionally averaged capture probability P(x) exhibited four phases: exponential decline phase, linear decline phase, equilibrium phase, and postequilibrium phase. The equilibrium capture probability P(e), derived as the intercept of the linear regression during the equilibrium phase, correctly projected N estimates that were not significantly different from the known number of workers in the arena. Because the area beneath the probability density function is a constant (50% in this study), preequilibrium regression parameters and P(e) were used to estimate the population boundary distance 1, which is the distance between the release point and the boundary beyond which the population is absent.

CORRELATION PURSUIT: FORWARD STEPWISE VARIABLE SELECTION FOR INDEX MODELS

PubMed Central

Zhong, Wenxuan; Zhang, Tingting; Zhu, Yu; Liu, Jun S.

2012-01-01

In this article, a stepwise procedure, correlation pursuit (COP), is developed for variable selection under the sufficient dimension reduction framework, in which the response variable Y is influenced by the predictors X1, X2, …, Xp through an unknown function of a few linear combinations of them. Unlike linear stepwise regression, COP does not impose a special form of relationship (such as linear) between the response variable and the predictor variables. The COP procedure selects variables that attain the maximum correlation between the transformed response and the linear combination of the variables. Various asymptotic properties of the COP procedure are established, and in particular, its variable selection performance under diverging number of predictors and sample size has been investigated. The excellent empirical performance of the COP procedure in comparison with existing methods are demonstrated by both extensive simulation studies and a real example in functional genomics. PMID:23243388

Predictors of physical performance and functional ability in people 50+ with and without fibromyalgia.

PubMed

Jones, C Jessie; Rutledge, Dana N; Aquino, Jordan

2010-07-01

The purposes of this study were to determine whether people with and without fibromyalgia (FM) age 50 yr and above showed differences in physical performance and perceived functional ability and to determine whether age, gender, depression, and physical activity level altered the impact of FM status on these factors. Dependent variables included perceived function and 6 performance measures (multidimensional balance, aerobic endurance, overall functional mobility, lower body strength, and gait velocity-normal or fast). Independent (predictor) variables were FM status, age, gender, depression, and physical activity level. Results indicated significant differences between adults with and without FM on all physical-performance measures and perceived function. Linear-regression models showed that the contribution of significant predictors was in expected directions. All regression models were significant, accounting for 16-65% of variance in the dependent variables.

Association between Social Activities and Cognitive Function among the Elderly in China: A Cross-Sectional Study.

PubMed

Fu, Chang; Li, Zhen; Mao, Zongfu

2018-01-30

Participation in social activities is one of important factors for older adults' health. The present study aims to examine the cross-sectional association between social activities and cognitive function among Chinese elderly. A total of 8966 individuals aged 60 and older from the 2015 China Health and Retirement Longitudinal Study were obtained for this study. Telephone interviews of cognitive status, episodic memory, and visuospatial abilities were assessed by questionnaire. We used the sum of all three of the above measures to represent the respondent's cognitive status as a whole. Types and frequencies of participation in social groups were used to measure social activities. Multiple linear regression analysis was used to explore the relationship between social activities and cognitive function. After adjustment for demographics, smoking, drinking, depression, hypertension, diabetes, basic activities of daily living, instrumental activities of daily living, and self-rated health, multiple linear regression analysis revealed that interaction with friends, participating in hobby groups, and sports groups were associated with better cognitive function among both men and women ( p < 0.05); doing volunteer work was associated with better cognitive function among women but not among men ( p < 0.05). These findings suggest that there is a cross-sectional association between participation in social activities and cognitive function among Chinese elderly. Longitudinal studies are needed to examine the effects of social activities on cognitive function.

Association between Social Activities and Cognitive Function among the Elderly in China: A Cross-Sectional Study

PubMed Central

Fu, Chang; Li, Zhen; Mao, Zongfu

2018-01-01

Participation in social activities is one of important factors for older adults’ health. The present study aims to examine the cross-sectional association between social activities and cognitive function among Chinese elderly. A total of 8966 individuals aged 60 and older from the 2015 China Health and Retirement Longitudinal Study were obtained for this study. Telephone interviews of cognitive status, episodic memory, and visuospatial abilities were assessed by questionnaire. We used the sum of all three of the above measures to represent the respondent’s cognitive status as a whole. Types and frequencies of participation in social groups were used to measure social activities. Multiple linear regression analysis was used to explore the relationship between social activities and cognitive function. After adjustment for demographics, smoking, drinking, depression, hypertension, diabetes, basic activities of daily living, instrumental activities of daily living, and self-rated health, multiple linear regression analysis revealed that interaction with friends, participating in hobby groups, and sports groups were associated with better cognitive function among both men and women (p < 0.05); doing volunteer work was associated with better cognitive function among women but not among men (p < 0.05). These findings suggest that there is a cross-sectional association between participation in social activities and cognitive function among Chinese elderly. Longitudinal studies are needed to examine the effects of social activities on cognitive function. PMID:29385773

Protocol Analysis as a Tool in Function and Task Analysis

DTIC Science & Technology

1999-10-01

Autocontingency The use of log-linear and logistic regression methods to analyse sequential data seems appealing , and is strongly advocated by...collection and analysis of observational data. Behavior Research Methods, Instruments, and Computers, 23(3), 415-429. Patrick, J. D. (1991). Snob : A

Prediction of HDR quality by combining perceptually transformed display measurements with machine learning

NASA Astrophysics Data System (ADS)

Choudhury, Anustup; Farrell, Suzanne; Atkins, Robin; Daly, Scott

2017-09-01

We present an approach to predict overall HDR display quality as a function of key HDR display parameters. We first performed subjective experiments on a high quality HDR display that explored five key HDR display parameters: maximum luminance, minimum luminance, color gamut, bit-depth and local contrast. Subjects rated overall quality for different combinations of these display parameters. We explored two models | a physical model solely based on physically measured display characteristics and a perceptual model that transforms physical parameters using human vision system models. For the perceptual model, we use a family of metrics based on a recently published color volume model (ICT-CP), which consists of the PQ luminance non-linearity (ST2084) and LMS-based opponent color, as well as an estimate of the display point spread function. To predict overall visual quality, we apply linear regression and machine learning techniques such as Multilayer Perceptron, RBF and SVM networks. We use RMSE and Pearson/Spearman correlation coefficients to quantify performance. We found that the perceptual model is better at predicting subjective quality than the physical model and that SVM is better at prediction than linear regression. The significance and contribution of each display parameter was investigated. In addition, we found that combined parameters such as contrast do not improve prediction. Traditional perceptual models were also evaluated and we found that models based on the PQ non-linearity performed better.

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

PubMed

Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

2018-06-01

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Alencar, M M; Albuquerque, L G

2010-12-01

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions. © 2010 Blackwell Verlag GmbH.

Development of Super-Ensemble techniques for ocean analyses: the Mediterranean Sea case

NASA Astrophysics Data System (ADS)

Pistoia, Jenny; Pinardi, Nadia; Oddo, Paolo; Collins, Matthew; Korres, Gerasimos; Drillet, Yann

2017-04-01

Short-term ocean analyses for Sea Surface Temperature SST in the Mediterranean Sea can be improved by a statistical post-processing technique, called super-ensemble. This technique consists in a multi-linear regression algorithm applied to a Multi-Physics Multi-Model Super-Ensemble (MMSE) dataset, a collection of different operational forecasting analyses together with ad-hoc simulations produced by modifying selected numerical model parameterizations. A new linear regression algorithm based on Empirical Orthogonal Function filtering techniques is capable to prevent overfitting problems, even if best performances are achieved when we add correlation to the super-ensemble structure using a simple spatial filter applied after the linear regression. Our outcomes show that super-ensemble performances depend on the selection of an unbiased operator and the length of the learning period, but the quality of the generating MMSE dataset has the largest impact on the MMSE analysis Root Mean Square Error (RMSE) evaluated with respect to observed satellite SST. Lower RMSE analysis estimates result from the following choices: 15 days training period, an overconfident MMSE dataset (a subset with the higher quality ensemble members), and the least square algorithm being filtered a posteriori.

Influence of CT-based depth correction of renal scintigraphy in evaluation of living kidney donors on side selection and postoperative renal function: is it necessary to know the relative renal function?

PubMed

Weinberger, Sarah; Klarholz-Pevere, Carola; Liefeldt, Lutz; Baeder, Michael; Steckhan, Nico; Friedersdorff, Frank

2018-03-22

To analyse the influence of CT-based depth correction in the assessment of split renal function in potential living kidney donors. In 116 consecutive living kidney donors preoperative split renal function was assessed using the CT-based depth correction. Influence on donor side selection and postoperative renal function of the living kidney donors were analyzed. Linear regression analysis was performed to identify predictors of postoperative renal function. A left versus right kidney depth variation of more than 1 cm was found in 40/114 donors (35%). 11 patients (10%) had a difference of more than 5% in relative renal function after depth correction. Kidney depth variation and changes in relative renal function after depth correction would have had influence on side selection in 30 of 114 living kidney donors. CT depth correction did not improve the predictability of postoperative renal function of the living kidney donor. In general, it was not possible to predict the postoperative renal function from preoperative total and relative renal function. In multivariate linear regression analysis, age and BMI were identified as most important predictors for postoperative renal function of the living kidney donors. Our results clearly indicate that concerning the postoperative renal function of living kidney donors, the relative renal function of the donated kidney seems to be less important than other factors. A multimodal assessment with consideration of all available results including kidney size, location of the kidney and split renal function remains necessary.

Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

DTIC Science & Technology

1974-01-01

REGRESSION MODEL - THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January 1974 Nelson Delfino d’Avila Mascarenha;? Image...Report 520 DIGITAL IMAGE RESTORATION UNDER A REGRESSION MODEL THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January...a two- dimensional form adequately describes the linear model . A dis- cretization is performed by using quadrature methods. By trans

Product unit neural network models for predicting the growth limits of Listeria monocytogenes.

PubMed

Valero, A; Hervás, C; García-Gimeno, R M; Zurera, G

2007-08-01

A new approach to predict the growth/no growth interface of Listeria monocytogenes as a function of storage temperature, pH, citric acid (CA) and ascorbic acid (AA) is presented. A linear logistic regression procedure was performed and a non-linear model was obtained by adding new variables by means of a Neural Network model based on Product Units (PUNN). The classification efficiency of the training data set and the generalization data of the new Logistic Regression PUNN model (LRPU) were compared with Linear Logistic Regression (LLR) and Polynomial Logistic Regression (PLR) models. 92% of the total cases from the LRPU model were correctly classified, an improvement on the percentage obtained using the PLR model (90%) and significantly higher than the results obtained with the LLR model, 80%. On the other hand predictions of LRPU were closer to data observed which permits to design proper formulations in minimally processed foods. This novel methodology can be applied to predictive microbiology for describing growth/no growth interface of food-borne microorganisms such as L. monocytogenes. The optimal balance is trying to find models with an acceptable interpretation capacity and with good ability to fit the data on the boundaries of variable range. The results obtained conclude that these kinds of models might well be very a valuable tool for mathematical modeling.

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

Applicational possibilities of linear and non-linear (polynomial) regression and analysis of variance. III. Stability determination of pharmaceutical preparations: stability of diclofenac-sodium in Diclofen injections.

PubMed

Arambasić, M B; Jatić-Slavković, D

2004-05-01

This paper presents the application of the regression analysis program and the program for comparing linear regressions (modified method for one-way, analysis of variance), writtens in BASIC program language, for instance, determination of content of Diclofenac-Sodium (active ingredient in DIKLOFEN injections, ampules á 75 mg/3 ml). Stability testing of Diclofenac-Sodium was done by isothermic method of accelerated aging at 4 different temperatures (30 degrees, 40 degrees, 50 degrees and 60 degrees C) as a function of time (4 different duration of treatment: (0-155, 0-145, 0-74 and 0-44 days). The decrease in stability (decrease in the mean value of the content of Diclofenac-Sodium (in %), at different temperatures as a function of time, is possible to describe by, linear dependance. According to the value for regression equation values, the times are assessed in which the content of Diclofenac-Sodium (in %) will decrease by 10%, of the initial value. The times are follows at 30 degrees C 761.02 days, at 40 degrees C 397.26 days, at 50 degrees C 201.96 days and at 60 degrees C 58.85 days. The estimated times (in days) in which the mean value for Diclofenac-Sodium content (in %) will by 10% of the initial values, as a junction of time, are most suitably described by 3rd order parabola. Based on the parameter values which describe the 3rd order parabola, the time was estimated in which Diclofenac-Sodium content mean value (in %) will fall by 10% of the initial one at average ambient temperatures of 20 degrees C and 25 degrees C. The times are: 1409.47 days (20 degrees C) and 1042.39 days (25 degrees C). Based on the value for Fischer's coefficien (F), the comparison of trenf of Diclofenac-Sodium content (in %) shows that, under the influence of different temperatures as a function of time, among them, depending on temperature value, there is: statistically very significant difference (P < .05) at 50 degrees C and lower toward 60 degrees C, i.e. statistically probably significant difference (P > 0.01) at 40 degrees C and lower towards 50 degrees C and there is no statistically significance difference (P > 0.05) at 30 degrees C towards 40 degrees C.

Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models.

PubMed

Chen, Baojiang; Qin, Jing

2014-05-10

In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study. Copyright © 2013 John Wiley & Sons, Ltd.

The microcomputer scientific software series 2: general linear model--regression.

Treesearch

Harold M. Rauscher

1983-01-01

The general linear model regression (GLMR) program provides the microcomputer user with a sophisticated regression analysis capability. The output provides a regression ANOVA table, estimators of the regression model coefficients, their confidence intervals, confidence intervals around the predicted Y-values, residuals for plotting, a check for multicollinearity, a...

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Across-Platform Imputation of DNA Methylation Levels Incorporating Nonlocal Information Using Penalized Functional Regression.

PubMed

Zhang, Guosheng; Huang, Kuan-Chieh; Xu, Zheng; Tzeng, Jung-Ying; Conneely, Karen N; Guan, Weihua; Kang, Jian; Li, Yun

2016-05-01

DNA methylation is a key epigenetic mark involved in both normal development and disease progression. Recent advances in high-throughput technologies have enabled genome-wide profiling of DNA methylation. However, DNA methylation profiling often employs different designs and platforms with varying resolution, which hinders joint analysis of methylation data from multiple platforms. In this study, we propose a penalized functional regression model to impute missing methylation data. By incorporating functional predictors, our model utilizes information from nonlocal probes to improve imputation quality. Here, we compared the performance of our functional model to linear regression and the best single probe surrogate in real data and via simulations. Specifically, we applied different imputation approaches to an acute myeloid leukemia dataset consisting of 194 samples and our method showed higher imputation accuracy, manifested, for example, by a 94% relative increase in information content and up to 86% more CpG sites passing post-imputation filtering. Our simulated association study further demonstrated that our method substantially improves the statistical power to identify trait-associated methylation loci. These findings indicate that the penalized functional regression model is a convenient and valuable imputation tool for methylation data, and it can boost statistical power in downstream epigenome-wide association study (EWAS). © 2016 WILEY PERIODICALS, INC.

A quasi-Monte-Carlo comparison of parametric and semiparametric regression methods for heavy-tailed and non-normal data: an application to healthcare costs.

PubMed

Jones, Andrew M; Lomas, James; Moore, Peter T; Rice, Nigel

2016-10-01

We conduct a quasi-Monte-Carlo comparison of the recent developments in parametric and semiparametric regression methods for healthcare costs, both against each other and against standard practice. The population of English National Health Service hospital in-patient episodes for the financial year 2007-2008 (summed for each patient) is randomly divided into two equally sized subpopulations to form an estimation set and a validation set. Evaluating out-of-sample using the validation set, a conditional density approximation estimator shows considerable promise in forecasting conditional means, performing best for accuracy of forecasting and among the best four for bias and goodness of fit. The best performing model for bias is linear regression with square-root-transformed dependent variables, whereas a generalized linear model with square-root link function and Poisson distribution performs best in terms of goodness of fit. Commonly used models utilizing a log-link are shown to perform badly relative to other models considered in our comparison.

Functional Capacity and Self-Esteem of People With Cerebral Palsy.

PubMed

Espín-Tello, Sandra Martina; Dickinson, Heather Olivia; Bueno-Lozano, Manuel; Jiménez-Bernadó, María Teresa; Caballero-Navarro, Ana Luisa

We assessed whether functional capacity predicts self-esteem in people with cerebral palsy (CP). We conducted a cross-sectional observational study of 108 people with CP, ages 16-65 yr, who were residents of Spain. Self-esteem was captured using the Rosenberg Self-Esteem Scale (RSES), and functional capacity using the Barthel Index (BI). Sociodemographic characteristics were recorded. The relationship between the RSES score and the BI score was analyzed using linear regression. RSES scores increased significantly as BI scores increased (regression coefficient = 0.047, 95% confidence interval [0.017, 0.078], p = .003). People with a higher level of education, active employment, and independent living arrangements tended to have better functional capacity and higher self-esteem. Greater functional capacity predicted higher self-esteem; this effect is probably partly mediated by education, employment, and living arrangements. Copyright © 2018 by the American Occupational Therapy Association, Inc.

Validation of the Omni Scale of Perceived Exertion in a sample of Spanish-speaking youth from the USA.

PubMed

Suminski, Richard R; Robertson, Robert J; Goss, Fredric L; Olvera, Norma

2008-08-01

Whether the translation of verbal descriptors from English to Spanish affects the validity of the Children's OMNI Scale of Perceived Exertion is not known, so the validity of a Spanish version of the OMNI was examined with 32 boys and 36 girls (9 to 12 years old) for whom Spanish was the primary language. Oxygen consumption, ventilation, respiratory rate, respiratory exchange ratio, heart rate, and ratings of perceived exertion for the overall body (RPE-O) were measured during an incremental treadmill test. All response values displayed significant linear increases across test stages. The linear regression analyses indicated RPE-O values were distributed as positive linear functions of oxygen consumption, ventilation, respiratory rate, respiratory exchange ratio, heart rate, and percent of maximal oxygen consumption. All regression models were statistically significant. The Spanish OMNI Scale is valid for estimating exercise effort during walking and running amongst Hispanic youth whose primary language is Spanish.

Multivariate meta-analysis for non-linear and other multi-parameter associations

PubMed Central

Gasparrini, A; Armstrong, B; Kenward, M G

2012-01-01

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22807043

Modeling of thermal degradation kinetics of the C-glucosyl xanthone mangiferin in an aqueous model solution as a function of pH and temperature and protective effect of honeybush extract matrix.

PubMed

Beelders, Theresa; de Beer, Dalene; Kidd, Martin; Joubert, Elizabeth

2018-01-01

Mangiferin, a C-glucosyl xanthone, abundant in mango and honeybush, is increasingly targeted for its bioactive properties and thus to enhance functional properties of food. The thermal degradation kinetics of mangiferin at pH3, 4, 5, 6 and 7 were each modeled at five temperatures ranging between 60 and 140°C. First-order reaction models were fitted to the data using non-linear regression to determine the reaction rate constant at each pH-temperature combination. The reaction rate constant increased with increasing temperature and pH. Comparison of the reaction rate constants at 100°C revealed an exponential relationship between the reaction rate constant and pH. The data for each pH were also modeled with the Arrhenius equation using non-linear and linear regression to determine the activation energy and pre-exponential factor. Activation energies decreased slightly with increasing pH. Finally, a multi-linear model taking into account both temperature and pH was developed for mangiferin degradation. Sterilization (121°C for 4min) of honeybush extracts dissolved at pH4, 5 and 7 did not cause noticeable degradation of mangiferin, although the multi-linear model predicted 34% degradation at pH7. The extract matrix is postulated to exert a protective effect as changes in potential precursor content could not fully explain the stability of mangiferin. Copyright © 2017 Elsevier Ltd. All rights reserved.

Using Artificial Neural Networks in Educational Research: Some Comparisons with Linear Statistical Models.

ERIC Educational Resources Information Center

Everson, Howard T.; And Others

This paper explores the feasibility of neural computing methods such as artificial neural networks (ANNs) and abductory induction mechanisms (AIM) for use in educational measurement. ANNs and AIMS methods are contrasted with more traditional statistical techniques, such as multiple regression and discriminant function analyses, for making…

A Comparison of Strategies for Estimating Conditional DIF

ERIC Educational Resources Information Center

Moses, Tim; Miao, Jing; Dorans, Neil J.

2010-01-01

In this study, the accuracies of four strategies were compared for estimating conditional differential item functioning (DIF), including raw data, logistic regression, log-linear models, and kernel smoothing. Real data simulations were used to evaluate the estimation strategies across six items, DIF and No DIF situations, and four sample size…

D.b.h./crown diameter relationships in mixed Appalachian hardwood stands

Treesearch

Neil I. Lamson; Neil I. Lamson

1987-01-01

Linear regression formulae for predicting crown diameter as a function of stem diameter are presented for nine species found in 50- to 80-year-old mixed hardwood stands in north-central West Virginia. Generally, crown diameter was closely related to tolerance; more tolerant species had larger crowns.

A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution.

PubMed

Nasari, Masoud M; Szyszkowicz, Mieczysław; Chen, Hong; Crouse, Daniel; Turner, Michelle C; Jerrett, Michael; Pope, C Arden; Hubbell, Bryan; Fann, Neal; Cohen, Aaron; Gapstur, Susan M; Diver, W Ryan; Stieb, David; Forouzanfar, Mohammad H; Kim, Sun-Young; Olives, Casey; Krewski, Daniel; Burnett, Richard T

2016-01-01

The effectiveness of regulatory actions designed to improve air quality is often assessed by predicting changes in public health resulting from their implementation. Risk of premature mortality from long-term exposure to ambient air pollution is the single most important contributor to such assessments and is estimated from observational studies generally assuming a log-linear, no-threshold association between ambient concentrations and death. There has been only limited assessment of this assumption in part because of a lack of methods to estimate the shape of the exposure-response function in very large study populations. In this paper, we propose a new class of variable coefficient risk functions capable of capturing a variety of potentially non-linear associations which are suitable for health impact assessment. We construct the class by defining transformations of concentration as the product of either a linear or log-linear function of concentration multiplied by a logistic weighting function. These risk functions can be estimated using hazard regression survival models with currently available computer software and can accommodate large population-based cohorts which are increasingly being used for this purpose. We illustrate our modeling approach with two large cohort studies of long-term concentrations of ambient air pollution and mortality: the American Cancer Society Cancer Prevention Study II (CPS II) cohort and the Canadian Census Health and Environment Cohort (CanCHEC). We then estimate the number of deaths attributable to changes in fine particulate matter concentrations over the 2000 to 2010 time period in both Canada and the USA using both linear and non-linear hazard function models.

Poor sleep quality predicts decreased cognitive function independently of chronic mountain sickness score in young soldiers with polycythemia stationed in Tibet.

PubMed

Kong, Fan-Yi; Li, Qiang; Liu, Shi-Xiang

2011-01-01

Little is known about the association between poor sleep and cognitive function in people with polycythemia at high altitude. The aim of this study was to survey the sleep quality of individuals with polycythemia at high altitude and determine its association with cognitive abilities. We surveyed 230 soldiers stationed in Tibet (all men; mean age 21-52±4.30 yr) at altitudes ranging from 3658 to 3996 m. All participants were given a blood tests for hemoglobin level and a questionnaire survey of cognitive function. Polycythemia was defined as excessive erythrocytosis (Hb≥21 g/dL in men or ≥19 g/dL in women). Poor sleepers were defined as having a global Pittsburgh Sleep Quality Index score (PSQI)>5. Cognitive abilities were determined by the Chinese revision of the Wechsler Adult Intelligence Scale and the Benton Visual Retention Test. Multiple linear regression analysis was used to determine the association between the PSQI and cognitive function. Logistic regression analysis was performed to determine the independent effect of sleep quality on cognitive function. The global PSQI score of enrolled participants was 8.14±3.79. Seventy-five (32.6%) soldiers were diagnosed with polycythemia. The proportion of poor sleepers was 1.45 times greater in those with polycythemia compared with those without polycythemia [95% (confidence interval) CI 1.82-2.56], and they had a statistically significant lower score for cognitive function. Multiple linear regression analysis showed that the global PSQI score was negatively associated with IQ (β=0.11, 95% CI -0.16 to -0.05) and digit symbol scores (β=0.66, 95% CI -0.86 to -0.44). Poor sleep quality was determined to be an independent predictor of impaired IQ [odds ratio (OR) 1.59, 95% CI 1.30-1.95] and digit symbol score (OR 1.18, 95% CI 1.07-1.31) in logistic regression analysis. The present study showed that for young soldiers with polycythemia at high altitude impaired subjective sleep quality was an independent predictor of decreased cognitive function, especially IQ and verbal short-term memory.

[Comparison of application of Cochran-Armitage trend test and linear regression analysis for rate trend analysis in epidemiology study].

PubMed

Wang, D Z; Wang, C; Shen, C F; Zhang, Y; Zhang, H; Song, G D; Xue, X D; Xu, Z L; Zhang, S; Jiang, G H

2017-05-10

We described the time trend of acute myocardial infarction (AMI) from 1999 to 2013 in Tianjin incidence rate with Cochran-Armitage trend (CAT) test and linear regression analysis, and the results were compared. Based on actual population, CAT test had much stronger statistical power than linear regression analysis for both overall incidence trend and age specific incidence trend (Cochran-Armitage trend P value

[Ultrasonic measurements of fetal thalamus, caudate nucleus and lenticular nucleus in prenatal diagnosis].

PubMed

Yang, Ruiqi; Wang, Fei; Zhang, Jialing; Zhu, Chonglei; Fan, Limei

2015-05-19

To establish the reference values of thalamus, caudate nucleus and lenticular nucleus diameters through fetal thalamic transverse section. A total of 265 fetuses at our hospital were randomly selected from November 2012 to August 2014. And the transverse and length diameters of thalamus, caudate nucleus and lenticular nucleus were measured. SPSS 19.0 statistical software was used to calculate the regression curve of fetal diameter changes and gestational weeks of pregnancy. P < 0.05 was considered as having statistical significance. The linear regression equation of fetal thalamic length diameter and gestational week was: Y = 0.051X+0.201, R = 0.876, linear regression equation of thalamic transverse diameter and fetal gestational week was: Y = 0.031X+0.229, R = 0.817, linear regression equation of fetal head of caudate nucleus length diameter and gestational age was: Y = 0.033X+0.101, R = 0.722, linear regression equation of fetal head of caudate nucleus transverse diameter and gestational week was: R = 0.025 - 0.046, R = 0.711, linear regression equation of fetal lentiform nucleus length diameter and gestational week was: Y = 0.046+0.229, R = 0.765, linear regression equation of fetal lentiform nucleus diameter and gestational week was: Y = 0.025 - 0.05, R = 0.772. Ultrasonic measurement of diameter of fetal thalamus caudate nucleus, and lenticular nucleus through thalamic transverse section is simple and convenient. And measurements increase with fetal gestational weeks and there is linear regression relationship between them.

Local Linear Regression for Data with AR Errors.

PubMed

Li, Runze; Li, Yan

2009-07-01

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

Orthogonal Regression: A Teaching Perspective

ERIC Educational Resources Information Center

Carr, James R.

2012-01-01

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is…

Extraction of object skeletons in multispectral imagery by the orthogonal regression fitting

NASA Astrophysics Data System (ADS)

Palenichka, Roman M.; Zaremba, Marek B.

2003-03-01

Accurate and automatic extraction of skeletal shape of objects of interest from satellite images provides an efficient solution to such image analysis tasks as object detection, object identification, and shape description. The problem of skeletal shape extraction can be effectively solved in three basic steps: intensity clustering (i.e. segmentation) of objects, extraction of a structural graph of the object shape, and refinement of structural graph by the orthogonal regression fitting. The objects of interest are segmented from the background by a clustering transformation of primary features (spectral components) with respect to each pixel. The structural graph is composed of connected skeleton vertices and represents the topology of the skeleton. In the general case, it is a quite rough piecewise-linear representation of object skeletons. The positions of skeleton vertices on the image plane are adjusted by means of the orthogonal regression fitting. It consists of changing positions of existing vertices according to the minimum of the mean orthogonal distances and, eventually, adding new vertices in-between if a given accuracy if not yet satisfied. Vertices of initial piecewise-linear skeletons are extracted by using a multi-scale image relevance function. The relevance function is an image local operator that has local maximums at the centers of the objects of interest.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Practical Session: Simple Linear Regression

NASA Astrophysics Data System (ADS)

Clausel, M.; Grégoire, G.

2014-12-01

Two exercises are proposed to illustrate the simple linear regression. The first one is based on the famous Galton's data set on heredity. We use the lm R command and get coefficients estimates, standard error of the error, R2, residuals …In the second example, devoted to data related to the vapor tension of mercury, we fit a simple linear regression, predict values, and anticipate on multiple linear regression. This pratical session is an excerpt from practical exercises proposed by A. Dalalyan at EPNC (see Exercises 1 and 2 of http://certis.enpc.fr/~dalalyan/Download/TP_ENPC_4.pdf).

Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation

NASA Astrophysics Data System (ADS)

Li, T.; Griffiths, W. D.; Chen, J.

2017-11-01

The Maximum Likelihood method and the Linear Least Squares (LLS) method have been widely used to estimate Weibull parameters for reliability of brittle and metal materials. In the last 30 years, many researchers focused on the bias of Weibull modulus estimation, and some improvements have been achieved, especially in the case of the LLS method. However, there is a shortcoming in these methods for a specific type of data, where the lower tail deviates dramatically from the well-known linear fit in a classic LLS Weibull analysis. This deviation can be commonly found from the measured properties of materials, and previous applications of the LLS method on this kind of dataset present an unreliable linear regression. This deviation was previously thought to be due to physical flaws ( i.e., defects) contained in materials. However, this paper demonstrates that this deviation can also be caused by the linear transformation of the Weibull function, occurring in the traditional LLS method. Accordingly, it may not be appropriate to carry out a Weibull analysis according to the linearized Weibull function, and the Non-linear Least Squares method (Non-LS) is instead recommended for the Weibull modulus estimation of casting properties.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Complexity analysis of spontaneous brain activity in mood disorders: A magnetoencephalography study of bipolar disorder and major depression.

PubMed

Fernández, Alberto; Al-Timemy, Ali H; Ferre, Francisco; Rubio, Gabriel; Escudero, Javier

2018-04-26

The lack of a biomarker for Bipolar Disorder (BD) causes problems in the differential diagnosis with other mood disorders such as major depression (MD), and misdiagnosis frequently occurs. Bearing this in mind, we investigated non-linear magnetoencephalography (MEG) patterns in BD and MD. Lempel-Ziv Complexity (LZC) was used to evaluate the resting-state MEG activity in a cross-sectional sample of 60 subjects, including 20 patients with MD, 16 patients with BD type-I, and 24 control (CON) subjects. Particular attention was paid to the role of age. The results were aggregated by scalp region. Overall, MD patients showed significantly higher LZC scores than BD patients and CONs. Linear regression analyses demonstrated distinct tendencies of complexity progression as a function of age, with BD patients showing a divergent tendency as compared with MD and CON groups. Logistic regressions confirmed such distinct relationship with age, which allowed the classification of diagnostic groups. The patterns of neural complexity in BD and MD showed not only quantitative differences in their non-linear MEG characteristics but also divergent trajectories of progression as a function of age. Moreover, neural complexity patterns in BD patients resembled those previously observed in schizophrenia, thus supporting preceding evidence of common neuropathological processes. Copyright © 2018 Elsevier Inc. All rights reserved.

Prediction of dynamical systems by symbolic regression

NASA Astrophysics Data System (ADS)

Quade, Markus; Abel, Markus; Shafi, Kamran; Niven, Robert K.; Noack, Bernd R.

2016-07-01

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.

Morse Code, Scrabble, and the Alphabet

ERIC Educational Resources Information Center

Richardson, Mary; Gabrosek, John; Reischman, Diann; Curtiss, Phyliss

2004-01-01

In this paper we describe an interactive activity that illustrates simple linear regression. Students collect data and analyze it using simple linear regression techniques taught in an introductory applied statistics course. The activity is extended to illustrate checks for regression assumptions and regression diagnostics taught in an…

Estimation of streamflow, base flow, and nitrate-nitrogen loads in Iowa using multiple linear regression models

USGS Publications Warehouse

Schilling, K.E.; Wolter, C.F.

2005-01-01

Nineteen variables, including precipitation, soils and geology, land use, and basin morphologic characteristics, were evaluated to develop Iowa regression models to predict total streamflow (Q), base flow (Qb), storm flow (Qs) and base flow percentage (%Qb) in gauged and ungauged watersheds in the state. Discharge records from a set of 33 watersheds across the state for the 1980 to 2000 period were separated into Qb and Qs. Multiple linear regression found that 75.5 percent of long term average Q was explained by rainfall, sand content, and row crop percentage variables, whereas 88.5 percent of Qb was explained by these three variables plus permeability and floodplain area variables. Qs was explained by average rainfall and %Qb was a function of row crop percentage, permeability, and basin slope variables. Regional regression models developed for long term average Q and Qb were adapted to annual rainfall and showed good correlation between measured and predicted values. Combining the regression model for Q with an estimate of mean annual nitrate concentration, a map of potential nitrate loads in the state was produced. Results from this study have important implications for understanding geomorphic and land use controls on streamflow and base flow in Iowa watersheds and similar agriculture dominated watersheds in the glaciated Midwest. (JAWRA) (Copyright ?? 2005).

Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology

NASA Astrophysics Data System (ADS)

Kang, Pilsang; Koo, Changhoi; Roh, Hokyu

2017-11-01

Since simple linear regression theory was established at the beginning of the 1900s, it has been used in a variety of fields. Unfortunately, it cannot be used directly for calibration. In practical calibrations, the observed measurements (the inputs) are subject to errors, and hence they vary, thus violating the assumption that the inputs are fixed. Therefore, in the case of calibration, the regression line fitted using the method of least squares is not consistent with the statistical properties of simple linear regression as already established based on this assumption. To resolve this problem, "classical regression" and "inverse regression" have been proposed. However, they do not completely resolve the problem. As a fundamental solution, we introduce "reversed inverse regression" along with a new methodology for deriving its statistical properties. In this study, the statistical properties of this regression are derived using the "error propagation rule" and the "method of simultaneous error equations" and are compared with those of the existing regression approaches. The accuracy of the statistical properties thus derived is investigated in a simulation study. We conclude that the newly proposed regression and methodology constitute the complete regression approach for univariate linear calibrations.

Does physical exposure throughout working life influence chair-rise performance in midlife? A retrospective cohort study of associations between work and physical function in Denmark.

PubMed

Møller, Anne; Reventlow, Susanne; Hansen, Åse Marie; Andersen, Lars L; Siersma, Volkert; Lund, Rikke; Avlund, Kirsten; Andersen, Johan Hviid; Mortensen, Ole Steen

2015-11-04

Our aim was to study associations between physical exposures throughout working life and physical function measured as chair-rise performance in midlife. The Copenhagen Aging and Midlife Biobank (CAMB) provided data about employment and measures of physical function. Individual job histories were assigned exposures from a job exposure matrix. Exposures were standardised to ton-years (lifting 1000 kg each day in 1 year), stand-years (standing/walking for 6 h each day in 1 year) and kneel-years (kneeling for 1 h each day in 1 year). The associations between exposure-years and chair-rise performance (number of chair-rises in 30 s) were analysed in multivariate linear and non-linear regression models adjusted for covariates. Mean age among the 5095 participants was 59 years in both genders, and, on average, men achieved 21.58 (SD=5.60) and women 20.38 (SD=5.33) chair-rises in 30 s. Physical exposures were associated with poorer chair-rise performance in both men and women, however, only associations between lifting and standing/walking and chair-rise remained statistically significant among men in the final model. Spline regression analyses showed non-linear associations and confirmed the findings. Higher physical exposure throughout working life is associated with slightly poorer chair-rise performance. The associations between exposure and outcome were non-linear. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

A comparison of methods for the analysis of binomial clustered outcomes in behavioral research.

PubMed

Ferrari, Alberto; Comelli, Mario

2016-12-01

In behavioral research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This clustered binary data are usually non-normally distributed, which can distort inference if the usual general linear model is applied and sample size is small. A number of more advanced methods is available, but they are often technically challenging and a comparative assessment of their performances in behavioral setups has not been performed. We studied the performances of some methods applicable to the analysis of proportions; namely linear regression, Poisson regression, beta-binomial regression and Generalized Linear Mixed Models (GLMMs). We report on a simulation study evaluating power and Type I error rate of these models in hypothetical scenarios met by behavioral researchers; plus, we describe results from the application of these methods on data from real experiments. Our results show that, while GLMMs are powerful instruments for the analysis of clustered binary outcomes, beta-binomial regression can outperform them in a range of scenarios. Linear regression gave results consistent with the nominal level of significance, but was overall less powerful. Poisson regression, instead, mostly led to anticonservative inference. GLMMs and beta-binomial regression are generally more powerful than linear regression; yet linear regression is robust to model misspecification in some conditions, whereas Poisson regression suffers heavily from violations of the assumptions when used to model proportion data. We conclude providing directions to behavioral scientists dealing with clustered binary data and small sample sizes. Copyright © 2016 Elsevier B.V. All rights reserved.

OPLS statistical model versus linear regression to assess sonographic predictors of stroke prognosis.

PubMed

Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi

2012-01-01

The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.

Risk prediction for myocardial infarction via generalized functional regression models.

PubMed

Ieva, Francesca; Paganoni, Anna M

2016-08-01

In this paper, we propose a generalized functional linear regression model for a binary outcome indicating the presence/absence of a cardiac disease with multivariate functional data among the relevant predictors. In particular, the motivating aim is the analysis of electrocardiographic traces of patients whose pre-hospital electrocardiogram (ECG) has been sent to 118 Dispatch Center of Milan (the Italian free-toll number for emergencies) by life support personnel of the basic rescue units. The statistical analysis starts with a preprocessing of ECGs treated as multivariate functional data. The signals are reconstructed from noisy observations. The biological variability is then removed by a nonlinear registration procedure based on landmarks. Thus, in order to perform a data-driven dimensional reduction, a multivariate functional principal component analysis is carried out on the variance-covariance matrix of the reconstructed and registered ECGs and their first derivatives. We use the scores of the Principal Components decomposition as covariates in a generalized linear model to predict the presence of the disease in a new patient. Hence, a new semi-automatic diagnostic procedure is proposed to estimate the risk of infarction (in the case of interest, the probability of being affected by Left Bundle Brunch Block). The performance of this classification method is evaluated and compared with other methods proposed in literature. Finally, the robustness of the procedure is checked via leave-j-out techniques. © The Author(s) 2013.

Interpretation of commonly used statistical regression models.

PubMed

Kasza, Jessica; Wolfe, Rory

2014-01-01

A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.

Testing the Dose–Response Specification in Epidemiology: Public Health and Policy Consequences for Lead

PubMed Central

Rothenberg, Stephen J.; Rothenberg, Jesse C.

2005-01-01

Statistical evaluation of the dose–response function in lead epidemiology is rarely attempted. Economic evaluation of health benefits of lead reduction usually assumes a linear dose–response function, regardless of the outcome measure used. We reanalyzed a previously published study, an international pooled data set combining data from seven prospective lead studies examining contemporaneous blood lead effect on IQ (intelligence quotient) of 7-year-old children (n = 1,333). We constructed alternative linear multiple regression models with linear blood lead terms (linear–linear dose response) and natural-log–transformed blood lead terms (log-linear dose response). We tested the two lead specifications for nonlinearity in the models, compared the two lead specifications for significantly better fit to the data, and examined the effects of possible residual confounding on the functional form of the dose–response relationship. We found that a log-linear lead–IQ relationship was a significantly better fit than was a linear–linear relationship for IQ (p = 0.009), with little evidence of residual confounding of included model variables. We substituted the log-linear lead–IQ effect in a previously published health benefits model and found that the economic savings due to U.S. population lead decrease between 1976 and 1999 (from 17.1 μg/dL to 2.0 μg/dL) was 2.2 times ($319 billion) that calculated using a linear–linear dose–response function ($149 billion). The Centers for Disease Control and Prevention action limit of 10 μg/dL for children fails to protect against most damage and economic cost attributable to lead exposure. PMID:16140626

A new graphic plot analysis for determination of neuroreceptor binding in positron emission tomography studies.

PubMed

Ito, Hiroshi; Yokoi, Takashi; Ikoma, Yoko; Shidahara, Miho; Seki, Chie; Naganawa, Mika; Takahashi, Hidehiko; Takano, Harumasa; Kimura, Yuichi; Ichise, Masanori; Suhara, Tetsuya

2010-01-01

In positron emission tomography (PET) studies with radioligands for neuroreceptors, tracer kinetics have been described by the standard two-tissue compartment model that includes the compartments of nondisplaceable binding and specific binding to receptors. In the present study, we have developed a new graphic plot analysis to determine the total distribution volume (V(T)) and nondisplaceable distribution volume (V(ND)) independently, and therefore the binding potential (BP(ND)). In this plot, Y(t) is the ratio of brain tissue activity to time-integrated arterial input function, and X(t) is the ratio of time-integrated brain tissue activity to time-integrated arterial input function. The x-intercept of linear regression of the plots for early phase represents V(ND), and the x-intercept of linear regression of the plots for delayed phase after the equilibrium time represents V(T). BP(ND) can be calculated by BP(ND)=V(T)/V(ND)-1. Dynamic PET scanning with measurement of arterial input function was performed on six healthy men after intravenous rapid bolus injection of [(11)C]FLB457. The plot yielded a curve in regions with specific binding while it yielded a straight line through all plot data in regions with no specific binding. V(ND), V(T), and BP(ND) values calculated by the present method were in good agreement with those by conventional non-linear least-squares fitting procedure. This method can be used to distinguish graphically whether the radioligand binding includes specific binding or not.

Use of probabilistic weights to enhance linear regression myoelectric control

NASA Astrophysics Data System (ADS)

Smith, Lauren H.; Kuiken, Todd A.; Hargrove, Levi J.

2015-12-01

Objective. Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Approach. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts’ law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Main results. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p < 0.05) by preventing extraneous movement at additional DOFs. Similar results were seen in experiments with two transradial amputees. Though goodness-of-fit evaluations suggested that the EMG feature distributions showed some deviations from the Gaussian, equal-covariance assumptions used in this experiment, the assumptions were sufficiently met to provide improved performance compared to linear regression control. Significance. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

A Method of Calculating Functional Independence Measure at Discharge from Functional Independence Measure Effectiveness Predicted by Multiple Regression Analysis Has a High Degree of Predictive Accuracy.

PubMed

Tokunaga, Makoto; Watanabe, Susumu; Sonoda, Shigeru

2017-09-01

Multiple linear regression analysis is often used to predict the outcome of stroke rehabilitation. However, the predictive accuracy may not be satisfactory. The objective of this study was to elucidate the predictive accuracy of a method of calculating motor Functional Independence Measure (mFIM) at discharge from mFIM effectiveness predicted by multiple regression analysis. The subjects were 505 patients with stroke who were hospitalized in a convalescent rehabilitation hospital. The formula "mFIM at discharge = mFIM effectiveness × (91 points - mFIM at admission) + mFIM at admission" was used. By including the predicted mFIM effectiveness obtained through multiple regression analysis in this formula, we obtained the predicted mFIM at discharge (A). We also used multiple regression analysis to directly predict mFIM at discharge (B). The correlation between the predicted and the measured values of mFIM at discharge was compared between A and B. The correlation coefficients were .916 for A and .878 for B. Calculating mFIM at discharge from mFIM effectiveness predicted by multiple regression analysis had a higher degree of predictive accuracy of mFIM at discharge than that directly predicted. Copyright © 2017 National Stroke Association. Published by Elsevier Inc. All rights reserved.

Health related quality of life in parents of six to eight year old children with Down syndrome.

PubMed

Marchal, Jan Pieter; Maurice-Stam, Heleen; Hatzmann, Janneke; van Trotsenburg, A S Paul; Grootenhuis, Martha A

2013-11-01

Raising a child with Down syndrome (DS) has been found to be associated with lowered health related quality of life (HRQoL) in the domains cognitive functioning, social functioning, daily activities and vitality. We aimed to explore which socio-demographics, child functioning and psychosocial variables were related to these HRQoL domains in parents of children with DS. Parents of 98 children with DS completed the TNO-AZL adult quality of life questionnaire (TAAQOL) and a questionnaire assessing socio-demographic, child functioning and psychosocial predictors. Using multiple linear regression analyses for each category of predictors, we selected relevant predictors for the final models. The final multiple linear regression models revealed that cognitive functioning was best predicted by the sleep of the child (β=.29, p<.01) and by the parent having given up a hobby (β=-.29, p<.01), social functioning by the quality of the partner relation (β=.34, p<.001), daily activities by the parent having to care for an ill friend or family member (β=-.31, p<.01), and vitality by the parent having enough personal time (β=.32, p<.01). Overall, psychosocial variables rather than socio-demographics or child functioning showed most consistent and powerful relations to the HRQoL domains of cognitive functioning, social functioning, daily activities and vitality. These psychosocial variables mainly related to social support and time pressure. Systematic screening of parents to detect problems timely, and interventions targeting the supportive network and the demands in time are recommended. Copyright © 2013 Elsevier Ltd. All rights reserved.

Simplified large African carnivore density estimators from track indices.

PubMed

Winterbach, Christiaan W; Ferreira, Sam M; Funston, Paul J; Somers, Michael J

2016-01-01

The range, population size and trend of large carnivores are important parameters to assess their status globally and to plan conservation strategies. One can use linear models to assess population size and trends of large carnivores from track-based surveys on suitable substrates. The conventional approach of a linear model with intercept may not intercept at zero, but may fit the data better than linear model through the origin. We assess whether a linear regression through the origin is more appropriate than a linear regression with intercept to model large African carnivore densities and track indices. We did simple linear regression with intercept analysis and simple linear regression through the origin and used the confidence interval for ß in the linear model y  =  αx  + ß, Standard Error of Estimate, Mean Squares Residual and Akaike Information Criteria to evaluate the models. The Lion on Clay and Low Density on Sand models with intercept were not significant ( P  > 0.05). The other four models with intercept and the six models thorough origin were all significant ( P  < 0.05). The models using linear regression with intercept all included zero in the confidence interval for ß and the null hypothesis that ß = 0 could not be rejected. All models showed that the linear model through the origin provided a better fit than the linear model with intercept, as indicated by the Standard Error of Estimate and Mean Square Residuals. Akaike Information Criteria showed that linear models through the origin were better and that none of the linear models with intercept had substantial support. Our results showed that linear regression through the origin is justified over the more typical linear regression with intercept for all models we tested. A general model can be used to estimate large carnivore densities from track densities across species and study areas. The formula observed track density = 3.26 × carnivore density can be used to estimate densities of large African carnivores using track counts on sandy substrates in areas where carnivore densities are 0.27 carnivores/100 km 2 or higher. To improve the current models, we need independent data to validate the models and data to test for non-linear relationship between track indices and true density at low densities.

[From clinical judgment to linear regression model.

PubMed

Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O

2013-01-01

When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models.

PubMed

Bignardi, A B; El Faro, L; Cardoso, V L; Machado, P F; Albuquerque, L G

2009-09-01

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Early post-stroke cognition in stroke rehabilitation patients predicts functional outcome at 13 months.

PubMed

Wagle, Jørgen; Farner, Lasse; Flekkøy, Kjell; Bruun Wyller, Torgeir; Sandvik, Leiv; Fure, Brynjar; Stensrød, Brynhild; Engedal, Knut

2011-01-01

To identify prognostic factors associated with functional outcome at 13 months in a sample of stroke rehabilitation patients. Specifically, we hypothesized that cognitive functioning early after stroke would predict long-term functional outcome independently of other factors. 163 stroke rehabilitation patients underwent a structured neuropsychological examination 2-3 weeks after hospital admittance, and their functional status was subsequently evaluated 13 months later with the modified Rankin Scale (mRS) as outcome measure. Three predictive models were built using linear regression analyses: a biological model (sociodemographics, apolipoprotein E genotype, prestroke vascular factors, lesion characteristics and neurological stroke-related impairment); a functional model (pre- and early post-stroke cognitive functioning, personal and instrumental activities of daily living, ADL, and depressive symptoms), and a combined model (including significant variables, with p value <0.05, from the biological and functional models). A combined model of 4 variables best predicted long-term functional outcome with explained variance of 49%: neurological impairment (National Institute of Health Stroke Scale; β = 0.402, p < 0.001), age (β = 0.233, p = 0.001), post-stroke cognitive functioning (Repeatable Battery of Neuropsychological Status, RBANS; β = -0.248, p = 0.001) and prestroke personal ADL (Barthel Index; β = -0.217, p = 0.002). Further linear regression analyses of which RBANS indexes and subtests best predicted long-term functional outcome showed that Coding (β = -0.484, p < 0.001) and Figure Copy (β = -0.233, p = 0.002) raw scores at baseline explained 42% of the variance in mRS scores at follow-up. Early post-stroke cognitive functioning as measured by the RBANS is a significant and independent predictor of long-term functional post-stroke outcome. Copyright © 2011 S. Karger AG, Basel.

Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian Province, southeast China.

PubMed

Hao, Xu; Yujun, Sun; Xinjie, Wang; Jin, Wang; Yao, Fu

2015-01-01

A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike's information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R2). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.

Comparing and Contrasting Neural Net Solutions to Classical Statistical Solutions.

ERIC Educational Resources Information Center

Van Nelson, C.; Neff, Kathryn J.

Data from two studies in which subjects were classified as successful or unsuccessful were analyzed using neural net technology after being analyzed with a linear regression function. Data were obtained from admission records of 201 students admitted to undergraduate and 285 students admitted to graduate programs. Data included grade point…

Bicycles, Birds, Bats and Balloons: New Applications for Algebra Classes.

ERIC Educational Resources Information Center

Yoshiwara, Bruce; Yoshiwara, Kathy

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…

Accumulation of nucleopolyhedrosis virus of the European pine sawfly (Hymenoptera: Diprionidae) as a function of larval weight

Treesearch

M.A. Mohamed; H.C. Coppel; J.D. Podgwaite; W.D. Rollinson

1983-01-01

Disease-free larvae of Neodiprion sertifer (Geoffroy) treated with its nucleopolyhedrosis virus in the field and under laboratory conditions showed a high correlation between virus accumulation and body weight. Simple linear regression models were found to fit viral accumulation versus body weight under either circumstance.

A Linear Dynamical Systems Approach to Streamflow Reconstruction Reveals History of Regime Shifts in Northern Thailand

NASA Astrophysics Data System (ADS)

Nguyen, Hung T. T.; Galelli, Stefano

2018-03-01

Catchment dynamics is not often modeled in streamflow reconstruction studies; yet, the streamflow generation process depends on both catchment state and climatic inputs. To explicitly account for this interaction, we contribute a linear dynamic model, in which streamflow is a function of both catchment state (i.e., wet/dry) and paleoclimatic proxies. The model is learned using a novel variant of the Expectation-Maximization algorithm, and it is used with a paleo drought record—the Monsoon Asia Drought Atlas—to reconstruct 406 years of streamflow for the Ping River (northern Thailand). Results for the instrumental period show that the dynamic model has higher accuracy than conventional linear regression; all performance scores improve by 45-497%. Furthermore, the reconstructed trajectory of the state variable provides valuable insights about the catchment history—e.g., regime-like behavior—thereby complementing the information contained in the reconstructed streamflow time series. The proposed technique can replace linear regression, since it only requires information on streamflow and climatic proxies (e.g., tree-rings, drought indices); furthermore, it is capable of readily generating stochastic streamflow replicates. With a marginal increase in computational requirements, the dynamic model brings more desirable features and value to streamflow reconstructions.

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.

PubMed

Wiedermann, Wolfgang; Artner, Richard; von Eye, Alexander

2017-01-01

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.

Variable Selection with Prior Information for Generalized Linear Models via the Prior LASSO Method.

PubMed

Jiang, Yuan; He, Yunxiao; Zhang, Heping

LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the Least Angle Regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real data set from a genome-wide association study.

Effects of measurement errors on psychometric measurements in ergonomics studies: Implications for correlations, ANOVA, linear regression, factor analysis, and linear discriminant analysis.

PubMed

Liu, Yan; Salvendy, Gavriel

2009-05-01

This paper aims to demonstrate the effects of measurement errors on psychometric measurements in ergonomics studies. A variety of sources can cause random measurement errors in ergonomics studies and these errors can distort virtually every statistic computed and lead investigators to erroneous conclusions. The effects of measurement errors on five most widely used statistical analysis tools have been discussed and illustrated: correlation; ANOVA; linear regression; factor analysis; linear discriminant analysis. It has been shown that measurement errors can greatly attenuate correlations between variables, reduce statistical power of ANOVA, distort (overestimate, underestimate or even change the sign of) regression coefficients, underrate the explanation contributions of the most important factors in factor analysis and depreciate the significance of discriminant function and discrimination abilities of individual variables in discrimination analysis. The discussions will be restricted to subjective scales and survey methods and their reliability estimates. Other methods applied in ergonomics research, such as physical and electrophysiological measurements and chemical and biomedical analysis methods, also have issues of measurement errors, but they are beyond the scope of this paper. As there has been increasing interest in the development and testing of theories in ergonomics research, it has become very important for ergonomics researchers to understand the effects of measurement errors on their experiment results, which the authors believe is very critical to research progress in theory development and cumulative knowledge in the ergonomics field.

Explicit criteria for prioritization of cataract surgery

PubMed Central

Ma Quintana, José; Escobar, Antonio; Bilbao, Amaia

2006-01-01

Background Consensus techniques have been used previously to create explicit criteria to prioritize cataract extraction; however, the appropriateness of the intervention was not included explicitly in previous studies. We developed a prioritization tool for cataract extraction according to the RAND method. Methods Criteria were developed using a modified Delphi panel judgment process. A panel of 11 ophthalmologists was assembled. Ratings were analyzed regarding the level of agreement among panelists. We studied the effect of all variables on the final panel score using general linear and logistic regression models. Priority scoring systems were developed by means of optimal scaling and general linear models. The explicit criteria developed were summarized by means of regression tree analysis. Results Eight variables were considered to create the indications. Of the 310 indications that the panel evaluated, 22.6% were considered high priority, 52.3% intermediate priority, and 25.2% low priority. Agreement was reached for 31.9% of the indications and disagreement for 0.3%. Logistic regression and general linear models showed that the preoperative visual acuity of the cataractous eye, visual function, and anticipated visual acuity postoperatively were the most influential variables. Alternative and simple scoring systems were obtained by optimal scaling and general linear models where the previous variables were also the most important. The decision tree also shows the importance of the previous variables and the appropriateness of the intervention. Conclusion Our results showed acceptable validity as an evaluation and management tool for prioritizing cataract extraction. It also provides easy algorithms for use in clinical practice. PMID:16512893

The effect of machine learning regression algorithms and sample size on individualized behavioral prediction with functional connectivity features.

PubMed

Cui, Zaixu; Gong, Gaolang

2018-06-02

Individualized behavioral/cognitive prediction using machine learning (ML) regression approaches is becoming increasingly applied. The specific ML regression algorithm and sample size are two key factors that non-trivially influence prediction accuracies. However, the effects of the ML regression algorithm and sample size on individualized behavioral/cognitive prediction performance have not been comprehensively assessed. To address this issue, the present study included six commonly used ML regression algorithms: ordinary least squares (OLS) regression, least absolute shrinkage and selection operator (LASSO) regression, ridge regression, elastic-net regression, linear support vector regression (LSVR), and relevance vector regression (RVR), to perform specific behavioral/cognitive predictions based on different sample sizes. Specifically, the publicly available resting-state functional MRI (rs-fMRI) dataset from the Human Connectome Project (HCP) was used, and whole-brain resting-state functional connectivity (rsFC) or rsFC strength (rsFCS) were extracted as prediction features. Twenty-five sample sizes (ranged from 20 to 700) were studied by sub-sampling from the entire HCP cohort. The analyses showed that rsFC-based LASSO regression performed remarkably worse than the other algorithms, and rsFCS-based OLS regression performed markedly worse than the other algorithms. Regardless of the algorithm and feature type, both the prediction accuracy and its stability exponentially increased with increasing sample size. The specific patterns of the observed algorithm and sample size effects were well replicated in the prediction using re-testing fMRI data, data processed by different imaging preprocessing schemes, and different behavioral/cognitive scores, thus indicating excellent robustness/generalization of the effects. The current findings provide critical insight into how the selected ML regression algorithm and sample size influence individualized predictions of behavior/cognition and offer important guidance for choosing the ML regression algorithm or sample size in relevant investigations. Copyright © 2018 Elsevier Inc. All rights reserved.

Linearity versus Nonlinearity of Offspring-Parent Regression: An Experimental Study of Drosophila Melanogaster

PubMed Central

Gimelfarb, A.; Willis, J. H.

1994-01-01

An experiment was conducted to investigate the offspring-parent regression for three quantitative traits (weight, abdominal bristles and wing length) in Drosophila melanogaster. Linear and polynomial models were fitted for the regressions of a character in offspring on both parents. It is demonstrated that responses by the characters to selection predicted by the nonlinear regressions may differ substantially from those predicted by the linear regressions. This is true even, and especially, if selection is weak. The realized heritability for a character under selection is shown to be determined not only by the offspring-parent regression but also by the distribution of the character and by the form and strength of selection. PMID:7828818

Linear regression analysis for comparing two measurers or methods of measurement: but which regression?

PubMed

Ludbrook, John

2010-07-01

1. There are two reasons for wanting to compare measurers or methods of measurement. One is to calibrate one method or measurer against another; the other is to detect bias. Fixed bias is present when one method gives higher (or lower) values across the whole range of measurement. Proportional bias is present when one method gives values that diverge progressively from those of the other. 2. Linear regression analysis is a popular method for comparing methods of measurement, but the familiar ordinary least squares (OLS) method is rarely acceptable. The OLS method requires that the x values are fixed by the design of the study, whereas it is usual that both y and x values are free to vary and are subject to error. In this case, special regression techniques must be used. 3. Clinical chemists favour techniques such as major axis regression ('Deming's method'), the Passing-Bablok method or the bivariate least median squares method. Other disciplines, such as allometry, astronomy, biology, econometrics, fisheries research, genetics, geology, physics and sports science, have their own preferences. 4. Many Monte Carlo simulations have been performed to try to decide which technique is best, but the results are almost uninterpretable. 5. I suggest that pharmacologists and physiologists should use ordinary least products regression analysis (geometric mean regression, reduced major axis regression): it is versatile, can be used for calibration or to detect bias and can be executed by hand-held calculator or by using the loss function in popular, general-purpose, statistical software.

Optimizing methods for linking cinematic features to fMRI data.

PubMed

Kauttonen, Janne; Hlushchuk, Yevhen; Tikka, Pia

2015-04-15

One of the challenges of naturalistic neurosciences using movie-viewing experiments is how to interpret observed brain activations in relation to the multiplicity of time-locked stimulus features. As previous studies have shown less inter-subject synchronization across viewers of random video footage than story-driven films, new methods need to be developed for analysis of less story-driven contents. To optimize the linkage between our fMRI data collected during viewing of a deliberately non-narrative silent film 'At Land' by Maya Deren (1944) and its annotated content, we combined the method of elastic-net regularization with the model-driven linear regression and the well-established data-driven independent component analysis (ICA) and inter-subject correlation (ISC) methods. In the linear regression analysis, both IC and region-of-interest (ROI) time-series were fitted with time-series of a total of 36 binary-valued and one real-valued tactile annotation of film features. The elastic-net regularization and cross-validation were applied in the ordinary least-squares linear regression in order to avoid over-fitting due to the multicollinearity of regressors, the results were compared against both the partial least-squares (PLS) regression and the un-regularized full-model regression. Non-parametric permutation testing scheme was applied to evaluate the statistical significance of regression. We found statistically significant correlation between the annotation model and 9 ICs out of 40 ICs. Regression analysis was also repeated for a large set of cubic ROIs covering the grey matter. Both IC- and ROI-based regression analyses revealed activations in parietal and occipital regions, with additional smaller clusters in the frontal lobe. Furthermore, we found elastic-net based regression more sensitive than PLS and un-regularized regression since it detected a larger number of significant ICs and ROIs. Along with the ISC ranking methods, our regression analysis proved a feasible method for ordering the ICs based on their functional relevance to the annotated cinematic features. The novelty of our method is - in comparison to the hypothesis-driven manual pre-selection and observation of some individual regressors biased by choice - in applying data-driven approach to all content features simultaneously. We found especially the combination of regularized regression and ICA useful when analyzing fMRI data obtained using non-narrative movie stimulus with a large set of complex and correlated features. Copyright © 2015. Published by Elsevier Inc.

Predonation Volume of Future Remnant Cortical Kidney Helps Predict Postdonation Renal Function in Live Kidney Donors.

PubMed

Fananapazir, Ghaneh; Benzl, Robert; Corwin, Michael T; Chen, Ling-Xin; Sageshima, Junichiro; Stewart, Susan L; Troppmann, Christoph

2018-07-01

Purpose To determine whether the predonation computed tomography (CT)-based volume of the future remnant kidney is predictive of postdonation renal function in living kidney donors. Materials and Methods This institutional review board-approved, retrospective, HIPAA-compliant study included 126 live kidney donors who had undergone predonation renal CT between January 2007 and December 2014 as well as 2-year postdonation measurement of estimated glomerular filtration rate (eGFR). The whole kidney volume and cortical volume of the future remnant kidney were measured and standardized for body surface area (BSA). Bivariate linear associations between the ratios of whole kidney volume to BSA and cortical volume to BSA were obtained. A linear regression model for 2-year postdonation eGFR that incorporated donor age, sex, and either whole kidney volume-to-BSA ratio or cortical volume-to-BSA ratio was created, and the coefficient of determination (R 2 ) for the model was calculated. Factors not statistically additive in assessing 2-year eGFR were removed by using backward elimination, and the coefficient of determination for this parsimonious model was calculated. Results Correlation was slightly better for cortical volume-to-BSA ratio than for whole kidney volume-to-BSA ratio (r = 0.48 vs r = 0.44, respectively). The linear regression model incorporating all donor factors had an R 2 of 0.66. The only factors that were significantly additive to the equation were cortical volume-to-BSA ratio and predonation eGFR (P = .01 and P < .01, respectively), and the final parsimonious linear regression model incorporating these two variables explained almost the same amount of variance (R 2 = 0.65) as did the full model. Conclusion The cortical volume of the future remnant kidney helped predict postdonation eGFR at 2 years. The cortical volume-to-BSA ratio should thus be considered for addition as an important variable to living kidney donor evaluation and selection guidelines. © RSNA, 2018.

Olfaction Is Related to Motor Function in Older Adults.

PubMed

Tian, Qu; Resnick, Susan M; Studenski, Stephanie A

2017-08-01

Among older adults, both olfaction and motor function predict future cognitive decline and dementia, suggesting potential shared causal pathways. However, it is not known whether olfactory and motor function are independently related in late life. We assessed cross-sectional associations of olfaction with motor and cognitive function, using concurrent data on olfactory function, mobility, balance, fine motor function, manual dexterity, and cognition in 163 Baltimore Longitudinal Study of Aging participants aged 60 and older without common neurological diseases (n = 114 with available cognitive data). Using multiple linear regression, we adjusted for age, sex, race, smoking history, height, and weight for mobility and balance, and education for cognition. We used multiple linear regression to test whether olfaction-motor associations were independent of cognition and depressive symptoms. Olfactory scores were significantly associated with mobility (usual gait speed, rapid gait speed, 400-m walk time, and Health ABC Physical Performance Battery score), balance, fine motor function, and manual dexterity (all p < .05). In those with available cognitive data, additional adjustment for depressive symptoms, verbal memory, or visuoperceptual speed demonstrated especially strong independent relationships with challenging motor tasks such as 400-m walk and nondominant hand manual dexterity (p < .005). This study demonstrates for the first time that, in older adults, olfactory function is associated with mobility, balance, fine motor function, and manual dexterity, and independent of cognitive function, with challenging upper and lower extremity motor function tasks. Longitudinal studies are needed to determine if olfactory performance predicts future mobility and functional decline. Published by Oxford University Press on behalf of The Gerontological Society of America 2016. This work is written by (a) US Government employee(s) and is in the public domain in the US.

Unitary Response Regression Models

ERIC Educational Resources Information Center

Lipovetsky, S.

2007-01-01

The dependent variable in a regular linear regression is a numerical variable, and in a logistic regression it is a binary or categorical variable. In these models the dependent variable has varying values. However, there are problems yielding an identity output of a constant value which can also be modelled in a linear or logistic regression with…

An Expert System for the Evaluation of Cost Models

DTIC Science & Technology

1990-09-01

contrast to the condition of equal error variance, called homoscedasticity. (Reference: Applied Linear Regression Models by John Neter - page 423...normal. (Reference: Applied Linear Regression Models by John Neter - page 125) Click Here to continue -> Autocorrelation Click Here for the index - Index...over time. Error terms correlated over time are said to be autocorrelated or serially correlated. (REFERENCE: Applied Linear Regression Models by John

Evaluation of confidence intervals for a steady-state leaky aquifer model

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

1999-01-01

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. and Cooley, R.L., Water Resources Research, 1987, 23(7), 1237-1250] was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle.

PubMed

Boligon, A A; Baldi, F; Mercadante, M E Z; Lobo, R B; Pereira, R J; Albuquerque, L G

2011-06-28

We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.

Compound Identification Using Penalized Linear Regression on Metabolomics

PubMed Central

Liu, Ruiqi; Wu, Dongfeng; Zhang, Xiang; Kim, Seongho

2014-01-01

Compound identification is often achieved by matching the experimental mass spectra to the mass spectra stored in a reference library based on mass spectral similarity. Because the number of compounds in the reference library is much larger than the range of mass-to-charge ratio (m/z) values so that the data become high dimensional data suffering from singularity. For this reason, penalized linear regressions such as ridge regression and the lasso are used instead of the ordinary least squares regression. Furthermore, two-step approaches using the dot product and Pearson’s correlation along with the penalized linear regression are proposed in this study. PMID:27212894

HT-FRTC: a fast radiative transfer code using kernel regression

NASA Astrophysics Data System (ADS)

Thelen, Jean-Claude; Havemann, Stephan; Lewis, Warren

2016-09-01

The HT-FRTC is a principal component based fast radiative transfer code that can be used across the electromagnetic spectrum from the microwave through to the ultraviolet to calculate transmittance, radiance and flux spectra. The principal components cover the spectrum at a very high spectral resolution, which allows very fast line-by-line, hyperspectral and broadband simulations for satellite-based, airborne and ground-based sensors. The principal components are derived during a code training phase from line-by-line simulations for a diverse set of atmosphere and surface conditions. The derived principal components are sensor independent, i.e. no extra training is required to include additional sensors. During the training phase we also derive the predictors which are required by the fast radiative transfer code to determine the principal component scores from the monochromatic radiances (or fluxes, transmittances). These predictors are calculated for each training profile at a small number of frequencies, which are selected by a k-means cluster algorithm during the training phase. Until recently the predictors were calculated using a linear regression. However, during a recent rewrite of the code the linear regression was replaced by a Gaussian Process (GP) regression which resulted in a significant increase in accuracy when compared to the linear regression. The HT-FRTC has been trained with a large variety of gases, surface properties and scatterers. Rayleigh scattering as well as scattering by frozen/liquid clouds, hydrometeors and aerosols have all been included. The scattering phase function can be fully accounted for by an integrated line-by-line version of the Edwards-Slingo spherical harmonics radiation code or approximately by a modification to the extinction (Chou scaling).

Relationship between rice yield and climate variables in southwest Nigeria using multiple linear regression and support vector machine analysis

NASA Astrophysics Data System (ADS)

Oguntunde, Philip G.; Lischeid, Gunnar; Dietrich, Ottfried

2018-03-01

This study examines the variations of climate variables and rice yield and quantifies the relationships among them using multiple linear regression, principal component analysis, and support vector machine (SVM) analysis in southwest Nigeria. The climate and yield data used was for a period of 36 years between 1980 and 2015. Similar to the observed decrease ( P < 0.001) in rice yield, pan evaporation, solar radiation, and wind speed declined significantly. Eight principal components exhibited an eigenvalue > 1 and explained 83.1% of the total variance of predictor variables. The SVM regression function using the scores of the first principal component explained about 75% of the variance in rice yield data and linear regression about 64%. SVM regression between annual solar radiation values and yield explained 67% of the variance. Only the first component of the principal component analysis (PCA) exhibited a clear long-term trend and sometimes short-term variance similar to that of rice yield. Short-term fluctuations of the scores of the PC1 are closely coupled to those of rice yield during the 1986-1993 and the 2006-2013 periods thereby revealing the inter-annual sensitivity of rice production to climate variability. Solar radiation stands out as the climate variable of highest influence on rice yield, and the influence was especially strong during monsoon and post-monsoon periods, which correspond to the vegetative, booting, flowering, and grain filling stages in the study area. The outcome is expected to provide more in-depth regional-specific climate-rice linkage for screening of better cultivars that can positively respond to future climate fluctuations as well as providing information that may help optimized planting dates for improved radiation use efficiency in the study area.

Control Variate Selection for Multiresponse Simulation.

DTIC Science & Technology

1987-05-01

M. H. Knuter, Applied Linear Regression Mfodels, Richard D. Erwin, Inc., Homewood, Illinois, 1983. Neuts, Marcel F., Probability, Allyn and Bacon...1982. Neter, J., V. Wasserman, and M. H. Knuter, Applied Linear Regression .fodels, Richard D. Erwin, Inc., Homewood, Illinois, 1983. Neuts, Marcel F...Aspects of J%,ultivariate Statistical Theory, John Wiley and Sons, New York, New York, 1982. dY Neter, J., W. Wasserman, and M. H. Knuter, Applied Linear Regression Mfodels

An Investigation of the Fit of Linear Regression Models to Data from an SAT[R] Validity Study. Research Report 2011-3

ERIC Educational Resources Information Center

Kobrin, Jennifer L.; Sinharay, Sandip; Haberman, Shelby J.; Chajewski, Michael

2011-01-01

This study examined the adequacy of a multiple linear regression model for predicting first-year college grade point average (FYGPA) using SAT[R] scores and high school grade point average (HSGPA). A variety of techniques, both graphical and statistical, were used to examine if it is possible to improve on the linear regression model. The results…

High correlations between MRI brain volume measurements based on NeuroQuant® and FreeSurfer.

PubMed

Ross, David E; Ochs, Alfred L; Tate, David F; Tokac, Umit; Seabaugh, John; Abildskov, Tracy J; Bigler, Erin D

2018-05-30

NeuroQuant ® (NQ) and FreeSurfer (FS) are commonly used computer-automated programs for measuring MRI brain volume. Previously they were reported to have high intermethod reliabilities but often large intermethod effect size differences. We hypothesized that linear transformations could be used to reduce the large effect sizes. This study was an extension of our previously reported study. We performed NQ and FS brain volume measurements on 60 subjects (including normal controls, patients with traumatic brain injury, and patients with Alzheimer's disease). We used two statistical approaches in parallel to develop methods for transforming FS volumes into NQ volumes: traditional linear regression, and Bayesian linear regression. For both methods, we used regression analyses to develop linear transformations of the FS volumes to make them more similar to the NQ volumes. The FS-to-NQ transformations based on traditional linear regression resulted in effect sizes which were small to moderate. The transformations based on Bayesian linear regression resulted in all effect sizes being trivially small. To our knowledge, this is the first report describing a method for transforming FS to NQ data so as to achieve high reliability and low effect size differences. Machine learning methods like Bayesian regression may be more useful than traditional methods. Copyright © 2018 Elsevier B.V. All rights reserved.

Quantile Regression in the Study of Developmental Sciences

PubMed Central

Petscher, Yaacov; Logan, Jessica A. R.

2014-01-01

Linear regression analysis is one of the most common techniques applied in developmental research, but only allows for an estimate of the average relations between the predictor(s) and the outcome. This study describes quantile regression, which provides estimates of the relations between the predictor(s) and outcome, but across multiple points of the outcome’s distribution. Using data from the High School and Beyond and U.S. Sustained Effects Study databases, quantile regression is demonstrated and contrasted with linear regression when considering models with: (a) one continuous predictor, (b) one dichotomous predictor, (c) a continuous and a dichotomous predictor, and (d) a longitudinal application. Results from each example exhibited the differential inferences which may be drawn using linear or quantile regression. PMID:24329596

Improving validation methods for molecular diagnostics: application of Bland-Altman, Deming and simple linear regression analyses in assay comparison and evaluation for next-generation sequencing

PubMed Central

Misyura, Maksym; Sukhai, Mahadeo A; Kulasignam, Vathany; Zhang, Tong; Kamel-Reid, Suzanne; Stockley, Tracy L

2018-01-01

Aims A standard approach in test evaluation is to compare results of the assay in validation to results from previously validated methods. For quantitative molecular diagnostic assays, comparison of test values is often performed using simple linear regression and the coefficient of determination (R2), using R2 as the primary metric of assay agreement. However, the use of R2 alone does not adequately quantify constant or proportional errors required for optimal test evaluation. More extensive statistical approaches, such as Bland-Altman and expanded interpretation of linear regression methods, can be used to more thoroughly compare data from quantitative molecular assays. Methods We present the application of Bland-Altman and linear regression statistical methods to evaluate quantitative outputs from next-generation sequencing assays (NGS). NGS-derived data sets from assay validation experiments were used to demonstrate the utility of the statistical methods. Results Both Bland-Altman and linear regression were able to detect the presence and magnitude of constant and proportional error in quantitative values of NGS data. Deming linear regression was used in the context of assay comparison studies, while simple linear regression was used to analyse serial dilution data. Bland-Altman statistical approach was also adapted to quantify assay accuracy, including constant and proportional errors, and precision where theoretical and empirical values were known. Conclusions The complementary application of the statistical methods described in this manuscript enables more extensive evaluation of performance characteristics of quantitative molecular assays, prior to implementation in the clinical molecular laboratory. PMID:28747393

Functional linear models for zero-inflated count data with application to modeling hospitalizations in patients on dialysis.

PubMed

Sentürk, Damla; Dalrymple, Lorien S; Nguyen, Danh V

2014-11-30

We propose functional linear models for zero-inflated count data with a focus on the functional hurdle and functional zero-inflated Poisson (ZIP) models. Although the hurdle model assumes the counts come from a mixture of a degenerate distribution at zero and a zero-truncated Poisson distribution, the ZIP model considers a mixture of a degenerate distribution at zero and a standard Poisson distribution. We extend the generalized functional linear model framework with a functional predictor and multiple cross-sectional predictors to model counts generated by a mixture distribution. We propose an estimation procedure for functional hurdle and ZIP models, called penalized reconstruction, geared towards error-prone and sparsely observed longitudinal functional predictors. The approach relies on dimension reduction and pooling of information across subjects involving basis expansions and penalized maximum likelihood techniques. The developed functional hurdle model is applied to modeling hospitalizations within the first 2 years from initiation of dialysis, with a high percentage of zeros, in the Comprehensive Dialysis Study participants. Hospitalization counts are modeled as a function of sparse longitudinal measurements of serum albumin concentrations, patient demographics, and comorbidities. Simulation studies are used to study finite sample properties of the proposed method and include comparisons with an adaptation of standard principal components regression. Copyright © 2014 John Wiley & Sons, Ltd.

Estimating top-of-atmosphere thermal infrared radiance using MERRA-2 atmospheric data

NASA Astrophysics Data System (ADS)

Kleynhans, Tania; Montanaro, Matthew; Gerace, Aaron; Kanan, Christopher

2017-05-01

Thermal infrared satellite images have been widely used in environmental studies. However, satellites have limited temporal resolution, e.g., 16 day Landsat or 1 to 2 day Terra MODIS. This paper investigates the use of the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) reanalysis data product, produced by NASA's Global Modeling and Assimilation Office (GMAO) to predict global topof-atmosphere (TOA) thermal infrared radiance. The high temporal resolution of the MERRA-2 data product presents opportunities for novel research and applications. Various methods were applied to estimate TOA radiance from MERRA-2 variables namely (1) a parameterized physics based method, (2) Linear regression models and (3) non-linear Support Vector Regression. Model prediction accuracy was evaluated using temporally and spatially coincident Moderate Resolution Imaging Spectroradiometer (MODIS) thermal infrared data as reference data. This research found that Support Vector Regression with a radial basis function kernel produced the lowest error rates. Sources of errors are discussed and defined. Further research is currently being conducted to train deep learning models to predict TOA thermal radiance

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

The influence of attention deficits on functional recovery post stroke during the first 12 months after discharge from hospital.

PubMed

Hyndman, D; Pickering, R M; Ashburn, A

2008-06-01

Attention deficits have been linked to poor recovery after stroke and may predict outcome. We explored the influence of attention on functional recovery post stroke in the first 12 months after discharge from hospital. People with stroke completed measures of attention, balance, mobility and activities of daily living (ADL) ability at the point of discharge from hospital, and 6 and 12 months later. We used correlational analysis and stepwise linear regression to explore potential predictors of outcome. We recruited 122 men and women, mean age 70 years. At discharge, 56 (51%) had deficits of divided attention, 45 (37%) of sustained attention, 43 (36%) of auditory selective attention and 41 (37%) had visual selective attention deficits. Attention at discharge correlated with mobility, balance and ADL outcomes 12 months later. After controlling for the level of the outcome at discharge, correlations remained significant in only five of the 12 relationships. Stepwise linear regression revealed that the outcome measured at discharge, days until discharge and number of medications were better predictors of outcome: in no case was an attention variable at discharge selected as a predictor of outcome at 12 months. Although attention and function correlated significantly, this correlation was reduced after controlling for functional ability at discharge. Furthermore, side of lesion and the attention variables were not demonstrated as important predictors of outcome 12 months later.

Fatigue in Type 2 Diabetes: Impact on Quality of Life and Predictors.

PubMed

Singh, Rupali; Teel, Cynthia; Sabus, Carla; McGinnis, Patricia; Kluding, Patricia

2016-01-01

Fatigue is a persistent symptom, impacting quality of life (QoL) and functional status in people with type 2 diabetes, yet the symptom of fatigue has not been fully explored. The purpose of this study was to explore the relationship between fatigue, QoL functional status and to investigate the predictors of fatigue. These possible predictors included body mass index (BMI), Hemoglobin A1C (HbA1C), sleep quality, pain, number of complications from diabetes, years since diagnosis and depression. Forty-eight individuals with type 2 diabetes (22 females, 26 males; 59.66±7.24 years of age; 10.45 ±7.38 years since diagnosis) participated in the study. Fatigue was assessed by using Multidimensional Fatigue Inventory (MFI-20). Other outcomes included: QoL (Audit of Diabetes Dependent QoL), and functional status (6 minute walk test), BMI, HbA1c, sleep (Pittsburg sleep quality index, PSQI), pain (Visual Analog Scale), number of complications, years since diagnosis, and depression (Beck's depression Inventory-2). The Pearson correlation analysis followed by multivariable linear regression model was used. Fatigue was negatively related to quality of life and functional status. Multivariable linear regression analysis revealed sleep, pain and BMI as the independent predictors of fatigue signaling the presence of physiological (sleep, pain, BMI) phenomenon that could undermine health outcomes.

Fatigue in Type 2 Diabetes: Impact on Quality of Life and Predictors

PubMed Central

Teel, Cynthia; Sabus, Carla; McGinnis, Patricia; Kluding, Patricia

2016-01-01

Fatigue is a persistent symptom, impacting quality of life (QoL) and functional status in people with type 2 diabetes, yet the symptom of fatigue has not been fully explored. The purpose of this study was to explore the relationship between fatigue, QoL functional status and to investigate the predictors of fatigue. These possible predictors included body mass index (BMI), Hemoglobin A1C (HbA1C), sleep quality, pain, number of complications from diabetes, years since diagnosis and depression. Forty-eight individuals with type 2 diabetes (22 females, 26 males; 59.66±7.24 years of age; 10.45 ±7.38 years since diagnosis) participated in the study. Fatigue was assessed by using Multidimensional Fatigue Inventory (MFI-20). Other outcomes included: QoL (Audit of Diabetes Dependent QoL), and functional status (6 minute walk test), BMI, HbA1c, sleep (Pittsburg sleep quality index, PSQI), pain (Visual Analog Scale), number of complications, years since diagnosis, and depression (Beck’s depression Inventory-2). The Pearson correlation analysis followed by multivariable linear regression model was used. Fatigue was negatively related to quality of life and functional status. Multivariable linear regression analysis revealed sleep, pain and BMI as the independent predictors of fatigue signaling the presence of physiological (sleep, pain, BMI) phenomenon that could undermine health outcomes. PMID:27824886

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

Modeling of boldine alkaloid adsorption onto pure and propyl-sulfonic acid-modified mesoporous silicas. A comparative study.

PubMed

Geszke-Moritz, Małgorzata; Moritz, Michał

2016-12-01

The present study deals with the adsorption of boldine onto pure and propyl-sulfonic acid-functionalized SBA-15, SBA-16 and mesocellular foam (MCF) materials. Siliceous adsorbents were characterized by nitrogen sorption analysis, transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier-transform infrared (FT-IR) spectroscopy and thermogravimetric analysis. The equilibrium adsorption data were analyzed using the Langmuir, Freundlich, Redlich-Peterson, and Temkin isotherms. Moreover, the Dubinin-Radushkevich and Dubinin-Astakhov isotherm models based on the Polanyi adsorption potential were employed. The latter was calculated using two alternative formulas including solubility-normalized (S-model) and empirical C-model. In order to find the best-fit isotherm, both linear regression and nonlinear fitting analysis were carried out. The Dubinin-Astakhov (S-model) isotherm revealed the best fit to the experimental points for adsorption of boldine onto pure mesoporous materials using both linear and nonlinear fitting analysis. Meanwhile, the process of boldine sorption onto modified silicas was described the best by the Langmuir and Temkin isotherms using linear regression and nonlinear fitting analysis, respectively. The values of adsorption energy (below 8kJ/mol) indicate the physical nature of boldine adsorption onto unmodified silicas whereas the ionic interactions seem to be the main force of alkaloid adsorption onto functionalized sorbents (energy of adsorption above 8kJ/mol). Copyright © 2016 Elsevier B.V. All rights reserved.

Temperament affects sympathetic nervous function in a normal population.

PubMed

Kim, Bora; Lee, Jae-Hon; Kang, Eun-Ho; Yu, Bum-Hee

2012-09-01

Although specific temperaments have been known to be related to autonomic nervous function in some psychiatric disorders, there are few studies that have examined the relationship between temperaments and autonomic nervous function in a normal population. In this study, we examined the effect of temperament on the sympathetic nervous function in a normal population. Sixty eight healthy subjects participated in the present study. Temperament was assessed using the Korean version of the Cloninger Temperament and Character Inventory (TCI). Autonomic nervous function was determined by measuring skin temperature in a resting state, which was recorded for 5 minutes from the palmar surface of the left 5th digit using a thermistor secured with a Velcro® band. Pearson's correlation analysis and multiple linear regression were used to examine the relationship between temperament and skin temperature. A higher harm avoidance score was correlated with a lower skin temperature (i.e. an increased sympathetic tone; r=-0.343, p=0.004) whereas a higher persistence score was correlated with a higher skin temperature (r=0.433, p=0.001). Hierarchical linear regression analysis revealed that harm avoidance was able to predict the variance of skin temperature independently, with a variance of 7.1% after controlling for sex, blood pressure and state anxiety and persistence was the factor predicting the variance of skin temperature with a variance of 5.0%. These results suggest that high harm avoidance is related to an increased sympathetic nervous function whereas high persistence is related to decreased sympathetic nervous function in a normal population.

Temperament Affects Sympathetic Nervous Function in a Normal Population

PubMed Central

Kim, Bora; Lee, Jae-Hon; Kang, Eun-Ho

2012-01-01

Objective Although specific temperaments have been known to be related to autonomic nervous function in some psychiatric disorders, there are few studies that have examined the relationship between temperaments and autonomic nervous function in a normal population. In this study, we examined the effect of temperament on the sympathetic nervous function in a normal population. Methods Sixty eight healthy subjects participated in the present study. Temperament was assessed using the Korean version of the Cloninger Temperament and Character Inventory (TCI). Autonomic nervous function was determined by measuring skin temperature in a resting state, which was recorded for 5 minutes from the palmar surface of the left 5th digit using a thermistor secured with a Velcro® band. Pearson's correlation analysis and multiple linear regression were used to examine the relationship between temperament and skin temperature. Results A higher harm avoidance score was correlated with a lower skin temperature (i.e. an increased sympathetic tone; r=-0.343, p=0.004) whereas a higher persistence score was correlated with a higher skin temperature (r=0.433, p=0.001). Hierarchical linear regression analysis revealed that harm avoidance was able to predict the variance of skin temperature independently, with a variance of 7.1% after controlling for sex, blood pressure and state anxiety and persistence was the factor predicting the variance of skin temperature with a variance of 5.0%. Conclusion These results suggest that high harm avoidance is related to an increased sympathetic nervous function whereas high persistence is related to decreased sympathetic nervous function in a normal population. PMID:22993530

Corticospinal excitability as a predictor of functional gains at the affected upper limb following robotic training in chronic stroke survivors

PubMed Central

Milot, Marie-Hélène; Spencer, Steven J.; Chan, Vicky; Allington, James P.; Klein, Julius; Chou, Cathy; Pearson-Fuhrhop, Kristin; Bobrow, James E.; Reinkensmeyer, David J.; Cramer, Steven C.

2014-01-01

Background Robotic training can help improve function of a paretic limb following a stroke, but individuals respond differently to the training. A predictor of functional gains might improve the ability to select those individuals more likely to benefit from robot based therapy. Studies evaluating predictors of functional improvement after a robotic training are scarce. One study has found that white matter tract integrity predicts functional gains following a robotic training of the hand and wrist. Objective Determine the predictive ability of behavioral and brain measures to improve selection of individuals for robotic training. Methods Twenty subjects with chronic stroke participated in an 8-week course of robotic exoskeletal training for the arm. Before training, a clinical evaluation, fMRI, diffusion tensor imaging, and transcranial magnetic stimulation (TMS) were each measured as predictors. Final functional gain was defined as change in the Box and Block Test (BBT). Measures significant in bivariate analysis were fed into a multivariate linear regression model. Results Training was associated with an average gain of 6±5 blocks on the BBT (p<0.0001). Bivariate analysis revealed that lower baseline motor evoked potential (MEP) amplitude on TMS, and lower laterality M1 index on fMRI each significantly correlated with greater BBT change. In the multivariate linear regression analysis, baseline MEP magnitude was the only measure that remained significant. Conclusion Subjects with lower baseline MEP magnitude benefited the most from robotic training of the affected arm. These subjects might have reserve remaining for the training to boost corticospinal excitability, translating into functional gains. PMID:24642382

The Role of Data Range in Linear Regression

ERIC Educational Resources Information Center

da Silva, M. A. Salgueiro; Seixas, T. M.

2017-01-01

Measuring one physical quantity as a function of another often requires making some choices prior to the measurement process. Two of these choices are: the data range where measurements should focus and the number (n) of data points to acquire in the chosen data range. Here, we consider data range as the interval of variation of the independent…

Age, Sex, and Body Composition as Predictors of Children's Performance on Basic Motor Abilities and Health-Related Fitness Items.

ERIC Educational Resources Information Center

Pissanos, Becky W.; And Others

1983-01-01

Step-wise linear regressions were used to relate children's age, sex, and body composition to performance on basic motor abilities including balance, speed, agility, power, coordination, and reaction time, and to health-related fitness items including flexibility, muscle strength and endurance and cardiovascular functions. Eighty subjects were in…

Incremental online learning in high dimensions.

PubMed

Vijayakumar, Sethu; D'Souza, Aaron; Schaal, Stefan

2005-12-01

Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high-dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally efficient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression. We discuss when and how local learning techniques can successfully work in high-dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the LWPR algorithm. The properties of LWPR are that it (1) learns rapidly with second-order learning methods based on incremental training, (2) uses statistically sound stochastic leave-one-out cross validation for learning without the need to memorize training data, (3) adjusts its weighting kernels based on only local information in order to minimize the danger of negative interference of incremental learning, (4) has a computational complexity that is linear in the number of inputs, and (5) can deal with a large number of-possibly redundant-inputs, as shown in various empirical evaluations with up to 90 dimensional data sets. For a probabilistic interpretation, predictive variance and confidence intervals are derived. To our knowledge, LWPR is the first truly incremental spatially localized learning method that can successfully and efficiently operate in very high-dimensional spaces.

Effect of pencil grasp on the speed and legibility of handwriting in children.

PubMed

Schwellnus, Heidi; Carnahan, Heather; Kushki, Azadeh; Polatajko, Helene; Missiuna, Cheryl; Chau, Tom

2012-01-01

Pencil grasps other than the dynamic tripod may be functional for handwriting. This study examined the impact of grasp on handwriting speed and legibility. We videotaped 120 typically developing fourth-grade students while they performed a writing task. We categorized the grasps they used and evaluated their writing for speed and legibility using a handwriting assessment. Using linear regression analysis, we examined the relationship between grasp and handwriting. We documented six categories of pencil grasp: four mature grasp patterns, one immature grasp pattern, and one alternating grasp pattern. Multiple linear regression results revealed no significant effect for mature grasp on either legibility or speed. Pencil grasp patterns did not influence handwriting speed or legibility in this sample of typically developing children. This finding adds to the mounting body of evidence that alternative grasps may be acceptable for fast and legible handwriting. Copyright © 2012 by the American Occupational Therapy Association, Inc.

Influence of salinity and temperature on acute toxicity of cadmium to Mysidopsis bahia molenock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voyer, R.A.; Modica, G.

1990-01-01

Acute toxicity tests were conducted to compare estimates of toxicity, as modified by salinity and temperature, based on response surface techniques with those derived using conventional test methods, and to compare effect of a single episodic exposure to cadmium as a function of salinity with that of continuous exposure. Regression analysis indicated that mortality following continuous 96-hr exposure is related to linear and quadratic effects of salinity and cadmium at 20 C, and to the linear and quadratic effects of cadmium only at 25C. LC50s decreased with increases in temperature and decreases in salinity. Based on the regression model developed,more » 96-hr LC50s ranged from 15.5 to 28.0 micro Cd/L at 10 and 30% salinities, respectively, at 25C; and from 47 to 85 microgram Cd/L at these salinities at 20C.« less

Conditionally Unbiased Bounded Influence Robust Regression with Applications to Generalized Linear Models.

DTIC Science & Technology

1987-03-01

some general results and definitions from robust statistics (see Hampel et. al.. 1986). The influence function of an M-Lstimator is IC (y.x.0) = D_...estimator is (4,T T T (\\cond(YXGB) . Yx(x,O.B) ) . where X~xO.) =x T T8 xT-lx 1/2 = x x v(x . b/(x B x) ) - B. The influence function of this...the influence function for (3.7) and (3.8) is equal to -. Eo[\\Pcond(y.X.,B)] -1 cond(Yx. ,B). (4.3) On the other hand, the influence function for the

Spiritual Coping: A Gateway to Enhancing Family Communication During Cancer Treatment.

PubMed

Prouty, Anne M; Fischer, Judith; Purdom, Ann; Cobos, Everardo; Helmeke, Karen B

2016-02-01

The researchers examined the spiritual coping, family communication, and family functioning of 95 participants in 34 families by an online survey. Multilevel linear regression was used to test whether individuals' and families' higher endorsement of more use of spiritual coping strategies to deal with a member's cancer would be associated with higher scores on family communication and family functioning, and whether better communication would also be associated with higher family functioning scores. Results revealed that spiritual coping was positively associated with family communication, and family communication was positively associated with healthier family functioning. The researchers provide suggestions for further research.

Estimating energy expenditure from heart rate in older adults: a case for calibration.

PubMed

Schrack, Jennifer A; Zipunnikov, Vadim; Goldsmith, Jeff; Bandeen-Roche, Karen; Crainiceanu, Ciprian M; Ferrucci, Luigi

2014-01-01

Accurate measurement of free-living energy expenditure is vital to understanding changes in energy metabolism with aging. The efficacy of heart rate as a surrogate for energy expenditure is rooted in the assumption of a linear function between heart rate and energy expenditure, but its validity and reliability in older adults remains unclear. To assess the validity and reliability of the linear function between heart rate and energy expenditure in older adults using different levels of calibration. Heart rate and energy expenditure were assessed across five levels of exertion in 290 adults participating in the Baltimore Longitudinal Study of Aging. Correlation and random effects regression analyses assessed the linearity of the relationship between heart rate and energy expenditure and cross-validation models assessed predictive performance. Heart rate and energy expenditure were highly correlated (r=0.98) and linear regardless of age or sex. Intra-person variability was low but inter-person variability was high, with substantial heterogeneity of the random intercept (s.d. =0.372) despite similar slopes. Cross-validation models indicated individual calibration data substantially improves accuracy predictions of energy expenditure from heart rate, reducing the potential for considerable measurement bias. Although using five calibration measures provided the greatest reduction in the standard deviation of prediction errors (1.08 kcals/min), substantial improvement was also noted with two (0.75 kcals/min). These findings indicate standard regression equations may be used to make population-level inferences when estimating energy expenditure from heart rate in older adults but caution should be exercised when making inferences at the individual level without proper calibration.

Comparison of Neural Network and Linear Regression Models in Statistically Predicting Mental and Physical Health Status of Breast Cancer Survivors

DTIC Science & Technology

2015-07-15

Long-term effects on cancer survivors’ quality of life of physical training versus physical training combined with cognitive-behavioral therapy ...COMPARISON OF NEURAL NETWORK AND LINEAR REGRESSION MODELS IN STATISTICALLY PREDICTING MENTAL AND PHYSICAL HEALTH STATUS OF BREAST...34Comparison of Neural Network and Linear Regression Models in Statistically Predicting Mental and Physical Health Status of Breast Cancer Survivors

Prediction of the Main Engine Power of a New Container Ship at the Preliminary Design Stage

NASA Astrophysics Data System (ADS)

Cepowski, Tomasz

2017-06-01

The paper presents mathematical relationships that allow us to forecast the estimated main engine power of new container ships, based on data concerning vessels built in 2005-2015. The presented approximations allow us to estimate the engine power based on the length between perpendiculars and the number of containers the ship will carry. The approximations were developed using simple linear regression and multivariate linear regression analysis. The presented relations have practical application for estimation of container ship engine power needed in preliminary parametric design of the ship. It follows from the above that the use of multiple linear regression to predict the main engine power of a container ship brings more accurate solutions than simple linear regression.

Systemic Factors Associated With Prosocial Skills and Maladaptive Functioning in Youth Exposed to Intimate Partner Violence.

PubMed

Howell, Kathryn H; Thurston, Idia B; Hasselle, Amanda J; Decker, Kristina; Jamison, Lacy E

2018-04-01

Children are frequently present in homes in which intimate partner violence (IPV) occurs. Following exposure to IPV, children may develop behavioral health difficulties, struggle with regulating emotions, or exhibit aggression. Despite the negative outcomes associated with witnessing IPV, many children also display resilience. Guided by Bronfenbrenner's bioecological model, this study examined person-level, process-level (microsystem), and context-level (mesosystem) factors associated with positive and negative functioning among youth exposed to IPV. Participants were 118 mothers who reported on their 6- to 14-year-old children. All mothers experienced severe physical, psychological, and/or sexual IPV in the past 6 months. Linear regression modeling was conducted separately for youth maladaptive functioning and prosocial skills. The linear regression model for maladaptive functioning was significant, F(6, 110) = 9.32, p < .001, adj R 2 = 27%, with more severe IPV (β = .18, p < .05) and more negative parenting practices (β = .34, p < .001) associated with worse child outcomes. The model for prosocial skills was also significant, F(6, 110) = 3.34, p < .01, adj. R 2 = 14%, with less negative parenting practices (β = -.26, p < .001) and greater community connectedness (β = .17, p < .05) linked to more prosocial skills. These findings provide critical knowledge on specific mutable factors associated with positive and negative functioning among children in the context of IPV exposure. Such factors could be incorporated into strength-based interventions following family violence.

Impact of sociodemographic variables on executive functions.

PubMed

Campanholo, Kenia Repiso; Boa, Izadora Nogueira Fonte; Hodroj, Flávia Cristina da Silva Araujo; Guerra, Glaucia Rosana Benute; Miotto, Eliane Correa; de Lucia, Mara Cristina Souza

2017-01-01

Executive functions (EFs) regulate human behavior and allow individuals to interact and act in the world. EFs are sensitive to sociodemographic variables such as age, which promotes their decline, and to others that can exert a neuroprotective effect. To assess the predictive role of education, occupation and family income on decline in executive functions among a sample with a wide age range. A total of 925 participants aged 18-89 years with 1-28 years' education were submitted to assessment of executive functions using the Card Sorting Test (CST), Phonemic Verbal Fluency (FAS) Task and Semantic Verbal Fluency (SVF) Task. Data on income, occupation and educational level were collected for the sample. The data were analyzed using Linear Regression, as well as Pearson's and Spearman's Correlation. Age showed a significant negative correlation (p<0.001) with performance on the CST, FAS and SVF, whereas education, income and occupation were positively associated (p<0.001) with the tasks applied. After application of the multivariate linear regression model, a significant positive relationship with the FAS was maintained only for education (p<0.001) and income (p<0.001). The negative relationship of age (p<0.001) and positive relationship of both education (p<0.001) and income (p<0.001and p=0.003) were evident on the CST and SVF. Educational level and income positively influenced participants' results on executive function tests, attenuating expected decline for age. However, no relationship was found between occupation and the cognitive variables investigated.

Impact of sociodemographic variables on executive functions

PubMed Central

Campanholo, Kenia Repiso; Boa, Izadora Nogueira Fonte; Hodroj, Flávia Cristina da Silva Araujo; Guerra, Glaucia Rosana Benute; Miotto, Eliane Correa; de Lucia, Mara Cristina Souza

2017-01-01

Executive functions (EFs) regulate human behavior and allow individuals to interact and act in the world. EFs are sensitive to sociodemographic variables such as age, which promotes their decline, and to others that can exert a neuroprotective effect. Objective To assess the predictive role of education, occupation and family income on decline in executive functions among a sample with a wide age range. Methods A total of 925 participants aged 18-89 years with 1-28 years' education were submitted to assessment of executive functions using the Card Sorting Test (CST), Phonemic Verbal Fluency (FAS) Task and Semantic Verbal Fluency (SVF) Task. Data on income, occupation and educational level were collected for the sample. The data were analyzed using Linear Regression, as well as Pearson's and Spearman's Correlation. Results Age showed a significant negative correlation (p<0.001) with performance on the CST, FAS and SVF, whereas education, income and occupation were positively associated (p<0.001) with the tasks applied. After application of the multivariate linear regression model, a significant positive relationship with the FAS was maintained only for education (p<0.001) and income (p<0.001). The negative relationship of age (p<0.001) and positive relationship of both education (p<0.001) and income (p<0.001and p=0.003) were evident on the CST and SVF. Conclusion Educational level and income positively influenced participants' results on executive function tests, attenuating expected decline for age. However, no relationship was found between occupation and the cognitive variables investigated. PMID:29213495

Pulse Pressure, Instead of Brachium-Ankle Pulse Wave Velocity, is Associated with Reduced Kidney Function in a Chinese Han Population.

PubMed

Jia, Linpei; Zhang, Weiguang; Ma, Jie; Chen, Xizhao; Chen, Lei; Li, Zuoxiang; Cai, Guangyan; Huang, Jing; Zhang, Jinping; Bai, Xiaojuan; Feng, Zhe; Sun, Xuefeng; Chen, Xiangmei

2017-01-01

In this study, we aim to investigate the association between renal function and arterial stiffness in a Chinese Han population, and further to discuss the effects of smoking on renal function. We collected the data of the brachium-ankle pulse wave velocity (baPWV), blood pressure, blood chemistry and smoking status. Then, the multiple linear regression was done to explore the relationship between estimated glomerular filtration (eGFR) and baPWV. Further, the parameters were compared among the four groups divided according to the quartiles of baPWV. Finally, the baPWV, eGFR and albuminuria values were compared between smokers and non-smokers. baPWV is associated with eGFR in the correlation analysis and univariate linear regression model. After adjustment, the pulse pressure (PP) instead of baPWV showed a significant association with eGFR. Nevertheless, the eGFR values differed among the four baPWV groups; the baPWV values were significantly higher in the subjects at the CKD (eGFR<60 mL/min/1.73 m2) and the early CKD stage (eGFR60-80 mL/min/1.73 m2). The baPWV values and the ratio of proteinuria were significantly increased in smokers. PP but not baPWV is a predictor of declined renal function. Smokers have worse arterial stiffness and worse renal function. © 2017 The Author(s)Published by S. Karger AG, Basel.

Estimation of Standard Error of Regression Effects in Latent Regression Models Using Binder's Linearization. Research Report. ETS RR-07-09

ERIC Educational Resources Information Center

Li, Deping; Oranje, Andreas

2007-01-01

Two versions of a general method for approximating standard error of regression effect estimates within an IRT-based latent regression model are compared. The general method is based on Binder's (1983) approach, accounting for complex samples and finite populations by Taylor series linearization. In contrast, the current National Assessment of…

Regression assumptions in clinical psychology research practice-a systematic review of common misconceptions.

PubMed

Ernst, Anja F; Albers, Casper J

2017-01-01

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking.

Regression assumptions in clinical psychology research practice—a systematic review of common misconceptions

PubMed Central

Ernst, Anja F.

2017-01-01

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking. PMID:28533971

Estimating linear temporal trends from aggregated environmental monitoring data

USGS Publications Warehouse

Erickson, Richard A.; Gray, Brian R.; Eager, Eric A.

2017-01-01

Trend estimates are often used as part of environmental monitoring programs. These trends inform managers (e.g., are desired species increasing or undesired species decreasing?). Data collected from environmental monitoring programs is often aggregated (i.e., averaged), which confounds sampling and process variation. State-space models allow sampling variation and process variations to be separated. We used simulated time-series to compare linear trend estimations from three state-space models, a simple linear regression model, and an auto-regressive model. We also compared the performance of these five models to estimate trends from a long term monitoring program. We specifically estimated trends for two species of fish and four species of aquatic vegetation from the Upper Mississippi River system. We found that the simple linear regression had the best performance of all the given models because it was best able to recover parameters and had consistent numerical convergence. Conversely, the simple linear regression did the worst job estimating populations in a given year. The state-space models did not estimate trends well, but estimated population sizes best when the models converged. We found that a simple linear regression performed better than more complex autoregression and state-space models when used to analyze aggregated environmental monitoring data.

Comparing The Effectiveness of a90/95 Calculations (Preprint)

DTIC Science & Technology

2006-09-01

Nachtsheim, John Neter, William Li, Applied Linear Statistical Models , 5th ed., McGraw-Hill/Irwin, 2005 5. Mood, Graybill and Boes, Introduction...curves is based on methods that are only valid for ordinary linear regression. Requirements for a valid Ordinary Least-Squares Regression Model There... linear . For example is a linear model ; is not. 2. Uniform variance (homoscedasticity

Correlation and simple linear regression.

PubMed

Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G

2003-06-01

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

Mixed kernel function support vector regression for global sensitivity analysis

NASA Astrophysics Data System (ADS)

Cheng, Kai; Lu, Zhenzhou; Wei, Yuhao; Shi, Yan; Zhou, Yicheng

2017-11-01

Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on an assigned output response. Amongst the wide sensitivity analyses in literature, the Sobol indices have attracted much attention since they can provide accurate information for most models. In this paper, a mixed kernel function (MKF) based support vector regression (SVR) model is employed to evaluate the Sobol indices at low computational cost. By the proposed derivation, the estimation of the Sobol indices can be obtained by post-processing the coefficients of the SVR meta-model. The MKF is constituted by the orthogonal polynomials kernel function and Gaussian radial basis kernel function, thus the MKF possesses both the global characteristic advantage of the polynomials kernel function and the local characteristic advantage of the Gaussian radial basis kernel function. The proposed approach is suitable for high-dimensional and non-linear problems. Performance of the proposed approach is validated by various analytical functions and compared with the popular polynomial chaos expansion (PCE). Results demonstrate that the proposed approach is an efficient method for global sensitivity analysis.

Improving validation methods for molecular diagnostics: application of Bland-Altman, Deming and simple linear regression analyses in assay comparison and evaluation for next-generation sequencing.

PubMed

Misyura, Maksym; Sukhai, Mahadeo A; Kulasignam, Vathany; Zhang, Tong; Kamel-Reid, Suzanne; Stockley, Tracy L

2018-02-01

A standard approach in test evaluation is to compare results of the assay in validation to results from previously validated methods. For quantitative molecular diagnostic assays, comparison of test values is often performed using simple linear regression and the coefficient of determination (R 2 ), using R 2 as the primary metric of assay agreement. However, the use of R 2 alone does not adequately quantify constant or proportional errors required for optimal test evaluation. More extensive statistical approaches, such as Bland-Altman and expanded interpretation of linear regression methods, can be used to more thoroughly compare data from quantitative molecular assays. We present the application of Bland-Altman and linear regression statistical methods to evaluate quantitative outputs from next-generation sequencing assays (NGS). NGS-derived data sets from assay validation experiments were used to demonstrate the utility of the statistical methods. Both Bland-Altman and linear regression were able to detect the presence and magnitude of constant and proportional error in quantitative values of NGS data. Deming linear regression was used in the context of assay comparison studies, while simple linear regression was used to analyse serial dilution data. Bland-Altman statistical approach was also adapted to quantify assay accuracy, including constant and proportional errors, and precision where theoretical and empirical values were known. The complementary application of the statistical methods described in this manuscript enables more extensive evaluation of performance characteristics of quantitative molecular assays, prior to implementation in the clinical molecular laboratory. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Acoustic-articulatory mapping in vowels by locally weighted regression

PubMed Central

McGowan, Richard S.; Berger, Michael A.

2009-01-01

A method for mapping between simultaneously measured articulatory and acoustic data is proposed. The method uses principal components analysis on the articulatory and acoustic variables, and mapping between the domains by locally weighted linear regression, or loess [Cleveland, W. S. (1979). J. Am. Stat. Assoc. 74, 829–836]. The latter method permits local variation in the slopes of the linear regression, assuming that the function being approximated is smooth. The methodology is applied to vowels of four speakers in the Wisconsin X-ray Microbeam Speech Production Database, with formant analysis. Results are examined in terms of (1) examples of forward (articulation-to-acoustics) mappings and inverse mappings, (2) distributions of local slopes and constants, (3) examples of correlations among slopes and constants, (4) root-mean-square error, and (5) sensitivity of formant frequencies to articulatory change. It is shown that the results are qualitatively correct and that loess performs better than global regression. The forward mappings show different root-mean-square error properties than the inverse mappings indicating that this method is better suited for the forward mappings than the inverse mappings, at least for the data chosen for the current study. Some preliminary results on sensitivity of the first two formant frequencies to the two most important articulatory principal components are presented. PMID:19813812

Using Linear Equating to Map PROMIS(®) Global Health Items and the PROMIS-29 V2.0 Profile Measure to the Health Utilities Index Mark 3.

PubMed

Hays, Ron D; Revicki, Dennis A; Feeny, David; Fayers, Peter; Spritzer, Karen L; Cella, David

2016-10-01

Preference-based health-related quality of life (HR-QOL) scores are useful as outcome measures in clinical studies, for monitoring the health of populations, and for estimating quality-adjusted life-years. This was a secondary analysis of data collected in an internet survey as part of the Patient-Reported Outcomes Measurement Information System (PROMIS(®)) project. To estimate Health Utilities Index Mark 3 (HUI-3) preference scores, we used the ten PROMIS(®) global health items, the PROMIS-29 V2.0 single pain intensity item and seven multi-item scales (physical functioning, fatigue, pain interference, depressive symptoms, anxiety, ability to participate in social roles and activities, sleep disturbance), and the PROMIS-29 V2.0 items. Linear regression analyses were used to identify significant predictors, followed by simple linear equating to avoid regression to the mean. The regression models explained 48 % (global health items), 61 % (PROMIS-29 V2.0 scales), and 64 % (PROMIS-29 V2.0 items) of the variance in the HUI-3 preference score. Linear equated scores were similar to observed scores, although differences tended to be larger for older study participants. HUI-3 preference scores can be estimated from the PROMIS(®) global health items or PROMIS-29 V2.0. The estimated HUI-3 scores from the PROMIS(®) health measures can be used for economic applications and as a measure of overall HR-QOL in research.

U.S. Army Armament Research, Development and Engineering Center Grain Evaluation Software to Numerically Predict Linear Burn Regression for Solid Propellant Grain Geometries

DTIC Science & Technology

2017-10-01

ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID PROPELLANT GRAIN GEOMETRIES Brian...author(s) and should not be construed as an official Department of the Army position, policy, or decision, unless so designated by other documentation...U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID

Generalized regression neural network (GRNN)-based approach for colored dissolved organic matter (CDOM) retrieval: case study of Connecticut River at Middle Haddam Station, USA.

PubMed

Heddam, Salim

2014-11-01

The prediction of colored dissolved organic matter (CDOM) using artificial neural network approaches has received little attention in the past few decades. In this study, colored dissolved organic matter (CDOM) was modeled using generalized regression neural network (GRNN) and multiple linear regression (MLR) models as a function of Water temperature (TE), pH, specific conductance (SC), and turbidity (TU). Evaluation of the prediction accuracy of the models is based on the root mean square error (RMSE), mean absolute error (MAE), coefficient of correlation (CC), and Willmott's index of agreement (d). The results indicated that GRNN can be applied successfully for prediction of colored dissolved organic matter (CDOM).

Linear regression in astronomy. II

NASA Technical Reports Server (NTRS)

Feigelson, Eric D.; Babu, Gutti J.

1992-01-01

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

Effects of acceleration in the Gz axis on human cardiopulmonary responses to exercise.

PubMed

Bonjour, Julien; Bringard, Aurélien; Antonutto, Guglielmo; Capelli, Carlo; Linnarsson, Dag; Pendergast, David R; Ferretti, Guido

2011-12-01

The aim of this paper was to develop a model from experimental data allowing a prediction of the cardiopulmonary responses to steady-state submaximal exercise in varying gravitational environments, with acceleration in the G(z) axis (a (g)) ranging from 0 to 3 g. To this aim, we combined data from three different experiments, carried out at Buffalo, at Stockholm and inside the Mir Station. Oxygen consumption, as expected, increased linearly with a (g). In contrast, heart rate increased non-linearly with a (g), whereas stroke volume decreased non-linearly: both were described by quadratic functions. Thus, the relationship between cardiac output and a (g) was described by a fourth power regression equation. Mean arterial pressure increased with a (g) non linearly, a relation that we interpolated again with a quadratic function. Thus, total peripheral resistance varied linearly with a (g). These data led to predict that maximal oxygen consumption would decrease drastically as a (g) is increased. Maximal oxygen consumption would become equal to resting oxygen consumption when a (g) is around 4.5 g, thus indicating the practical impossibility for humans to stay and work on the biggest Planets of the Solar System.

Modeling the effects of AADT on predicting multiple-vehicle crashes at urban and suburban signalized intersections.

PubMed

Chen, Chen; Xie, Yuanchang

2016-06-01

Annual Average Daily Traffic (AADT) is often considered as a main covariate for predicting crash frequencies at urban and suburban intersections. A linear functional form is typically assumed for the Safety Performance Function (SPF) to describe the relationship between the natural logarithm of expected crash frequency and covariates derived from AADTs. Such a linearity assumption has been questioned by many researchers. This study applies Generalized Additive Models (GAMs) and Piecewise Linear Negative Binomial (PLNB) regression models to fit intersection crash data. Various covariates derived from minor-and major-approach AADTs are considered. Three different dependent variables are modeled, which are total multiple-vehicle crashes, rear-end crashes, and angle crashes. The modeling results suggest that a nonlinear functional form may be more appropriate. Also, the results show that it is important to take into consideration the joint safety effects of multiple covariates. Additionally, it is found that the ratio of minor to major-approach AADT has a varying impact on intersection safety and deserves further investigations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling non-linear growth responses to temperature and hydrology in wetland trees

NASA Astrophysics Data System (ADS)

Keim, R.; Allen, S. T.

2016-12-01

Growth responses of wetland trees to flooding and climate variations are difficult to model because they depend on multiple, apparently interacting factors, but are a critical link in hydrological control of wetland carbon budgets. To more generally understand tree growth to hydrological forcing, we modeled non-linear responses of tree ring growth to flooding and climate at sub-annual time steps, using Vaganov-Shashkin response functions. We calibrated the model to six baldcypress tree-ring chronologies from two hydrologically distinct sites in southern Louisiana, and tested several hypotheses of plasticity in wetlands tree responses to interacting environmental variables. The model outperformed traditional multiple linear regression. More importantly, optimized response parameters were generally similar among sites with varying hydrological conditions, suggesting generality to the functions. Model forms that included interacting responses to multiple forcing factors were more effective than were single response functions, indicating the principle of a single limiting factor is not correct in wetlands and both climatic and hydrological variables must be considered in predicting responses to hydrological or climate change.

A Constrained Linear Estimator for Multiple Regression

ERIC Educational Resources Information Center

Davis-Stober, Clintin P.; Dana, Jason; Budescu, David V.

2010-01-01

"Improper linear models" (see Dawes, Am. Psychol. 34:571-582, "1979"), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of "improper" linear models as "proper" statistical models with a single predictor. We…

Indoor molds and lung function in healthy adults.

PubMed

Hernberg, Samu; Sripaiboonkij, Penpatra; Quansah, Reginald; Jaakkola, Jouni J K; Jaakkola, Maritta S

2014-05-01

Indoor mold exposure is common worldwide and constitutes an important health problem. There are very few studies assessing the relation between mold exposure and lung function levels among non-asthmatic adults. Our objective was to assess the relations between dampness and mold exposures at home and at work and lung function. In particular, we elaborated the importance of different exposure indicators. In a population-based study, 269 non-asthmatic adults from South Finland answered a questionnaire on indoor dampness and mold exposures at home or at work and other factors potentially influencing lung function, and performed spirometry. Multiple linear regression model was applied to study the relations between exposures and spirometric lung function levels. In linear regression adjusting for confounding, FEV1 level was reduced on average 200 ml related to mold odor at home (effect estimate -0.20, 95% CI -0.60 to 0.21) and FVC level was reduced on average 460 ml (-0.46, -0.95 to 0.03) respectively. Exposure to mold odor at home or at work or both was related to reduced FEV1 (-0.15, -0.42 to 0.12) and FVC (-0.22, -0.55 to 0.11) levels. Women had on average 510 ml reduced FEV1 levels (-0.51, -1.0 to 0.03) and 820 ml reduced FVC levels (-0.82, -1.4 to -0.20) related to mold odor exposure at home. Mold odor exposure was related to lower lung function levels among non-asthmatic adults, especially among women. Copyright © 2014 Elsevier Ltd. All rights reserved.

On the design of classifiers for crop inventories

NASA Technical Reports Server (NTRS)

Heydorn, R. P.; Takacs, H. C.

1986-01-01

Crop proportion estimators that use classifications of satellite data to correct, in an additive way, a given estimate acquired from ground observations are discussed. A linear version of these estimators is optimal, in terms of minimum variance, when the regression of the ground observations onto the satellite observations in linear. When this regression is not linear, but the reverse regression (satellite observations onto ground observations) is linear, the estimator is suboptimal but still has certain appealing variance properties. In this paper expressions are derived for those regressions which relate the intercepts and slopes to conditional classification probabilities. These expressions are then used to discuss the question of classifier designs that can lead to low-variance crop proportion estimates. Variance expressions for these estimates in terms of classifier omission and commission errors are also derived.

Executive functions and consumption of fruits/ vegetables and high saturated fat foods in young adults.

PubMed

Limbers, Christine A; Young, Danielle

2015-05-01

Executive functions play a critical role in regulating eating behaviors and have been shown to be associated with overeating which over time can result in overweight and obesity. There has been a paucity of research examining the associations among healthy dietary behaviors and executive functions utilizing behavioral rating scales of executive functioning. The objective of the present cross-sectional study was to evaluate the associations among fruit and vegetable consumption, intake of foods high in saturated fat, and executive functions using the Behavioral Rating Inventory of Executive Functioning-Adult Version. A total of 240 university students completed the Behavioral Rating Inventory of Executive Functioning-Adult Version, the 26-Item Eating Attitudes Test, and the Diet subscale of the Summary of Diabetes Self-Care Activities Questionnaire. Multiple linear regression analysis was conducted with two separate models in which fruit and vegetable consumption and saturated fat intake were the outcomes. Demographic variables, body mass index, and eating styles were controlled for in the analysis. Better initiation skills were associated with greater intake of fruits and vegetables in the last 7 days (standardized beta = -0.17; p < 0.05). Stronger inhibitory control was associated with less consumption of high fat foods in the last 7 days (standardized beta = 0.20; p < 0.05) in the multiple linear regression analysis. Executive functions that predict fruit and vegetable consumption are distinct from those that predict avoidance of foods high in saturated fat. Future research should investigate whether continued skill enhancement in initiation and inhibition following standard behavioral interventions improves long-term maintenance of weight loss. © The Author(s) 2015.

Corticospinal excitability as a predictor of functional gains at the affected upper limb following robotic training in chronic stroke survivors.

PubMed

Milot, Marie-Hélène; Spencer, Steven J; Chan, Vicky; Allington, James P; Klein, Julius; Chou, Cathy; Pearson-Fuhrhop, Kristin; Bobrow, James E; Reinkensmeyer, David J; Cramer, Steven C

2014-01-01

Robotic training can help improve function of a paretic limb following a stroke, but individuals respond differently to the training. A predictor of functional gains might improve the ability to select those individuals more likely to benefit from robot-based therapy. Studies evaluating predictors of functional improvement after a robotic training are scarce. One study has found that white matter tract integrity predicts functional gains following a robotic training of the hand and wrist. Objective. To determine the predictive ability of behavioral and brain measures in order to improve selection of individuals for robotic training. Twenty subjects with chronic stroke participated in an 8-week course of robotic exoskeletal training for the arm. Before training, a clinical evaluation, functional magnetic resonance imaging (fMRI), diffusion tensor imaging, and transcranial magnetic stimulation (TMS) were each measured as predictors. Final functional gain was defined as change in the Box and Block Test (BBT). Measures significant in bivariate analysis were fed into a multivariate linear regression model. Training was associated with an average gain of 6 ± 5 blocks on the BBT (P < .0001). Bivariate analysis revealed that lower baseline motor-evoked potential (MEP) amplitude on TMS, and lower laterality M1 index on fMRI each significantly correlated with greater BBT change. In the multivariate linear regression analysis, baseline MEP magnitude was the only measure that remained significant. Subjects with lower baseline MEP magnitude benefited the most from robotic training of the affected arm. These subjects might have reserve remaining for the training to boost corticospinal excitability, translating into functional gains. © The Author(s) 2014.

Applying Occam's Razor To The Proton Radius Puzzle

NASA Astrophysics Data System (ADS)

Higinbotham, Douglas

2016-09-01

Over the past five decades, ever more complex mathematical functions have been used to extract the radius of the proton from electron scattering data. For example, in 1963 the proton radius was extracted with linear and quadratic fits of low Q2 data (< 3 fm-2) and by 2014 a non-linear regression of two tenth order power series functions with thirty-one normalization parameters and data out to 25 fm-2 was used. But for electron scattering, the radius of the proton is determined by extracting the slope of the charge form factor at a Q2 of zero. By using higher precision data than was available in 1963 and focusing on the low Q2 data from 1974 to today, we find extrapolating functions consistently produce a proton radius of around 0.84 fm. A result that is in agreement with modern Lamb shift measurements.

Individual differences in long-range time representation.

PubMed

Agostino, Camila S; Caetano, Marcelo S; Balci, Fuat; Claessens, Peter M E; Zana, Yossi

2017-04-01

On the basis of experimental data, long-range time representation has been proposed to follow a highly compressed power function, which has been hypothesized to explain the time inconsistency found in financial discount rate preferences. The aim of this study was to evaluate how well linear and power function models explain empirical data from individual participants tested in different procedural settings. The line paradigm was used in five different procedural variations with 35 adult participants. Data aggregated over the participants showed that fitted linear functions explained more than 98% of the variance in all procedures. A linear regression fit also outperformed a power model fit for the aggregated data. An individual-participant-based analysis showed better fits of a linear model to the data of 14 participants; better fits of a power function with an exponent β > 1 to the data of 12 participants; and better fits of a power function with β < 1 to the data of the remaining nine participants. Of the 35 volunteers, the null hypothesis β = 1 was rejected for 20. The dispersion of the individual β values was approximated well by a normal distribution. These results suggest that, on average, humans perceive long-range time intervals not in a highly compressed, biased manner, but rather in a linear pattern. However, individuals differ considerably in their subjective time scales. This contribution sheds new light on the average and individual psychophysical functions of long-range time representation, and suggests that any attribution of deviation from exponential discount rates in intertemporal choice to the compressed nature of subjective time must entail the characterization of subjective time on an individual-participant basis.

Live Donor Renal Anatomic Asymmetry and Posttransplant Renal Function.

PubMed

Tanriover, Bekir; Fernandez, Sonalis; Campenot, Eric S; Newhouse, Jeffrey H; Oyfe, Irina; Mohan, Prince; Sandikci, Burhaneddin; Radhakrishnan, Jai; Wexler, Jennifer J; Carroll, Maureen A; Sharif, Sairah; Cohen, David J; Ratner, Lloyd E; Hardy, Mark A

2015-08-01

Relationship between live donor renal anatomic asymmetry and posttransplant recipient function has not been studied extensively. We analyzed 96 live kidney donors, who had anatomical asymmetry (>10% renal length and/or volume difference calculated from computerized tomography angiograms) and their matching recipients. Split function differences (SFD) were quantified with technetium-dimercaptosuccinic acid renography. Implantation biopsies at time 0 were semiquantitatively scored. A comprehensive model using donor renal volume adjusted to recipient weight (Vol/Wgt), SFD, and biopsy score was used to predict recipient estimated glomerular filtration rate (eGFR) at 1 year. Primary analysis consisted of a logistic regression model of outcome (odds of developing eGFR>60 mL/min/1.73 m(2) at 1 year), a linear regression model of outcome (predicting recipient eGFR at one-year, using the chronic kidney disease-epidemiology collaboration formula), and a Monte Carlo simulation based on the linear regression model (N=10,000 iterations). In the study cohort, the mean Vol/Wgt and eGFR at 1 year were 2.04 mL/kg and 60.4 mL/min/1.73 m(2), respectively. Volume and split ratios between 2 donor kidneys were strongly correlated (r = 0.79, P < 0.001). The biopsy scores among SFD categories (<5%, 5%-10%, >10%) were not different (P = 0.190). On multivariate models, only Vol/Wgt was significantly associated with higher odds of having eGFR > 60 mL/min/1.73 m (odds ratio, 8.94, 95% CI 2.47-32.25, P = 0.001) and had a strong discriminatory power in predicting the risk of eGFR less than 60 mL/min/1.73 m(2) at 1 year [receiver operating curve (ROC curve), 0.78, 95% CI, 0.68-0.89]. In the presence of donor renal anatomic asymmetry, Vol/Wgt appears to be a major determinant of recipient renal function at 1 year after transplantation. Renography can be replaced with CT volume calculation in estimating split renal function.

Live Donor Renal Anatomic Asymmetry and Post-Transplant Renal Function

PubMed Central

Tanriover, Bekir; Fernandez, Sonalis; Campenot, Eric S.; Newhouse, Jeffrey H.; Oyfe, Irina; Mohan, Prince; Sandikci, Burhaneddin; Radhakrishnan, Jai; Wexler, Jennifer J.; Carroll, Maureen A.; Sharif, Sairah; Cohen, David J.; Ratner, Lloyd E.; Hardy, Mark A.

2014-01-01

Background Relationship between live donor renal anatomic asymmetry and post-transplant recipient function has not been studied extensively. Methods We analyzed 96 live-kidney donors, who had anatomical asymmetry (>10% renal length and/or volume difference calculated from CT angiograms) and their matching recipients. Split function differences (SFD) were quantified with 99mTc-DMSA renography. Implantation biopsies at time-zero were semi-quantitatively scored. A comprehensive model utilizing donor renal volume adjusted to recipient weight (Vol/Wgt), SFD, and biopsy score was used to predict recipient estimated glomerular filtration rate (eGFR) at one-year. Primary analysis consisted of a logistic regression model of outcome (odds of developing eGFR>60ml/min/1.73 m2 at one-year), a linear regression model of outcome (predicting recipient eGFR at one-year, using the CKD-EPI formula), and a Monte Carlo simulation based on the linear regression model (N=10,000 iterations). Results In the study cohort, the mean Vol/Wgt and eGFR at one-year were 2.04 ml/kg and 60.4 ml/min/1.73m2, respectively. Volume and split ratios between two donor kidneys were strongly correlated (r=0.79, p-value<0.001). The biopsy scores among SFD categories (<5%, 5–10%, >10%) were not different (p=0.190). On multivariate models, only Vol/Wgt was significantly associated with higher odds of having eGFR>60ml/min/1.73 m2 (OR=8.94, 95% CI 2.47–32.25, p=0.001) and had a strong discriminatory power in predicting the risk of eGFR<60ml/min/1.73m2 at one-year (ROC curve=0.78, 95% CI 0.68–0.89). Conclusion In the presence of donor renal anatomic asymmetry, Vol/Wgt appears to be a major determinant of recipient renal function at one-year post-transplantation. Renography can be replaced with CT volume calculation in estimating split renal function. PMID:25719258

Preliminary results on predation of gypsy moth egg masses in Slovakia

Treesearch

Marek Turcani; Andrew Liebhold; Michael McManus; Julius Novotny

2003-01-01

Predation of gypsy moth egg masses was studied in Slovakia from 1999-2002. Predation on naturally laid egg masses was recorded and linear regression was used to test the hypothesis that predation follows a type II vs. type III functional response. We also investigated the role of egg mass predation in gypsy moth population dynamics. The relative contribution of...

Estimating cost of large-fire suppression for three Forest Service regions

Treesearch

Eric L. Smith; Gonz& aacute; lez-Cab& aacute; n Armando

1987-01-01

The annual costs attributable to large fire suppression in three Forest Service Regions (1970-1981) were estimated as a function of fire perimeters using linear regression. Costs calculated on a per chain of perimeterbasis were highest for the Pacific Northwest Region, next highest for the Northern Region, and lowest for the Intermountain Region. Recent costs in real...

Estimating V0[subscript 2]max Using a Personalized Step Test

ERIC Educational Resources Information Center

Webb, Carrie; Vehrs, Pat R.; George, James D.; Hager, Ronald

2014-01-01

The purpose of this study was to develop a step test with a personalized step rate and step height to predict cardiorespiratory fitness in 80 college-aged males and females using the self-reported perceived functional ability scale and data collected during the step test. Multiple linear regression analysis yielded a model (R = 0.90, SEE = 3.43…

Analysis of the Effects of the Commander’s Battle Positioning on Unit Combat Performance

DTIC Science & Technology

1991-03-01

Analysis ......... .. 58 Logistic Regression Analysis ......... .. 61 Canonical Correlation Analysis ........ .. 62 Descriminant Analysis...entails classifying objects into two or more distinct groups, or responses. Dillon defines descriminant analysis as "deriving linear combinations of the...object given it’s predictor variables. The second objective is, through analysis of the parameters of the descriminant functions, determine those

Altered central nervous system processing of baroreceptor input following hindlimb unloading in rats

NASA Technical Reports Server (NTRS)

Moffitt, J. A.; Schadt, J. C.; Hasser, E. M.

1999-01-01

The effect of cardiovascular deconditioning on central nervous system processing of baroreceptor afferent activity was evaluated following 14 days of hindlimb unloading (HU). Inactin-anesthetized rats were instrumented with catheters, renal sympathetic nerve electrodes, and aortic depressor nerve electrodes for measurement of mean arterial pressure, heart rate, renal sympathetic nerve activity (RSNA), and aortic depressor nerve activity (ADNA). Baroreceptor and baroreflex functions were assessed during infusion of phenylephrine and sodium nitroprusside. Central processing of baroreceptor afferent input was evaluated by linear regression relating RSNA to ADNA. The maximum baroreflex-elicited increase in RSNA was significantly reduced in HU rats (122 +/- 3.8 vs. 144 +/- 4.9% of baseline RSNA), whereas ADNA was not altered. The slope (-0.18 +/- 0.04 vs. -0.40 +/- 0.04) and y-intercept (121 +/- 3.2 vs. 146 +/- 4.3) of the linear regression relating increases in efferent RSNA to decreases in afferent ADNA during hypotension were significantly reduced in HU rats. There were no differences during increases in arterial pressure. Results demonstrate that the attenuation in baroreflex-mediated increases in RSNA following HU is due to changes in central processing of baroreceptor afferent information rather than aortic baroreceptor function.

Status of tuberculosis-related stigma and associated factors: a cross-sectional study in central China.

PubMed

Yin, Xiaoxv; Yan, Shijiao; Tong, Yeqing; Peng, Xin; Yang, Tingting; Lu, Zuxun; Gong, Yanhong

2018-02-01

Tuberculosis (TB) poses a significant challenge to public health worldwide. Stigma is a major obstacle to TB control by leading to delay in diagnosis and treatment non-adherence. This study aimed to evaluate the status of TB-related stigma and its associated factors among TB patients in China. Cross-sectional survey. Thus, 1342 TB patients were recruited from TB dispensaries in three counties in Hubei Province using a multistage sampling method and surveyed using a structured anonymous questionnaire including validated scales to measure TB-related stigma. A generalised linear regression model was used to identify the factors associated with TB-related stigma. The average score on the TB-related Stigma Scale was 9.33 (SD = 4.25). Generalised linear regression analysis revealed that knowledge about TB (ß = -0.18, P = 0.0025), family function (ß = -0.29, P < 0.0001) and doctor-patient communication (ß = -0.32, P = 0.0005) were negatively associated with TB-related stigma. TB-related stigma was high among TB patients in China. Interventions concentrating on reducing TB patients' stigma in China should focus on improving patients' family function and patients' knowledge about TB. © 2017 John Wiley & Sons Ltd.

Model Checking Techniques for Assessing Functional Form Specifications in Censored Linear Regression Models.

PubMed

León, Larry F; Cai, Tianxi

2012-04-01

In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of "robust" residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as "robust" censored data analogs to the processes considered by Lin, Wei & Ying (2002). The null distributions of these stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reects model misspecification or natural variation. We illustrate the methods with a well known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In our simulation experiments, the proposed test statistics have good power of detecting misspecification while at the same time controlling the size of the test.

Spatially resolved regression analysis of pre-treatment FDG, FLT and Cu-ATSM PET from post-treatment FDG PET: an exploratory study

PubMed Central

Bowen, Stephen R; Chappell, Richard J; Bentzen, Søren M; Deveau, Michael A; Forrest, Lisa J; Jeraj, Robert

2012-01-01

Purpose To quantify associations between pre-radiotherapy and post-radiotherapy PET parameters via spatially resolved regression. Materials and methods Ten canine sinonasal cancer patients underwent PET/CT scans of [18F]FDG (FDGpre), [18F]FLT (FLTpre), and [61Cu]Cu-ATSM (Cu-ATSMpre). Following radiotherapy regimens of 50 Gy in 10 fractions, veterinary patients underwent FDG PET/CT scans at three months (FDGpost). Regression of standardized uptake values in baseline FDGpre, FLTpre and Cu-ATSMpre tumour voxels to those in FDGpost images was performed for linear, log-linear, generalized-linear and mixed-fit linear models. Goodness-of-fit in regression coefficients was assessed by R2. Hypothesis testing of coefficients over the patient population was performed. Results Multivariate linear model fits of FDGpre to FDGpost were significantly positive over the population (FDGpost~0.17 FDGpre, p=0.03), and classified slopes of RECIST non-responders and responders to be different (0.37 vs. 0.07, p=0.01). Generalized-linear model fits related FDGpre to FDGpost by a linear power law (FDGpost~FDGpre0.93, p<0.001). Univariate mixture model fits of FDGpre improved R2 from 0.17 to 0.52. Neither baseline FLT PET nor Cu-ATSM PET uptake contributed statistically significant multivariate regression coefficients. Conclusions Spatially resolved regression analysis indicates that pre-treatment FDG PET uptake is most strongly associated with three-month post-treatment FDG PET uptake in this patient population, though associations are histopathology-dependent. PMID:22682748

Linear regression analysis of survival data with missing censoring indicators.

PubMed

Wang, Qihua; Dinse, Gregg E

2011-04-01

Linear regression analysis has been studied extensively in a random censorship setting, but typically all of the censoring indicators are assumed to be observed. In this paper, we develop synthetic data methods for estimating regression parameters in a linear model when some censoring indicators are missing. We define estimators based on regression calibration, imputation, and inverse probability weighting techniques, and we prove all three estimators are asymptotically normal. The finite-sample performance of each estimator is evaluated via simulation. We illustrate our methods by assessing the effects of sex and age on the time to non-ambulatory progression for patients in a brain cancer clinical trial.

Perinatal Medical Variables Predict Executive Function within a Sample of Preschoolers Born Very Low Birth Weight

PubMed Central

Duvall, Susanne W.; Erickson, Sarah J.; MacLean, Peggy; Lowe, Jean R.

2014-01-01

The goal was to identify perinatal predictors of early executive dysfunction in preschoolers born very low birth weight. Fifty-seven preschoolers completed three executive function tasks (Dimensional Change Card Sort-Separated (inhibition, working memory and cognitive flexibility), Bear Dragon (inhibition and working memory) and Gift Delay Open (inhibition)). Relationships between executive function and perinatal medical severity factors (gestational age, days on ventilation, size for gestational age, maternal steroids and number of surgeries), and chronological age were investigated by multiple linear regression and logistic regression. Different perinatal medical severity factors were predictive of executive function tasks, with gestational age predicting Bear Dragon and Gift Open; and number of surgeries and maternal steroids predicting performance on Dimensional Change Card Sort-Separated. By understanding the relationship between perinatal medical severity factors and preschool executive outcomes, we may be able to identify children at highest risk for future executive dysfunction, thereby focusing targeted early intervention services. PMID:25117418

An Analysis of COLA (Cost of Living Adjustment) Allocation within the United States Coast Guard.

DTIC Science & Technology

1983-09-01

books Applied Linear Regression [Ref. 39], and Statistical Methods in Research and Production [Ref. 40], or any other book on regression. In the event...Indexes, Master’s Thesis, Air Force Institute of Technology, Wright-Patterson AFB, 1976. 39. Weisberg, Stanford, Applied Linear Regression , Wiley, 1980. 40

Testing hypotheses for differences between linear regression lines

Treesearch

Stanley J. Zarnoch

2009-01-01

Five hypotheses are identified for testing differences between simple linear regression lines. The distinctions between these hypotheses are based on a priori assumptions and illustrated with full and reduced models. The contrast approach is presented as an easy and complete method for testing for overall differences between the regressions and for making pairwise...

Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.

ERIC Educational Resources Information Center

Schafer, William D.; Wang, Yuh-Yin

A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

Teaching the Concept of Breakdown Point in Simple Linear Regression.

ERIC Educational Resources Information Center

Chan, Wai-Sum

2001-01-01

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

Estimating monotonic rates from biological data using local linear regression.

PubMed

Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

2017-03-01

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

Locally linear regression for pose-invariant face recognition.

PubMed

Chai, Xiujuan; Shan, Shiguang; Chen, Xilin; Gao, Wen

2007-07-01

The variation of facial appearance due to the viewpoint (/pose) degrades face recognition systems considerably, which is one of the bottlenecks in face recognition. One of the possible solutions is generating virtual frontal view from any given nonfrontal view to obtain a virtual gallery/probe face. Following this idea, this paper proposes a simple, but efficient, novel locally linear regression (LLR) method, which generates the virtual frontal view from a given nonfrontal face image. We first justify the basic assumption of the paper that there exists an approximate linear mapping between a nonfrontal face image and its frontal counterpart. Then, by formulating the estimation of the linear mapping as a prediction problem, we present the regression-based solution, i.e., globally linear regression. To improve the prediction accuracy in the case of coarse alignment, LLR is further proposed. In LLR, we first perform dense sampling in the nonfrontal face image to obtain many overlapped local patches. Then, the linear regression technique is applied to each small patch for the prediction of its virtual frontal patch. Through the combination of all these patches, the virtual frontal view is generated. The experimental results on the CMU PIE database show distinct advantage of the proposed method over Eigen light-field method.

Multi-linear regression of sea level in the south west Pacific as a first step towards local sea level projections

NASA Astrophysics Data System (ADS)

Kumar, Vandhna; Meyssignac, Benoit; Melet, Angélique; Ganachaud, Alexandre

2017-04-01

Rising sea levels are a critical concern in small island nations. The problem is especially serious in the western south Pacific, where the total sea level rise over the last 60 years is up to 3 times the global average. In this study, we attempt to reconstruct sea levels at selected sites in the region (Suva, Lautoka, Noumea - Fiji and New Caledonia) as a mutiple-linear regression of atmospheric and oceanic variables. We focus on interannual-to-decadal scale variability, and lower (including the global mean sea level rise) over the 1979-2014 period. Sea levels are taken from tide gauge records and the ORAS4 reanalysis dataset, and are expressed as a sum of steric and mass changes as a preliminary step. The key development in our methodology is using leading wind stress curl as a proxy for the thermosteric component. This is based on the knowledge that wind stress curl anomalies can modulate the thermocline depth and resultant sea levels via Rossby wave propagation. The analysis is primarily based on correlation between local sea level and selected predictors, the dominant one being wind stress curl. In the first step, proxy boxes for wind stress curl are determined via regions of highest correlation. The proportion of sea level explained via linear regression is then removed, leaving a residual. This residual is then correlated with other locally acting potential predictors: halosteric sea level, the zonal and meridional wind stress components, and sea surface temperature. The statistically significant predictors are used in a multi-linear regression function to simulate the observed sea level. The method is able to reproduce between 40 to 80% of the variance in observed sea level. Based on the skill of the model, it has high potential in sea level projection and downscaling studies.

SU-G-BRA-08: Diaphragm Motion Tracking Based On KV CBCT Projections with a Constrained Linear Regression Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, J; Chao, M

2016-06-15

Purpose: To develop a novel strategy to extract the respiratory motion of the thoracic diaphragm from kilovoltage cone beam computed tomography (CBCT) projections by a constrained linear regression optimization technique. Methods: A parabolic function was identified as the geometric model and was employed to fit the shape of the diaphragm on the CBCT projections. The search was initialized by five manually placed seeds on a pre-selected projection image. Temporal redundancies, the enabling phenomenology in video compression and encoding techniques, inherent in the dynamic properties of the diaphragm motion together with the geometrical shape of the diaphragm boundary and the associatedmore » algebraic constraint that significantly reduced the searching space of viable parabolic parameters was integrated, which can be effectively optimized by a constrained linear regression approach on the subsequent projections. The innovative algebraic constraints stipulating the kinetic range of the motion and the spatial constraint preventing any unphysical deviations was able to obtain the optimal contour of the diaphragm with minimal initialization. The algorithm was assessed by a fluoroscopic movie acquired at anteriorposterior fixed direction and kilovoltage CBCT projection image sets from four lung and two liver patients. The automatic tracing by the proposed algorithm and manual tracking by a human operator were compared in both space and frequency domains. Results: The error between the estimated and manual detections for the fluoroscopic movie was 0.54mm with standard deviation (SD) of 0.45mm, while the average error for the CBCT projections was 0.79mm with SD of 0.64mm for all enrolled patients. The submillimeter accuracy outcome exhibits the promise of the proposed constrained linear regression approach to track the diaphragm motion on rotational projection images. Conclusion: The new algorithm will provide a potential solution to rendering diaphragm motion and ultimately improving tumor motion management for radiation therapy of cancer patients.« less

Daily Suspended Sediment Discharge Prediction Using Multiple Linear Regression and Artificial Neural Network

NASA Astrophysics Data System (ADS)

Uca; Toriman, Ekhwan; Jaafar, Othman; Maru, Rosmini; Arfan, Amal; Saleh Ahmar, Ansari

2018-01-01

Prediction of suspended sediment discharge in a catchments area is very important because it can be used to evaluation the erosion hazard, management of its water resources, water quality, hydrology project management (dams, reservoirs, and irrigation) and to determine the extent of the damage that occurred in the catchments. Multiple Linear Regression analysis and artificial neural network can be used to predict the amount of daily suspended sediment discharge. Regression analysis using the least square method, whereas artificial neural networks using Radial Basis Function (RBF) and feedforward multilayer perceptron with three learning algorithms namely Levenberg-Marquardt (LM), Scaled Conjugate Descent (SCD) and Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFGS). The number neuron of hidden layer is three to sixteen, while in output layer only one neuron because only one output target. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2 ) and coefficient of efficiency (CE) of the multiple linear regression (MLRg) value Model 2 (6 input variable independent) has the lowest the value of MAE and RMSE (0.0000002 and 13.6039) and highest R2 and CE (0.9971 and 0.9971). When compared between LM, SCG and RBF, the BFGS model structure 3-7-1 is the better and more accurate to prediction suspended sediment discharge in Jenderam catchment. The performance value in testing process, MAE and RMSE (13.5769 and 17.9011) is smallest, meanwhile R2 and CE (0.9999 and 0.9998) is the highest if it compared with the another BFGS Quasi-Newton model (6-3-1, 9-10-1 and 12-12-1). Based on the performance statistics value, MLRg, LM, SCG, BFGS and RBF suitable and accurately for prediction by modeling the non-linear complex behavior of suspended sediment responses to rainfall, water depth and discharge. The comparison between artificial neural network (ANN) and MLRg, the MLRg Model 2 accurately for to prediction suspended sediment discharge (kg/day) in Jenderan catchment area.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

[Application of ordinary Kriging method in entomologic ecology].

PubMed

Zhang, Runjie; Zhou, Qiang; Chen, Cuixian; Wang, Shousong

2003-01-01

Geostatistics is a statistic method based on regional variables and using the tool of variogram to analyze the spatial structure and the patterns of organism. In simulating the variogram within a great range, though optimal simulation cannot be obtained, the simulation method of a dialogue between human and computer can be used to optimize the parameters of the spherical models. In this paper, the method mentioned above and the weighted polynomial regression were utilized to simulate the one-step spherical model, the two-step spherical model and linear function model, and the available nearby samples were used to draw on the ordinary Kriging procedure, which provided a best linear unbiased estimate of the constraint of the unbiased estimation. The sum of square deviation between the estimating and measuring values of varying theory models were figured out, and the relative graphs were shown. It was showed that the simulation based on the two-step spherical model was the best simulation, and the one-step spherical model was better than the linear function model.

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Effect of Malmquist bias on correlation studies with IRAS data base

NASA Technical Reports Server (NTRS)

Verter, Frances

1993-01-01

The relationships between galaxy properties in the sample of Trinchieri et al. (1989) are reexamined with corrections for Malmquist bias. The linear correlations are tested and linear regressions are fit for log-log plots of L(FIR), L(H-alpha), and L(B) as well as ratios of these quantities. The linear correlations for Malmquist bias are corrected using the method of Verter (1988), in which each galaxy observation is weighted by the inverse of its sampling volume. The linear regressions are corrected for Malmquist bias by a new method invented here in which each galaxy observation is weighted by its sampling volume. The results of correlation and regressions among the sample are significantly changed in the anticipated sense that the corrected correlation confidences are lower and the corrected slopes of the linear regressions are lower. The elimination of Malmquist bias eliminates the nonlinear rise in luminosity that has caused some authors to hypothesize additional components of FIR emission.

Disorganized Symptoms Predicted Worse Functioning Outcome in Schizophrenia Patients with Established Illness.

PubMed

Ortiz, Bruno Bertolucci; Gadelha, Ary; Higuchi, Cinthia Hiroko; Noto, Cristiano; Medeiros, Daiane; Pitta, José Cássio do Nascimento; de Araújo Filho, Gerardo Maria; Hallak, Jaime Eduardo Cecílio; Bressan, Rodrigo Affonseca

Most patients with schizophrenia will have subsequent relapses of the disorder, with continuous impairments in functioning. However, evidence is lacking on how symptoms influence functioning at different phases of the disease. This study aims to investigate the relationship between symptom dimensions and functioning at different phases: acute exacerbation, nonremission and remission. Patients with schizophrenia were grouped into acutely ill (n=89), not remitted (n=89), and remitted (n=69). Three exploratory stepwise linear regression analyses were performed for each phase of schizophrenia, in which the five PANSS factors and demographic variables were entered as the independent variables and the total Global Assessment of Functioning Scale (GAF) score was entered as the dependent variable. An additional exploratory stepwise logistic regression analysis was performed to predict subsequent remission at discharge in the inpatient population. The Disorganized factor was the most significant predictor for acutely ill patients (p<0.001), while the Hostility factor was the most significant for not-remitted patients and the Negative factor was the most significant for remitted patients (p=0.001 and p<0.001, respectively). In the logistic regression, the Disorganized factor score presented a significant negative association with remission (p=0.007). Higher disorganization symptoms showed the greatest impact in functioning at acute phase, and prevented patients from achieving remission, suggesting it may be a marker of symptom severity and worse outcome in schizophrenia.

A Quantitative Study of the Relationship between the Distribution of Different Types of Collagen and the Mechanical Behavior of Rabbit Medial Collateral Ligaments

PubMed Central

Wan, Chao; Hao, Zhixiu; Wen, Shizhu; Leng, Huijie

2014-01-01

The mechanical properties of ligaments are key contributors to the stability and function of musculoskeletal joints. Ligaments are generally composed of ground substance, collagen (mainly type I and III collagen), and minimal elastin fibers. However, no consensus has been reached about whether the distribution of different types of collagen correlates with the mechanical behaviors of ligaments. The main objective of this study was to determine whether the collagen type distribution is correlated with the mechanical properties of ligaments. Using axial tensile tests and picrosirius red staining-polarization observations, the mechanical behaviors and the ratios of the various types of collagen were investigated for twenty-four rabbit medial collateral ligaments from twenty-four rabbits of different ages, respectively. One-way analysis of variance was used in the comparison of the Young's modulus in the linear region of the stress-strain curves and the ratios of type I and III collagen for the specimens (the mid-substance specimens of the ligaments) with different ages. A multiple linear regression was performed using the collagen contents (the ratios of type I and III collagen) and the Young's modulus of the specimens. During the maturation of the ligaments, the type I collagen content increased, and the type III collagen content decreased. A significant and strong correlation () was identified by multiple linear regression between the collagen contents (i.e., the ratios of type I and type III collagen) and the mechanical properties of the specimens. The collagen content of ligaments might provide a new perspective for evaluating the linear modulus of global stress-strain curves for ligaments and open a new door for studying the mechanical behaviors and functions of connective tissues. PMID:25062068

A quantitative study of the relationship between the distribution of different types of collagen and the mechanical behavior of rabbit medial collateral ligaments.

PubMed

Wan, Chao; Hao, Zhixiu; Wen, Shizhu; Leng, Huijie

2014-01-01

The mechanical properties of ligaments are key contributors to the stability and function of musculoskeletal joints. Ligaments are generally composed of ground substance, collagen (mainly type I and III collagen), and minimal elastin fibers. However, no consensus has been reached about whether the distribution of different types of collagen correlates with the mechanical behaviors of ligaments. The main objective of this study was to determine whether the collagen type distribution is correlated with the mechanical properties of ligaments. Using axial tensile tests and picrosirius red staining-polarization observations, the mechanical behaviors and the ratios of the various types of collagen were investigated for twenty-four rabbit medial collateral ligaments from twenty-four rabbits of different ages, respectively. One-way analysis of variance was used in the comparison of the Young's modulus in the linear region of the stress-strain curves and the ratios of type I and III collagen for the specimens (the mid-substance specimens of the ligaments) with different ages. A multiple linear regression was performed using the collagen contents (the ratios of type I and III collagen) and the Young's modulus of the specimens. During the maturation of the ligaments, the type I collagen content increased, and the type III collagen content decreased. A significant and strong correlation (R2 = 0.839, P < 0.05) was identified by multiple linear regression between the collagen contents (i.e., the ratios of type I and type III collagen) and the mechanical properties of the specimens. The collagen content of ligaments might provide a new perspective for evaluating the linear modulus of global stress-strain curves for ligaments and open a new door for studying the mechanical behaviors and functions of connective tissues.

SOCR Analyses - an Instructional Java Web-based Statistical Analysis Toolkit.

PubMed

Chu, Annie; Cui, Jenny; Dinov, Ivo D

2009-03-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test.The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website.In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models.

A novel approach for prediction of tacrolimus blood concentration in liver transplantation patients in the intensive care unit through support vector regression.

PubMed

Van Looy, Stijn; Verplancke, Thierry; Benoit, Dominique; Hoste, Eric; Van Maele, Georges; De Turck, Filip; Decruyenaere, Johan

2007-01-01

Tacrolimus is an important immunosuppressive drug for organ transplantation patients. It has a narrow therapeutic range, toxic side effects, and a blood concentration with wide intra- and interindividual variability. Hence, it is of the utmost importance to monitor tacrolimus blood concentration, thereby ensuring clinical effect and avoiding toxic side effects. Prediction models for tacrolimus blood concentration can improve clinical care by optimizing monitoring of these concentrations, especially in the initial phase after transplantation during intensive care unit (ICU) stay. This is the first study in the ICU in which support vector machines, as a new data modeling technique, are investigated and tested in their prediction capabilities of tacrolimus blood concentration. Linear support vector regression (SVR) and nonlinear radial basis function (RBF) SVR are compared with multiple linear regression (MLR). Tacrolimus blood concentrations, together with 35 other relevant variables from 50 liver transplantation patients, were extracted from our ICU database. This resulted in a dataset of 457 blood samples, on average between 9 and 10 samples per patient, finally resulting in a database of more than 16,000 data values. Nonlinear RBF SVR, linear SVR, and MLR were performed after selection of clinically relevant input variables and model parameters. Differences between observed and predicted tacrolimus blood concentrations were calculated. Prediction accuracy of the three methods was compared after fivefold cross-validation (Friedman test and Wilcoxon signed rank analysis). Linear SVR and nonlinear RBF SVR had mean absolute differences between observed and predicted tacrolimus blood concentrations of 2.31 ng/ml (standard deviation [SD] 2.47) and 2.38 ng/ml (SD 2.49), respectively. MLR had a mean absolute difference of 2.73 ng/ml (SD 3.79). The difference between linear SVR and MLR was statistically significant (p < 0.001). RBF SVR had the advantage of requiring only 2 input variables to perform this prediction in comparison to 15 and 16 variables needed by linear SVR and MLR, respectively. This is an indication of the superior prediction capability of nonlinear SVR. Prediction of tacrolimus blood concentration with linear and nonlinear SVR was excellent, and accuracy was superior in comparison with an MLR model.

Analyzing Multilevel Data: Comparing Findings from Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2013-01-01

This study examined the differing conclusions one may come to depending upon the type of analysis chosen, hierarchical linear modeling or ordinary least squares (OLS) regression. To illustrate this point, this study examined the influences of seniors' self-reported critical thinking abilities three ways: (1) an OLS regression with the student…

The impact of global signal regression on resting state correlations: Are anti-correlated networks introduced?

PubMed Central

Murphy, Kevin; Birn, Rasmus M.; Handwerker, Daniel A.; Jones, Tyler B.; Bandettini, Peter A.

2009-01-01

Low-frequency fluctuations in fMRI signal have been used to map several consistent resting state networks in the brain. Using the posterior cingulate cortex as a seed region, functional connectivity analyses have found not only positive correlations in the default mode network but negative correlations in another resting state network related to attentional processes. The interpretation is that the human brain is intrinsically organized into dynamic, anti-correlated functional networks. Global variations of the BOLD signal are often considered nuisance effects and are commonly removed using a general linear model (GLM) technique. This global signal regression method has been shown to introduce negative activation measures in standard fMRI analyses. The topic of this paper is whether such a correction technique could be the cause of anti-correlated resting state networks in functional connectivity analyses. Here we show that, after global signal regression, correlation values to a seed voxel must sum to a negative value. Simulations also show that small phase differences between regions can lead to spurious negative correlation values. A combination breath holding and visual task demonstrates that the relative phase of global and local signals can affect connectivity measures and that, experimentally, global signal regression leads to bell-shaped correlation value distributions, centred on zero. Finally, analyses of negatively correlated networks in resting state data show that global signal regression is most likely the cause of anti-correlations. These results call into question the interpretation of negatively correlated regions in the brain when using global signal regression as an initial processing step. PMID:18976716

The impact of global signal regression on resting state correlations: are anti-correlated networks introduced?

PubMed

Murphy, Kevin; Birn, Rasmus M; Handwerker, Daniel A; Jones, Tyler B; Bandettini, Peter A

2009-02-01

Low-frequency fluctuations in fMRI signal have been used to map several consistent resting state networks in the brain. Using the posterior cingulate cortex as a seed region, functional connectivity analyses have found not only positive correlations in the default mode network but negative correlations in another resting state network related to attentional processes. The interpretation is that the human brain is intrinsically organized into dynamic, anti-correlated functional networks. Global variations of the BOLD signal are often considered nuisance effects and are commonly removed using a general linear model (GLM) technique. This global signal regression method has been shown to introduce negative activation measures in standard fMRI analyses. The topic of this paper is whether such a correction technique could be the cause of anti-correlated resting state networks in functional connectivity analyses. Here we show that, after global signal regression, correlation values to a seed voxel must sum to a negative value. Simulations also show that small phase differences between regions can lead to spurious negative correlation values. A combination breath holding and visual task demonstrates that the relative phase of global and local signals can affect connectivity measures and that, experimentally, global signal regression leads to bell-shaped correlation value distributions, centred on zero. Finally, analyses of negatively correlated networks in resting state data show that global signal regression is most likely the cause of anti-correlations. These results call into question the interpretation of negatively correlated regions in the brain when using global signal regression as an initial processing step.

Application of Multiregressive Linear Models, Dynamic Kriging Models and Neural Network Models to Predictive Maintenance of Hydroelectric Power Systems

NASA Astrophysics Data System (ADS)

Lucifredi, A.; Mazzieri, C.; Rossi, M.

2000-05-01

Since the operational conditions of a hydroelectric unit can vary within a wide range, the monitoring system must be able to distinguish between the variations of the monitored variable caused by variations of the operation conditions and those due to arising and progressing of failures and misoperations. The paper aims to identify the best technique to be adopted for the monitoring system. Three different methods have been implemented and compared. Two of them use statistical techniques: the first, the linear multiple regression, expresses the monitored variable as a linear function of the process parameters (independent variables), while the second, the dynamic kriging technique, is a modified technique of multiple linear regression representing the monitored variable as a linear combination of the process variables in such a way as to minimize the variance of the estimate error. The third is based on neural networks. Tests have shown that the monitoring system based on the kriging technique is not affected by some problems common to the other two models e.g. the requirement of a large amount of data for their tuning, both for training the neural network and defining the optimum plane for the multiple regression, not only in the system starting phase but also after a trivial operation of maintenance involving the substitution of machinery components having a direct impact on the observed variable. Or, in addition, the necessity of different models to describe in a satisfactory way the different ranges of operation of the plant. The monitoring system based on the kriging statistical technique overrides the previous difficulties: it does not require a large amount of data to be tuned and is immediately operational: given two points, the third can be immediately estimated; in addition the model follows the system without adapting itself to it. The results of the experimentation performed seem to indicate that a model based on a neural network or on a linear multiple regression is not optimal, and that a different approach is necessary to reduce the amount of work during the learning phase using, when available, all the information stored during the initial phase of the plant to build the reference baseline, elaborating, if it is the case, the raw information available. A mixed approach using the kriging statistical technique and neural network techniques could optimise the result.

The prediction of intelligence in preschool children using alternative models to regression.

PubMed

Finch, W Holmes; Chang, Mei; Davis, Andrew S; Holden, Jocelyn E; Rothlisberg, Barbara A; McIntosh, David E

2011-12-01

Statistical prediction of an outcome variable using multiple independent variables is a common practice in the social and behavioral sciences. For example, neuropsychologists are sometimes called upon to provide predictions of preinjury cognitive functioning for individuals who have suffered a traumatic brain injury. Typically, these predictions are made using standard multiple linear regression models with several demographic variables (e.g., gender, ethnicity, education level) as predictors. Prior research has shown conflicting evidence regarding the ability of such models to provide accurate predictions of outcome variables such as full-scale intelligence (FSIQ) test scores. The present study had two goals: (1) to demonstrate the utility of a set of alternative prediction methods that have been applied extensively in the natural sciences and business but have not been frequently explored in the social sciences and (2) to develop models that can be used to predict premorbid cognitive functioning in preschool children. Predictions of Stanford-Binet 5 FSIQ scores for preschool-aged children is used to compare the performance of a multiple regression model with several of these alternative methods. Results demonstrate that classification and regression trees provided more accurate predictions of FSIQ scores than does the more traditional regression approach. Implications of these results are discussed.

Boosting structured additive quantile regression for longitudinal childhood obesity data.

PubMed

Fenske, Nora; Fahrmeir, Ludwig; Hothorn, Torsten; Rzehak, Peter; Höhle, Michael

2013-07-25

Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.

Impact of the Holocaust on the Rehabilitation Outcome of Older Patients Sustaining a Hip Fracture.

PubMed

Mizrahi, Eliyahu H; Lubart, Emilia; Heymann, Anthony; Leibovitz, Arthur

2017-04-01

Holocaust survivors report a much higher prevalence of osteoporosis and fracture in the hip joint compared to those who were not Holocaust survivors. To evaluate whether being a Holocaust survivor could affect the functional outcome of hip fracture in patients 64 years of age and older undergoing rehabilitation. A retrospective cohort study compromising 140 consecutive hip fracture patients was conducted in a geriatric and rehabilitation department of a university-affiliated hospital. Being a Holocaust survivor was based on registry data. Functional outcome was assessed by the Functional Independence Measure (FIM)TM at admission and discharge from the rehabilitation ward. Data were analyzed by t-test, chi-square test, and linear regression analysis. Total and motor FIM scores at admission (P = 0.004 and P = 0.006, respectively) and total and motor FIM gain scores at discharge (P = 0.008 and P = 0.004 respectively) were significantly higher in non-Holocaust survivors compared with Holocaust survivors. A linear regression analysis showed that being a Holocaust survivor was predictive of lower total FIM scores at discharge (β = -0.17, P = 0.004). Hip fracture in Holocaust survivors showed lower total, motor FIM and gain scores at discharge compared to non-Holocaust survivor patients. These results suggest that being a Holocaust survivor could adversely affect the rehabilitation outcome following fracture of the hip and internal fixation.

Analyzing Multilevel Data: An Empirical Comparison of Parameter Estimates of Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2011-01-01

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

Computational Tools for Probing Interactions in Multiple Linear Regression, Multilevel Modeling, and Latent Curve Analysis

ERIC Educational Resources Information Center

Preacher, Kristopher J.; Curran, Patrick J.; Bauer, Daniel J.

2006-01-01

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

Determining the response of sea level to atmospheric pressure forcing using TOPEX/POSEIDON data

NASA Technical Reports Server (NTRS)

Fu, Lee-Lueng; Pihos, Greg

1994-01-01

The static response of sea level to the forcing of atmospheric pressure, the so-called inverted barometer (IB) effect, is investigated using TOPEX/POSEIDON data. This response, characterized by the rise and fall of sea level to compensate for the change of atmospheric pressure at a rate of -1 cm/mbar, is not associated with any ocean currents and hence is normally treated as an error to be removed from sea level observation. Linear regression and spectral transfer function analyses are applied to sea level and pressure to examine the validity of the IB effect. In regions outside the tropics, the regression coefficient is found to be consistently close to the theoretical value except for the regions of western boundary currents, where the mesoscale variability interferes with the IB effect. The spectral transfer function shows near IB response at periods of 30 degrees is -0.84 +/- 0.29 cm/mbar (1 standard deviation). The deviation from = 1 cm /mbar is shown to be caused primarily by the effect of wind forcing on sea level, based on multivariate linear regression model involving both pressure and wind forcing. The regression coefficient for pressure resulting from the multivariate analysis is -0.96 +/- 0.32 cm/mbar. In the tropics the multivariate analysis fails because sea level in the tropics is primarily responding to remote wind forcing. However, after removing from the data the wind-forced sea level estimated by a dynamic model of the tropical Pacific, the pressure regression coefficient improves from -1.22 +/- 0.69 cm/mbar to -0.99 +/- 0.46 cm/mbar, clearly revealing an IB response. The result of the study suggests that with a proper removal of the effect of wind forcing the IB effect is valid in most of the open ocean at periods longer than 20 days and spatial scales larger than 500 km.

Comparison of two-concentration with multi-concentration linear regressions: Retrospective data analysis of multiple regulated LC-MS bioanalytical projects.

PubMed

Musuku, Adrien; Tan, Aimin; Awaiye, Kayode; Trabelsi, Fethi

2013-09-01

Linear calibration is usually performed using eight to ten calibration concentration levels in regulated LC-MS bioanalysis because a minimum of six are specified in regulatory guidelines. However, we have previously reported that two-concentration linear calibration is as reliable as or even better than using multiple concentrations. The purpose of this research is to compare two-concentration with multiple-concentration linear calibration through retrospective data analysis of multiple bioanalytical projects that were conducted in an independent regulated bioanalytical laboratory. A total of 12 bioanalytical projects were randomly selected: two validations and two studies for each of the three most commonly used types of sample extraction methods (protein precipitation, liquid-liquid extraction, solid-phase extraction). When the existing data were retrospectively linearly regressed using only the lowest and the highest concentration levels, no extra batch failure/QC rejection was observed and the differences in accuracy and precision between the original multi-concentration regression and the new two-concentration linear regression are negligible. Specifically, the differences in overall mean apparent bias (square root of mean individual bias squares) are within the ranges of -0.3% to 0.7% and 0.1-0.7% for the validations and studies, respectively. The differences in mean QC concentrations are within the ranges of -0.6% to 1.8% and -0.8% to 2.5% for the validations and studies, respectively. The differences in %CV are within the ranges of -0.7% to 0.9% and -0.3% to 0.6% for the validations and studies, respectively. The average differences in study sample concentrations are within the range of -0.8% to 2.3%. With two-concentration linear regression, an average of 13% of time and cost could have been saved for each batch together with 53% of saving in the lead-in for each project (the preparation of working standard solutions, spiking, and aliquoting). Furthermore, examples are given as how to evaluate the linearity over the entire concentration range when only two concentration levels are used for linear regression. To conclude, two-concentration linear regression is accurate and robust enough for routine use in regulated LC-MS bioanalysis and it significantly saves time and cost as well. Copyright © 2013 Elsevier B.V. All rights reserved.

A Linear Regression and Markov Chain Model for the Arabian Horse Registry

DTIC Science & Technology

1993-04-01

as a tax deduction? Yes No T-4367 68 26. Regardless of previous equine tax deductions, do you consider your current horse activities to be... (Mark one...E L T-4367 A Linear Regression and Markov Chain Model For the Arabian Horse Registry Accesion For NTIS CRA&I UT 7 4:iC=D 5 D-IC JA" LI J:13tjlC,3 lO...the Arabian Horse Registry, which needed to forecast its future registration of purebred Arabian horses . A linear regression model was utilized to

Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study.

PubMed

Zhu, Hongxiao; Morris, Jeffrey S; Wei, Fengrong; Cox, Dennis D

2017-07-01

Many scientific studies measure different types of high-dimensional signals or images from the same subject, producing multivariate functional data. These functional measurements carry different types of information about the scientific process, and a joint analysis that integrates information across them may provide new insights into the underlying mechanism for the phenomenon under study. Motivated by fluorescence spectroscopy data in a cervical pre-cancer study, a multivariate functional response regression model is proposed, which treats multivariate functional observations as responses and a common set of covariates as predictors. This novel modeling framework simultaneously accounts for correlations between functional variables and potential multi-level structures in data that are induced by experimental design. The model is fitted by performing a two-stage linear transformation-a basis expansion to each functional variable followed by principal component analysis for the concatenated basis coefficients. This transformation effectively reduces the intra-and inter-function correlations and facilitates fast and convenient calculation. A fully Bayesian approach is adopted to sample the model parameters in the transformed space, and posterior inference is performed after inverse-transforming the regression coefficients back to the original data domain. The proposed approach produces functional tests that flag local regions on the functional effects, while controlling the overall experiment-wise error rate or false discovery rate. It also enables functional discriminant analysis through posterior predictive calculation. Analysis of the fluorescence spectroscopy data reveals local regions with differential expressions across the pre-cancer and normal samples. These regions may serve as biomarkers for prognosis and disease assessment.

A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

1976-01-01

A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

Majorization Minimization by Coordinate Descent for Concave Penalized Generalized Linear Models

PubMed Central

Jiang, Dingfeng; Huang, Jian

2013-01-01

Recent studies have demonstrated theoretical attractiveness of a class of concave penalties in variable selection, including the smoothly clipped absolute deviation and minimax concave penalties. The computation of the concave penalized solutions in high-dimensional models, however, is a difficult task. We propose a majorization minimization by coordinate descent (MMCD) algorithm for computing the concave penalized solutions in generalized linear models. In contrast to the existing algorithms that use local quadratic or local linear approximation to the penalty function, the MMCD seeks to majorize the negative log-likelihood by a quadratic loss, but does not use any approximation to the penalty. This strategy makes it possible to avoid the computation of a scaling factor in each update of the solutions, which improves the efficiency of coordinate descent. Under certain regularity conditions, we establish theoretical convergence property of the MMCD. We implement this algorithm for a penalized logistic regression model using the SCAD and MCP penalties. Simulation studies and a data example demonstrate that the MMCD works sufficiently fast for the penalized logistic regression in high-dimensional settings where the number of covariates is much larger than the sample size. PMID:25309048

Towards an Early Software Effort Estimation Based on Functional and Non-Functional Requirements

NASA Astrophysics Data System (ADS)

Kassab, Mohamed; Daneva, Maya; Ormandjieva, Olga

The increased awareness of the non-functional requirements as a key to software project and product success makes explicit the need to include them in any software project effort estimation activity. However, the existing approaches to defining size-based effort relationships still pay insufficient attention to this need. This paper presents a flexible, yet systematic approach to the early requirements-based effort estimation, based on Non-Functional Requirements ontology. It complementarily uses one standard functional size measurement model and a linear regression technique. We report on a case study which illustrates the application of our solution approach in context and also helps evaluate our experiences in using it.

Determination and importance of temperature dependence of retention coefficient (RPHPLC) in QSAR model of nitrazepams' partition coefficient in bile acid micelles.

PubMed

Posa, Mihalj; Pilipović, Ana; Lalić, Mladena; Popović, Jovan

2011-02-15

Linear dependence between temperature (t) and retention coefficient (k, reversed phase HPLC) of bile acids is obtained. Parameters (a, intercept and b, slope) of the linear function k=f(t) highly correlate with bile acids' structures. Investigated bile acids form linear congeneric groups on a principal component (calculated from k=f(t)) score plot that are in accordance with conformations of the hydroxyl and oxo groups in a bile acid steroid skeleton. Partition coefficient (K(p)) of nitrazepam in bile acids' micelles is investigated. Nitrazepam molecules incorporated in micelles show modified bioavailability (depo effect, higher permeability, etc.). Using multiple linear regression method QSAR models of nitrazepams' partition coefficient, K(p) are derived on the temperatures of 25°C and 37°C. For deriving linear regression models on both temperatures experimentally obtained lipophilicity parameters are included (PC1 from data k=f(t)) and in silico descriptors of the shape of a molecule while on the higher temperature molecular polarisation is introduced. This indicates the fact that the incorporation mechanism of nitrazepam in BA micelles changes on the higher temperatures. QSAR models are derived using partial least squares method as well. Experimental parameters k=f(t) are shown to be significant predictive variables. Both QSAR models are validated using cross validation and internal validation method. PLS models have slightly higher predictive capability than MLR models. Copyright © 2010 Elsevier B.V. All rights reserved.

A comparison of several methods of solving nonlinear regression groundwater flow problems

USGS Publications Warehouse

Cooley, Richard L.

1985-01-01

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher-Reeves method, and this was followed closely by the quasi-Newton method. The Marquardt and quasi-linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi-linearization methods than for the other two. Hence the quasi-Newton (and perhaps Fletcher-Reeves) method might be more efficient than either the Marquardt or quasi-linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi-linearization metilod for three of the four problems. For all four problems the quasi-Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher-Reeves method required slightly less memory than the quasi-Newton method. Memory requirements were not excessive for any of the four methods.

Predicting VO[subscript 2max] in College-Aged Participants Using Cycle Ergometry and Perceived Functional Ability

ERIC Educational Resources Information Center

Nielson, David E.; George, James D.; Vehrs, Pat R.; Hager, Ron L.; Webb, Carrie V.

2010-01-01

The purpose of this study was to develop a multiple linear regression model to predict treadmill VO[subscript 2max] scores using both exercise and non-exercise data. One hundred five college-aged participants (53 male, 52 female) successfully completed a submaximal cycle ergometer test and a maximal graded exercise test on a motorized treadmill.…

The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions

ERIC Educational Resources Information Center

Molenaar, Dylan; Dolan, Conor V.; de Boeck, Paul

2012-01-01

The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in…

Preliminary results on predation of gypsy moth pupae during a period of latency in Slovakia

Treesearch

Marek Turcani; Andrew M. Liebhold; Michael McManus; J& #250; lius Novotn& #253

2003-01-01

Predation of gypsy moth pupae was studied from 2000 -2003 in Slovakia. Predation on artificially reared pupae was recorded and linear regression was used to test the hypothesis that predation follows a type II vs. type III functional response. The role of pupal predation in gypsy moth population dynamics was also investigated. The relative importance of predation of...

Preliminary Survey on TRY Forest Traits and Growth Index Relations - New Challenges

NASA Astrophysics Data System (ADS)

Lyubenova, Mariyana; Kattge, Jens; van Bodegom, Peter; Chikalanov, Alexandre; Popova, Silvia; Zlateva, Plamena; Peteva, Simona

2016-04-01

Forest ecosystems provide critical ecosystem goods and services, including food, fodder, water, shelter, nutrient cycling, and cultural and recreational value. Forests also store carbon, provide habitat for a wide range of species and help alleviate land degradation and desertification. Thus they have a potentially significant role to play in climate change adaptation planning through maintaining ecosystem services and providing livelihood options. Therefore the study of forest traits is such an important issue not just for individual countries but for the planet as a whole. We need to know what functional relations between forest traits exactly can express TRY data base and haw it will be significant for the global modeling and IPBES. The study of the biodiversity characteristics at all levels and functional links between them is extremely important for the selection of key indicators for assessing biodiversity and ecosystem services for sustainable natural capital control. By comparing the available information in tree data bases: TRY, ITR (International Tree Ring) and SP-PAM the 42 tree species are selected for the traits analyses. The dependence between location characteristics (latitude, longitude, altitude, annual precipitation, annual temperature and soil type) and forest traits (specific leaf area, leaf weight ratio, wood density and growth index) is studied by by multiply regression analyses (RDA) using the statistical software package Canoco 4.5. The Pearson correlation coefficient (measure of linear correlation), Kendal rank correlation coefficient (non parametric measure of statistical dependence) and Spearman correlation coefficient (monotonic function relationship between two variables) are calculated for each pair of variables (indexes) and species. After analysis of above mentioned correlation coefficients the dimensional linear regression models, multidimensional linear and nonlinear regression models and multidimensional neural networks models are built. The strongest dependence between It and WD was obtained. The research will support the work on: Strategic Plan for Biodiversity 2011-2020, modelling and implementation of ecosystem-based approaches to climate change adaptation and disaster risk reduction. Key words: Specific leaf area (SLA), Leaf weight ratio (LWR), Wood density (WD), Growth index (It)

A diagnostic analysis of the VVP single-doppler retrieval technique

NASA Technical Reports Server (NTRS)

Boccippio, Dennis J.

1995-01-01

A diagnostic analysis of the VVP (volume velocity processing) retrieval method is presented, with emphasis on understanding the technique as a linear, multivariate regression. Similarities and differences to the velocity-azimuth display and extended velocity-azimuth display retrieval techniques are discussed, using this framework. Conventional regression diagnostics are then employed to quantitatively determine situations in which the VVP technique is likely to fail. An algorithm for preparation and analysis of a robust VVP retrieval is developed and applied to synthetic and actual datasets with high temporal and spatial resolution. A fundamental (but quantifiable) limitation to some forms of VVP analysis is inadequate sampling dispersion in the n space of the multivariate regression, manifest as a collinearity between the basis functions of some fitted parameters. Such collinearity may be present either in the definition of these basis functions or in their realization in a given sampling configuration. This nonorthogonality may cause numerical instability, variance inflation (decrease in robustness), and increased sensitivity to bias from neglected wind components. It is shown that these effects prevent the application of VVP to small azimuthal sectors of data. The behavior of the VVP regression is further diagnosed over a wide range of sampling constraints, and reasonable sector limits are established.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-07-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach was justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatland sites in Finland and a tundra site in Siberia. The flux measurements were performed using transparent chambers on vegetated surfaces and opaque chambers on bare peat surfaces. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes and even lower for longer closure times. The degree of underestimation increased with increasing CO2 flux strength and is dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Random regression models using different functions to model milk flow in dairy cows.

PubMed

Laureano, M M M; Bignardi, A B; El Faro, L; Cardoso, V L; Tonhati, H; Albuquerque, L G

2014-09-12

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included direct additive genetic, permanent environmental, and residual random effects. In addition, the contemporary group and linear and quadratic effects of cow age at calving were included as fixed effects. Fourth-order orthogonal Legendre polynomial of days in milk was used to model the mean trend in milk flow. The additive genetic and permanent environmental covariance functions were estimated using random regression Legendre polynomials and B-spline functions of days in milk. The model using a third-order Legendre polynomial for additive genetic effects and a sixth-order polynomial for permanent environmental effects, which contained 7 residual classes, proved to be the most adequate to describe variations in milk flow, and was also the most parsimonious. The heritability in milk flow estimated by the most parsimonious model was of moderate to high magnitude.

A regularization corrected score method for nonlinear regression models with covariate error.

PubMed

Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

2013-03-01

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer. Copyright © 2013, The International Biometric Society.

Inferring gene regression networks with model trees

PubMed Central

2010-01-01

Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database) is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear regressions to separate areas of the search space favoring to infer localized similarities over a more global similarity. Furthermore, experimental results show the good performance of REGNET. PMID:20950452

Genomic prediction based on data from three layer lines using non-linear regression models.

PubMed

Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L

2014-11-06

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional occurrence of large negative accuracies when the evaluated line was not included in the training dataset. Furthermore, when using a multi-line training dataset, non-linear models provided information on the genotype data that was complementary to the linear models, which indicates that the underlying data distributions of the three studied lines were indeed heterogeneous.

Living environment and mobility of older adults.

PubMed

Cress, M Elaine; Orini, Stefania; Kinsler, Laura

2011-01-01

Older adults often elect to move into smaller living environments. Smaller living space and the addition of services provided by a retirement community (RC) may make living easier for the individual, but it may also reduce the amount of daily physical activity and ultimately reduce functional ability. With home size as an independent variable, the primary purpose of this study was to evaluate daily physical activity and physical function of community dwellers (CD; n = 31) as compared to residents of an RC (n = 30). In this cross-sectional study design, assessments included: the Continuous Scale Physical Functional Performance - 10 test, with a possible range of 0-100, higher scores reflecting better function; Step Activity Monitor (StepWatch 3.1); a physical activity questionnaire, the area of the home (in square meters). Groups were compared by one-way ANOVA. A general linear regression model was used to predict the number of steps per day at home. The level of significance was p < 0.05. Of the 61 volunteers (mean age: 79 ± 6.3 years; range: 65-94 years), the RC living space (68 ± 37.7 m(2)) was 62% smaller than the CD living space (182.8 ± 77.9 m(2); p = 0.001). After correcting for age, the RC took fewer total steps per day excluding exercise (p = 0.03) and had lower function (p = 0.005) than the CD. On average, RC residents take 3,000 steps less per day and have approximately 60% of the living space of a CD. Home size and physical function were primary predictors of the number of steps taken at home, as found using a general linear regression analysis. Copyright © 2010 S. Karger AG, Basel.

What makes patients with fibromyalgia feel better? Correlations between Patient Global Impression of Improvement and changes in clinical symptoms and function: a pooled analysis of 4 randomized placebo-controlled trials of duloxetine.

PubMed

Hudson, James I; Arnold, Lesley M; Bradley, Laurence A; Choy, Ernest H S; Mease, Philip J; Wang, Fujun; Ahl, Jonna; Wohlreich, Madelaine M

2009-11-01

To investigate the relationship between changes in clinical rating scale items and endpoint Patient Global Impression of Improvement (PGI-I). Data were pooled from 4 randomized, double-blind, placebo-controlled studies of duloxetine in patients with fibromyalgia (FM). Variables included in the analyses were those that assessed symptoms in FM domains of pain, fatigue, sleep, cognitive difficulties, emotional well-being, physical function, and impact on daily living. The association of endpoint PGI-I with changes from baseline in individual variables was assessed using Pearson product-moment correlations (r). Stepwise linear regression was used to identify those variables for which changes from baseline were statistically significant independent predictors of the endpoint PGI-I ratings. Changes in pain variables and interference of symptoms with the ability to work were highly correlated (r >or= 0.5 or r

A toolbox to visually explore cerebellar shape changes in cerebellar disease and dysfunction.

PubMed

Abulnaga, S Mazdak; Yang, Zhen; Carass, Aaron; Kansal, Kalyani; Jedynak, Bruno M; Onyike, Chiadi U; Ying, Sarah H; Prince, Jerry L

2016-02-27

The cerebellum plays an important role in motor control and is also involved in cognitive processes. Cerebellar function is specialized by location, although the exact topographic functional relationship is not fully understood. The spinocerebellar ataxias are a group of neurodegenerative diseases that cause regional atrophy in the cerebellum, yielding distinct motor and cognitive problems. The ability to study the region-specific atrophy patterns can provide insight into the problem of relating cerebellar function to location. In an effort to study these structural change patterns, we developed a toolbox in MATLAB to provide researchers a unique way to visually explore the correlation between cerebellar lobule shape changes and function loss, with a rich set of visualization and analysis modules. In this paper, we outline the functions and highlight the utility of the toolbox. The toolbox takes as input landmark shape representations of subjects' cerebellar substructures. A principal component analysis is used for dimension reduction. Following this, a linear discriminant analysis and a regression analysis can be performed to find the discriminant direction associated with a specific disease type, or the regression line of a specific functional measure can be generated. The characteristic structural change pattern of a disease type or of a functional score is visualized by sampling points on the discriminant or regression line. The sampled points are used to reconstruct synthetic cerebellar lobule shapes. We showed a few case studies highlighting the utility of the toolbox and we compare the analysis results with the literature.

A toolbox to visually explore cerebellar shape changes in cerebellar disease and dysfunction

NASA Astrophysics Data System (ADS)

Abulnaga, S. Mazdak; Yang, Zhen; Carass, Aaron; Kansal, Kalyani; Jedynak, Bruno M.; Onyike, Chiadi U.; Ying, Sarah H.; Prince, Jerry L.

2016-03-01

The cerebellum plays an important role in motor control and is also involved in cognitive processes. Cerebellar function is specialized by location, although the exact topographic functional relationship is not fully understood. The spinocerebellar ataxias are a group of neurodegenerative diseases that cause regional atrophy in the cerebellum, yielding distinct motor and cognitive problems. The ability to study the region-specific atrophy patterns can provide insight into the problem of relating cerebellar function to location. In an effort to study these structural change patterns, we developed a toolbox in MATLAB to provide researchers a unique way to visually explore the correlation between cerebellar lobule shape changes and function loss, with a rich set of visualization and analysis modules. In this paper, we outline the functions and highlight the utility of the toolbox. The toolbox takes as input landmark shape representations of subjects' cerebellar substructures. A principal component analysis is used for dimension reduction. Following this, a linear discriminant analysis and a regression analysis can be performed to find the discriminant direction associated with a specific disease type, or the regression line of a specific functional measure can be generated. The characteristic structural change pattern of a disease type or of a functional score is visualized by sampling points on the discriminant or regression line. The sampled points are used to reconstruct synthetic cerebellar lobule shapes. We showed a few case studies highlighting the utility of the toolbox and we compare the analysis results with the literature.

Biostatistics Series Module 6: Correlation and Linear Regression.

PubMed

Hazra, Avijit; Gogtay, Nithya

2016-01-01

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient ( r ). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P < 0.05. A 95% confidence interval of the correlation coefficient can also be calculated for an idea of the correlation in the population. The value r 2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.

Biostatistics Series Module 6: Correlation and Linear Regression

PubMed Central

Hazra, Avijit; Gogtay, Nithya

2016-01-01

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient (r). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P < 0.05. A 95% confidence interval of the correlation coefficient can also be calculated for an idea of the correlation in the population. The value r2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation (y = a + bx), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous. PMID:27904175

Influence of age on the correlations of hematological and biochemical variables with the stability of erythrocyte membrane in relation to sodium dodecyl sulfate.

PubMed

de Freitas, Mariana V; Marquez-Bernardes, Liandra F; de Arvelos, Letícia R; Paraíso, Lara F; Gonçalves E Oliveira, Ana Flávia M; Mascarenhas Netto, Rita de C; Neto, Morun Bernardino; Garrote-Filho, Mario S; de Souza, Paulo César A; Penha-Silva, Nilson

2014-10-01

To evaluate the influence of age on the relationships between biochemical and hematological variables and stability of erythrocyte membrane in relation to the sodium dodecyl sulfate (SDS) in population of 105 female volunteers between 20 and 90 years. The stability of RBC membrane was determined by non-linear regression of the dependency of the absorbance of hemoglobin released as a function of SDS concentration, represented by the half-transition point of the curve (D50) and the variation in the concentration of the detergent to promote lysis (dD). There was an age-dependent increase in the membrane stability in relation to SDS. Analyses by multiple linear regression showed that this stability increase is significantly related to the hematological variable red cell distribution width (RDW) and the biochemical variables blood albumin and cholesterol. The positive association between erythrocyte stability and RDW may reflect one possible mechanism involved in the clinical meaning of this hematological index.

Analysis and generation of groundwater concentration time series

NASA Astrophysics Data System (ADS)

Crăciun, Maria; Vamoş, Călin; Suciu, Nicolae

2018-01-01

Concentration time series are provided by simulated concentrations of a nonreactive solute transported in groundwater, integrated over the transverse direction of a two-dimensional computational domain and recorded at the plume center of mass. The analysis of a statistical ensemble of time series reveals subtle features that are not captured by the first two moments which characterize the approximate Gaussian distribution of the two-dimensional concentration fields. The concentration time series exhibit a complex preasymptotic behavior driven by a nonstationary trend and correlated fluctuations with time-variable amplitude. Time series with almost the same statistics are generated by successively adding to a time-dependent trend a sum of linear regression terms, accounting for correlations between fluctuations around the trend and their increments in time, and terms of an amplitude modulated autoregressive noise of order one with time-varying parameter. The algorithm generalizes mixing models used in probability density function approaches. The well-known interaction by exchange with the mean mixing model is a special case consisting of a linear regression with constant coefficients.

Global and system-specific resting-state fMRI fluctuations are uncorrelated: principal component analysis reveals anti-correlated networks.

PubMed

Carbonell, Felix; Bellec, Pierre; Shmuel, Amir

2011-01-01

The influence of the global average signal (GAS) on functional-magnetic resonance imaging (fMRI)-based resting-state functional connectivity is a matter of ongoing debate. The global average fluctuations increase the correlation between functional systems beyond the correlation that reflects their specific functional connectivity. Hence, removal of the GAS is a common practice for facilitating the observation of network-specific functional connectivity. This strategy relies on the implicit assumption of a linear-additive model according to which global fluctuations, irrespective of their origin, and network-specific fluctuations are super-positioned. However, removal of the GAS introduces spurious negative correlations between functional systems, bringing into question the validity of previous findings of negative correlations between fluctuations in the default-mode and the task-positive networks. Here we present an alternative method for estimating global fluctuations, immune to the complications associated with the GAS. Principal components analysis was applied to resting-state fMRI time-series. A global-signal effect estimator was defined as the principal component (PC) that correlated best with the GAS. The mean correlation coefficient between our proposed PC-based global effect estimator and the GAS was 0.97±0.05, demonstrating that our estimator successfully approximated the GAS. In 66 out of 68 runs, the PC that showed the highest correlation with the GAS was the first PC. Since PCs are orthogonal, our method provides an estimator of the global fluctuations, which is uncorrelated to the remaining, network-specific fluctuations. Moreover, unlike the regression of the GAS, the regression of the PC-based global effect estimator does not introduce spurious anti-correlations beyond the decrease in seed-based correlation values allowed by the assumed additive model. After regressing this PC-based estimator out of the original time-series, we observed robust anti-correlations between resting-state fluctuations in the default-mode and the task-positive networks. We conclude that resting-state global fluctuations and network-specific fluctuations are uncorrelated, supporting a Resting-State Linear-Additive Model. In addition, we conclude that the network-specific resting-state fluctuations of the default-mode and task-positive networks show artifact-free anti-correlations.

Using the Coefficient of Determination "R"[superscript 2] to Test the Significance of Multiple Linear Regression

ERIC Educational Resources Information Center

Quinino, Roberto C.; Reis, Edna A.; Bessegato, Lupercio F.

2013-01-01

This article proposes the use of the coefficient of determination as a statistic for hypothesis testing in multiple linear regression based on distributions acquired by beta sampling. (Contains 3 figures.)

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

PubMed

Lin, Huiming; Fu, Bo; Qin, Guoyou; Zhu, Zhongyi

2017-12-01

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study. © 2017, The International Biometric Society.

Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

PubMed

Faul, Franz; Erdfelder, Edgar; Buchner, Axel; Lang, Albert-Georg

2009-11-01

G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

Guidelines and Procedures for Computing Time-Series Suspended-Sediment Concentrations and Loads from In-Stream Turbidity-Sensor and Streamflow Data

USGS Publications Warehouse

Rasmussen, Patrick P.; Gray, John R.; Glysson, G. Douglas; Ziegler, Andrew C.

2009-01-01

In-stream continuous turbidity and streamflow data, calibrated with measured suspended-sediment concentration data, can be used to compute a time series of suspended-sediment concentration and load at a stream site. Development of a simple linear (ordinary least squares) regression model for computing suspended-sediment concentrations from instantaneous turbidity data is the first step in the computation process. If the model standard percentage error (MSPE) of the simple linear regression model meets a minimum criterion, this model should be used to compute a time series of suspended-sediment concentrations. Otherwise, a multiple linear regression model using paired instantaneous turbidity and streamflow data is developed and compared to the simple regression model. If the inclusion of the streamflow variable proves to be statistically significant and the uncertainty associated with the multiple regression model results in an improvement over that for the simple linear model, the turbidity-streamflow multiple linear regression model should be used to compute a suspended-sediment concentration time series. The computed concentration time series is subsequently used with its paired streamflow time series to compute suspended-sediment loads by standard U.S. Geological Survey techniques. Once an acceptable regression model is developed, it can be used to compute suspended-sediment concentration beyond the period of record used in model development with proper ongoing collection and analysis of calibration samples. Regression models to compute suspended-sediment concentrations are generally site specific and should never be considered static, but they represent a set period in a continually dynamic system in which additional data will help verify any change in sediment load, type, and source.

Predicting story goodness performance from cognitive measures following traumatic brain injury.

PubMed

Lê, Karen; Coelho, Carl; Mozeiko, Jennifer; Krueger, Frank; Grafman, Jordan

2012-05-01

This study examined the prediction of performance on measures of the Story Goodness Index (SGI; Lê, Coelho, Mozeiko, & Grafman, 2011) from executive function (EF) and memory measures following traumatic brain injury (TBI). It was hypothesized that EF and memory measures would significantly predict SGI outcomes. One hundred sixty-seven individuals with TBI participated in the study. Story retellings were analyzed using the SGI protocol. Three cognitive measures--Delis-Kaplan Executive Function System (D-KEFS; Delis, Kaplan, & Kramer, 2001) Sorting Test, Wechsler Memory Scale--Third Edition (WMS-III; Wechsler, 1997) Working Memory Primary Index (WMI), and WMS-III Immediate Memory Primary Index (IMI)--were entered into a multiple linear regression model for each discourse measure. Two sets of regression analyses were performed, the first with the Sorting Test as the first predictor and the second with it as the last. The first set of regression analyses identified the Sorting Test and IMI as the only significant predictors of performance on measures of the SGI. The second set identified all measures as significant predictors when evaluating each step of the regression function. The cognitive variables predicted performance on the SGI measures, although there were differences in the amount of explained variance. The results (a) suggest that storytelling ability draws on a number of underlying skills and (b) underscore the importance of using discrete cognitive tasks rather than broad cognitive indices to investigate the cognitive substrates of discourse.

The observation-based relationships between PM2.5 and AOD over China

NASA Astrophysics Data System (ADS)

Xin, Jinyuan; Gong, Chongshui; Liu, Zirui; Cong, Zhiyuan; Gao, Wenkang; Song, Tao; Pan, Yuepeng; Sun, Yang; Ji, Dongsheng; Wang, Lili; Tang, Guiqian; Wang, Yuesi

2016-09-01

This is the first investigation of the generalized linear regressions of PM2.5 and aerosol optical depth (AOD) with the Campaign on atmospheric Aerosol Research-China network over the large high-concentration aerosol region during the period from 2012 to 2013. The map of the PM2.5 and AOD levels showed large spatial differences in the aerosol concentrations and aerosol optical properties over China. The ranges of the annual mean PM2.5 and AOD were 10-117 µg/m3 and 0.12-1.11 from the clean regions to seriously polluted regions, from the almost "arctic" and the Tibetan Plateau to tropical environments. There were significant spatial agreements and correlations between the PM2.5 and AOD. However, the linear regression functions (PM2.5 = A*AOD + B) exhibited large differences in different regions and seasons. The slopes (A) were from 13 to 90, the intercepts (B) were from 0.8 to 33.3, and the correlation coefficients (R2) ranged from 0.06 to 0.75. The slopes (A) were much higher in the north (41-99) than in the south (13-64) because the extinction efficiency of hygroscopic aerosol was rapidly increasing with the increasing humidity from the dry north to the humid south. Meanwhile, the intercepts (B) were generally lower, and the correlation coefficients (R2) were much higher in the dry north than in the humid south. There was high consistency of AOD versus PM2.5 for all sites in three ranges of the atmospheric column precipitable water vapor (PWV). The segmented linear regression functions were y = 84.66x + 9.85 (PWV < 1.0), y = 69.47x + 11.87 (1.0 < PWV < 2.5), and y = 52.37x + 8.59 (PWV > 2.5). The correlation coefficients (R2) were high from 0.64 to 0.70 across China.

Extreme wind-wave modeling and analysis in the south Atlantic ocean

NASA Astrophysics Data System (ADS)

Campos, R. M.; Alves, J. H. G. M.; Guedes Soares, C.; Guimaraes, L. G.; Parente, C. E.

2018-04-01

A set of wave hindcasts is constructed using two different types of wind calibration, followed by an additional test retuning the input source term Sin in the wave model. The goal is to improve the simulation in extreme wave events in the South Atlantic Ocean without compromising average conditions. Wind fields are based on Climate Forecast System Reanalysis (CFSR/NCEP). The first wind calibration applies a simple linear regression model, with coefficients obtained from the comparison of CFSR against buoy data. The second is a method where deficiencies of the CFSR associated with severe sea state events are remedied, whereby "defective" winds are replaced with satellite data within cyclones. A total of six wind datasets forced WAVEWATCH-III and additional three tests with modified Sin in WAVEWATCH III lead to a total of nine wave hindcasts that are evaluated against satellite and buoy data for ambient and extreme conditions. The target variable considered is the significant wave height (Hs). The increase of sea-state severity shows a progressive increase of the hindcast underestimation which could be calculated as a function of percentiles. The wind calibration using a linear regression function shows similar results to the adjustments to Sin term (increase of βmax parameter) in WAVEWATCH-III - it effectively reduces the average bias of Hs but cannot avoid the increase of errors with percentiles. The use of blended scatterometer winds within cyclones could reduce the increasing wave hindcast errors mainly above the 93rd percentile and leads to a better representation of Hs at the peak of the storms. The combination of linear regression calibration of non-cyclonic winds with scatterometer winds within the cyclones generated a wave hindcast with small errors from calm to extreme conditions. This approach led to a reduction of the percentage error of Hs from 14% to less than 8% for extreme waves, while also improving the RMSE.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

GIS Tools to Estimate Average Annual Daily Traffic

DOT National Transportation Integrated Search

2012-06-01

This project presents five tools that were created for a geographical information system to estimate Annual Average Daily : Traffic using linear regression. Three of the tools can be used to prepare spatial data for linear regression. One tool can be...

Estimating extent of mortality associated with the Douglas-fir beetle in the Central and Northern Rockies

Treesearch

Jose F. Negron; Willis C. Schaupp; Kenneth E. Gibson; John Anhold; Dawn Hansen; Ralph Thier; Phil Mocettini

1999-01-01

Data collected from Douglas-fir stands infected by the Douglas-fir beetle in Wyoming, Montana, Idaho, and Utah, were used to develop models to estimate amount of mortality in terms of basal area killed. Models were built using stepwise linear regression and regression tree approaches. Linear regression models using initial Douglas-fir basal area were built for all...

[Prediction model of health workforce and beds in county hospitals of Hunan by multiple linear regression].

PubMed

Ling, Ru; Liu, Jiawang

2011-12-01

To construct prediction model for health workforce and hospital beds in county hospitals of Hunan by multiple linear regression. We surveyed 16 counties in Hunan with stratified random sampling according to uniform questionnaires,and multiple linear regression analysis with 20 quotas selected by literature view was done. Independent variables in the multiple linear regression model on medical personnels in county hospitals included the counties' urban residents' income, crude death rate, medical beds, business occupancy, professional equipment value, the number of devices valued above 10 000 yuan, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, and utilization rate of hospital beds. Independent variables in the multiple linear regression model on county hospital beds included the the population of aged 65 and above in the counties, disposable income of urban residents, medical personnel of medical institutions in county area, business occupancy, the total value of professional equipment, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, utilization rate of hospital beds, and length of hospitalization. The prediction model shows good explanatory and fitting, and may be used for short- and mid-term forecasting.

A new approach to correct the QT interval for changes in heart rate using a nonparametric regression model in beagle dogs.

PubMed

Watanabe, Hiroyuki; Miyazaki, Hiroyasu

2006-01-01

Over- and/or under-correction of QT intervals for changes in heart rate may lead to misleading conclusions and/or masking the potential of a drug to prolong the QT interval. This study examines a nonparametric regression model (Loess Smoother) to adjust the QT interval for differences in heart rate, with an improved fitness over a wide range of heart rates. 240 sets of (QT, RR) observations collected from each of 8 conscious and non-treated beagle dogs were used as the materials for investigation. The fitness of the nonparametric regression model to the QT-RR relationship was compared with four models (individual linear regression, common linear regression, and Bazett's and Fridericia's correlation models) with reference to Akaike's Information Criterion (AIC). Residuals were visually assessed. The bias-corrected AIC of the nonparametric regression model was the best of the models examined in this study. Although the parametric models did not fit, the nonparametric regression model improved the fitting at both fast and slow heart rates. The nonparametric regression model is the more flexible method compared with the parametric method. The mathematical fit for linear regression models was unsatisfactory at both fast and slow heart rates, while the nonparametric regression model showed significant improvement at all heart rates in beagle dogs.

Predicting location of recurrence using FDG, FLT, and Cu-ATSM PET in canine sinonasal tumors treated with radiotherapy

NASA Astrophysics Data System (ADS)

Bradshaw, Tyler; Fu, Rau; Bowen, Stephen; Zhu, Jun; Forrest, Lisa; Jeraj, Robert

2015-07-01

Dose painting relies on the ability of functional imaging to identify resistant tumor subvolumes to be targeted for additional boosting. This work assessed the ability of FDG, FLT, and Cu-ATSM PET imaging to predict the locations of residual FDG PET in canine tumors following radiotherapy. Nineteen canines with spontaneous sinonasal tumors underwent PET/CT imaging with radiotracers FDG, FLT, and Cu-ATSM prior to hypofractionated radiotherapy. Therapy consisted of 10 fractions of 4.2 Gy to the sinonasal cavity with or without an integrated boost of 0.8 Gy to the GTV. Patients had an additional FLT PET/CT scan after fraction 2, a Cu-ATSM PET/CT scan after fraction 3, and follow-up FDG PET/CT scans after radiotherapy. Following image registration, simple and multiple linear and logistic voxel regressions were performed to assess how well pre- and mid-treatment PET imaging predicted post-treatment FDG uptake. R2 and pseudo R2 were used to assess the goodness of fits. For simple linear regression models, regression coefficients for all pre- and mid-treatment PET images were significantly positive across the population (P < 0.05). However, there was large variability among patients in goodness of fits: R2 ranged from 0.00 to 0.85, with a median of 0.12. Results for logistic regression models were similar. Multiple linear regression models resulted in better fits (median R2 = 0.31), but there was still large variability between patients in R2. The R2 from regression models for different predictor variables were highly correlated across patients (R ≈ 0.8), indicating tumors that were poorly predicted with one tracer were also poorly predicted by other tracers. In conclusion, the high inter-patient variability in goodness of fits indicates that PET was able to predict locations of residual tumor in some patients, but not others. This suggests not all patients would be good candidates for dose painting based on a single biological target.

Predicting location of recurrence using FDG, FLT, and Cu-ATSM PET in canine sinonasal tumors treated with radiotherapy.

PubMed

Bradshaw, Tyler; Fu, Rau; Bowen, Stephen; Zhu, Jun; Forrest, Lisa; Jeraj, Robert

2015-07-07

Dose painting relies on the ability of functional imaging to identify resistant tumor subvolumes to be targeted for additional boosting. This work assessed the ability of FDG, FLT, and Cu-ATSM PET imaging to predict the locations of residual FDG PET in canine tumors following radiotherapy. Nineteen canines with spontaneous sinonasal tumors underwent PET/CT imaging with radiotracers FDG, FLT, and Cu-ATSM prior to hypofractionated radiotherapy. Therapy consisted of 10 fractions of 4.2 Gy to the sinonasal cavity with or without an integrated boost of 0.8 Gy to the GTV. Patients had an additional FLT PET/CT scan after fraction 2, a Cu-ATSM PET/CT scan after fraction 3, and follow-up FDG PET/CT scans after radiotherapy. Following image registration, simple and multiple linear and logistic voxel regressions were performed to assess how well pre- and mid-treatment PET imaging predicted post-treatment FDG uptake. R(2) and pseudo R(2) were used to assess the goodness of fits. For simple linear regression models, regression coefficients for all pre- and mid-treatment PET images were significantly positive across the population (P < 0.05). However, there was large variability among patients in goodness of fits: R(2) ranged from 0.00 to 0.85, with a median of 0.12. Results for logistic regression models were similar. Multiple linear regression models resulted in better fits (median R(2) = 0.31), but there was still large variability between patients in R(2). The R(2) from regression models for different predictor variables were highly correlated across patients (R ≈ 0.8), indicating tumors that were poorly predicted with one tracer were also poorly predicted by other tracers. In conclusion, the high inter-patient variability in goodness of fits indicates that PET was able to predict locations of residual tumor in some patients, but not others. This suggests not all patients would be good candidates for dose painting based on a single biological target.

Linear regression analysis: part 14 of a series on evaluation of scientific publications.

PubMed

Schneider, Astrid; Hommel, Gerhard; Blettner, Maria

2010-11-01

Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately. The performance and interpretation of linear regression analysis are subject to a variety of pitfalls, which are discussed here in detail. The reader is made aware of common errors of interpretation through practical examples. Both the opportunities for applying linear regression analysis and its limitations are presented.

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

PubMed

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation. Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Prediction of monthly rainfall in Victoria, Australia: Clusterwise linear regression approach

NASA Astrophysics Data System (ADS)

Bagirov, Adil M.; Mahmood, Arshad; Barton, Andrew

2017-05-01

This paper develops the Clusterwise Linear Regression (CLR) technique for prediction of monthly rainfall. The CLR is a combination of clustering and regression techniques. It is formulated as an optimization problem and an incremental algorithm is designed to solve it. The algorithm is applied to predict monthly rainfall in Victoria, Australia using rainfall data with five input meteorological variables over the period of 1889-2014 from eight geographically diverse weather stations. The prediction performance of the CLR method is evaluated by comparing observed and predicted rainfall values using four measures of forecast accuracy. The proposed method is also compared with the CLR using the maximum likelihood framework by the expectation-maximization algorithm, multiple linear regression, artificial neural networks and the support vector machines for regression models using computational results. The results demonstrate that the proposed algorithm outperforms other methods in most locations.

Prediction system of hydroponic plant growth and development using algorithm Fuzzy Mamdani method

NASA Astrophysics Data System (ADS)

Sudana, I. Made; Purnawirawan, Okta; Arief, Ulfa Mediaty

2017-03-01

Hydroponics is a method of farming without soil. One of the Hydroponic plants is Watercress (Nasturtium Officinale). The development and growth process of hydroponic Watercress was influenced by levels of nutrients, acidity and temperature. The independent variables can be used as input variable system to predict the value level of plants growth and development. The prediction system is using Fuzzy Algorithm Mamdani method. This system was built to implement the function of Fuzzy Inference System (Fuzzy Inference System/FIS) as a part of the Fuzzy Logic Toolbox (FLT) by using MATLAB R2007b. FIS is a computing system that works on the principle of fuzzy reasoning which is similar to humans' reasoning. Basically FIS consists of four units which are fuzzification unit, fuzzy logic reasoning unit, base knowledge unit and defuzzification unit. In addition to know the effect of independent variables on the plants growth and development that can be visualized with the function diagram of FIS output surface that is shaped three-dimensional, and statistical tests based on the data from the prediction system using multiple linear regression method, which includes multiple linear regression analysis, T test, F test, the coefficient of determination and donations predictor that are calculated using SPSS (Statistical Product and Service Solutions) software applications.

Relationship between Gender Roles and Sexual Assertiveness in Married Women.

PubMed

Azmoude, Elham; Firoozi, Mahbobe; Sadeghi Sahebzad, Elahe; Asgharipour, Neghar

2016-10-01

Evidence indicates that sexual assertiveness is one of the important factors affecting sexual satisfaction. According to some studies, traditional gender norms conflict with women's capability in expressing sexual desires. This study examined the relationship between gender roles and sexual assertiveness in married women in Mashhad, Iran. This cross-sectional study was conducted on 120 women who referred to Mashhad health centers through convenient sampling in 2014-15. Data were collected using Bem Sex Role Inventory (BSRI) and Hulbert index of sexual assertiveness. Data were analyzed using SPSS 16 by Pearson and Spearman's correlation tests and linear Regression Analysis. The mean scores of sexual assertiveness was 54.93±13.20. According to the findings, there was non-significant correlation between Femininity and masculinity score with sexual assertiveness (P=0.069 and P=0.080 respectively). Linear regression analysis indicated that among the predictor variables, only Sexual function satisfaction was identified as the sexual assertiveness summary predictor variables (P=0.001). Based on the results, sexual assertiveness in married women does not comply with gender role, but it is related to Sexual function satisfaction. So, counseling psychologists need to consider this variable when designing intervention programs for modifying sexual assertiveness and find other variables that affect sexual assertiveness.

Plasma amino acid profile associated with fatty liver disease and co-occurrence of metabolic risk factors.

PubMed

Yamakado, Minoru; Tanaka, Takayuki; Nagao, Kenji; Imaizumi, Akira; Komatsu, Michiharu; Daimon, Takashi; Miyano, Hiroshi; Tani, Mizuki; Toda, Akiko; Yamamoto, Hiroshi; Horimoto, Katsuhisa; Ishizaka, Yuko

2017-11-03

Fatty liver disease (FLD) increases the risk of diabetes, cardiovascular disease, and steatohepatitis, which leads to fibrosis, cirrhosis, and hepatocellular carcinoma. Thus, the early detection of FLD is necessary. We aimed to find a quantitative and feasible model for discriminating the FLD, based on plasma free amino acid (PFAA) profiles. We constructed models of the relationship between PFAA levels in 2,000 generally healthy Japanese subjects and the diagnosis of FLD by abdominal ultrasound scan by multiple logistic regression analysis with variable selection. The performance of these models for FLD discrimination was validated using an independent data set of 2,160 subjects. The generated PFAA-based model was able to identify FLD patients. The area under the receiver operating characteristic curve for the model was 0.83, which was higher than those of other existing liver function-associated markers ranging from 0.53 to 0.80. The value of the linear discriminant in the model yielded the adjusted odds ratio (with 95% confidence intervals) for a 1 standard deviation increase of 2.63 (2.14-3.25) in the multiple logistic regression analysis with known liver function-associated covariates. Interestingly, the linear discriminant values were significantly associated with the progression of FLD, and patients with nonalcoholic steatohepatitis also exhibited higher values.

A Tutorial on Multilevel Survival Analysis: Methods, Models and Applications

PubMed Central

Austin, Peter C.

2017-01-01

Summary Data that have a multilevel structure occur frequently across a range of disciplines, including epidemiology, health services research, public health, education and sociology. We describe three families of regression models for the analysis of multilevel survival data. First, Cox proportional hazards models with mixed effects incorporate cluster-specific random effects that modify the baseline hazard function. Second, piecewise exponential survival models partition the duration of follow-up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval. This is equivalent to a Poisson regression model that incorporates the duration of exposure within each interval. By incorporating cluster-specific random effects, generalised linear mixed models can be used to analyse these data. Third, after partitioning the duration of follow-up into mutually exclusive intervals, one can use discrete time survival models that use a complementary log–log generalised linear model to model the occurrence of the outcome of interest within each interval. Random effects can be incorporated to account for within-cluster homogeneity in outcomes. We illustrate the application of these methods using data consisting of patients hospitalised with a heart attack. We illustrate the application of these methods using three statistical programming languages (R, SAS and Stata). PMID:29307954

Relationship between Gender Roles and Sexual Assertiveness in Married Women

PubMed Central

Azmoude, Elham; Firoozi, Mahbobe; Sadeghi Sahebzad, Elahe; Asgharipour, Neghar

2016-01-01

ABSTRACT Background: Evidence indicates that sexual assertiveness is one of the important factors affecting sexual satisfaction. According to some studies, traditional gender norms conflict with women’s capability in expressing sexual desires. This study examined the relationship between gender roles and sexual assertiveness in married women in Mashhad, Iran. Methods: This cross-sectional study was conducted on 120 women who referred to Mashhad health centers through convenient sampling in 2014-15. Data were collected using Bem Sex Role Inventory (BSRI) and Hulbert index of sexual assertiveness. Data were analyzed using SPSS 16 by Pearson and Spearman’s correlation tests and linear Regression Analysis. Results: The mean scores of sexual assertiveness was 54.93±13.20. According to the findings, there was non-significant correlation between Femininity and masculinity score with sexual assertiveness (P=0.069 and P=0.080 respectively). Linear regression analysis indicated that among the predictor variables, only Sexual function satisfaction was identified as the sexual assertiveness summary predictor variables (P=0.001). Conclusion: Based on the results, sexual assertiveness in married women does not comply with gender role, but it is related to Sexual function satisfaction. So, counseling psychologists need to consider this variable when designing intervention programs for modifying sexual assertiveness and find other variables that affect sexual assertiveness. PMID:27713899

A Tutorial on Multilevel Survival Analysis: Methods, Models and Applications.

PubMed

Austin, Peter C

2017-08-01

Data that have a multilevel structure occur frequently across a range of disciplines, including epidemiology, health services research, public health, education and sociology. We describe three families of regression models for the analysis of multilevel survival data. First, Cox proportional hazards models with mixed effects incorporate cluster-specific random effects that modify the baseline hazard function. Second, piecewise exponential survival models partition the duration of follow-up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval. This is equivalent to a Poisson regression model that incorporates the duration of exposure within each interval. By incorporating cluster-specific random effects, generalised linear mixed models can be used to analyse these data. Third, after partitioning the duration of follow-up into mutually exclusive intervals, one can use discrete time survival models that use a complementary log-log generalised linear model to model the occurrence of the outcome of interest within each interval. Random effects can be incorporated to account for within-cluster homogeneity in outcomes. We illustrate the application of these methods using data consisting of patients hospitalised with a heart attack. We illustrate the application of these methods using three statistical programming languages (R, SAS and Stata).

A Unified and Comprehensible View of Parametric and Kernel Methods for Genomic Prediction with Application to Rice.

PubMed

Jacquin, Laval; Cao, Tuong-Vi; Ahmadi, Nourollah

2016-01-01

One objective of this study was to provide readers with a clear and unified understanding of parametric statistical and kernel methods, used for genomic prediction, and to compare some of these in the context of rice breeding for quantitative traits. Furthermore, another objective was to provide a simple and user-friendly R package, named KRMM, which allows users to perform RKHS regression with several kernels. After introducing the concept of regularized empirical risk minimization, the connections between well-known parametric and kernel methods such as Ridge regression [i.e., genomic best linear unbiased predictor (GBLUP)] and reproducing kernel Hilbert space (RKHS) regression were reviewed. Ridge regression was then reformulated so as to show and emphasize the advantage of the kernel "trick" concept, exploited by kernel methods in the context of epistatic genetic architectures, over parametric frameworks used by conventional methods. Some parametric and kernel methods; least absolute shrinkage and selection operator (LASSO), GBLUP, support vector machine regression (SVR) and RKHS regression were thereupon compared for their genomic predictive ability in the context of rice breeding using three real data sets. Among the compared methods, RKHS regression and SVR were often the most accurate methods for prediction followed by GBLUP and LASSO. An R function which allows users to perform RR-BLUP of marker effects, GBLUP and RKHS regression, with a Gaussian, Laplacian, polynomial or ANOVA kernel, in a reasonable computation time has been developed. Moreover, a modified version of this function, which allows users to tune kernels for RKHS regression, has also been developed and parallelized for HPC Linux clusters. The corresponding KRMM package and all scripts have been made publicly available.

New robust statistical procedures for the polytomous logistic regression models.

PubMed

Castilla, Elena; Ghosh, Abhik; Martin, Nirian; Pardo, Leandro

2018-05-17

This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications. © 2018, The International Biometric Society.

Application of artificial neural network to fMRI regression analysis.

PubMed

Misaki, Masaya; Miyauchi, Satoru

2006-01-15

We used an artificial neural network (ANN) to detect correlations between event sequences and fMRI (functional magnetic resonance imaging) signals. The layered feed-forward neural network, given a series of events as inputs and the fMRI signal as a supervised signal, performed a non-linear regression analysis. This type of ANN is capable of approximating any continuous function, and thus this analysis method can detect any fMRI signals that correlated with corresponding events. Because of the flexible nature of ANNs, fitting to autocorrelation noise is a problem in fMRI analyses. We avoided this problem by using cross-validation and an early stopping procedure. The results showed that the ANN could detect various responses with different time courses. The simulation analysis also indicated an additional advantage of ANN over non-parametric methods in detecting parametrically modulated responses, i.e., it can detect various types of parametric modulations without a priori assumptions. The ANN regression analysis is therefore beneficial for exploratory fMRI analyses in detecting continuous changes in responses modulated by changes in input values.

Efficient robust doubly adaptive regularized regression with applications.

PubMed

Karunamuni, Rohana J; Kong, Linglong; Tu, Wei

2018-01-01

We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robustness. Furthermore, the proposed procedure satisfies the oracle properties. The new procedure is designed to achieve sparse and robust solutions by imposing adaptive weights on both the decision loss and the penalty function. The proposed method of estimation and variable selection attains full efficiency when the model is correct and, at the same time, achieves maximum robustness when outliers are present. We examine the robustness properties using the finite-sample breakdown point and an influence function. We show that the proposed estimator attains the maximum breakdown point. Furthermore, there is no loss in efficiency when there are no outliers or the error distribution is normal. For practical implementation of the proposed method, we present a computational algorithm. We examine the finite-sample and robustness properties using Monte Carlo studies. Two datasets are also analyzed.

Nonparametric methods for drought severity estimation at ungauged sites

NASA Astrophysics Data System (ADS)

Sadri, S.; Burn, D. H.

2012-12-01

The objective in frequency analysis is, given extreme events such as drought severity or duration, to estimate the relationship between that event and the associated return periods at a catchment. Neural networks and other artificial intelligence approaches in function estimation and regression analysis are relatively new techniques in engineering, providing an attractive alternative to traditional statistical models. There are, however, few applications of neural networks and support vector machines in the area of severity quantile estimation for drought frequency analysis. In this paper, we compare three methods for this task: multiple linear regression, radial basis function neural networks, and least squares support vector regression (LS-SVR). The area selected for this study includes 32 catchments in the Canadian Prairies. From each catchment drought severities are extracted and fitted to a Pearson type III distribution, which act as observed values. For each method-duration pair, we use a jackknife algorithm to produce estimated values at each site. The results from these three approaches are compared and analyzed, and it is found that LS-SVR provides the best quantile estimates and extrapolating capacity.

Comparison of a Classical and Quantum Based Restricted Boltzmann Machine (RBM) for Application to Non-linear Multivariate Regression.

NASA Astrophysics Data System (ADS)

Dorband, J. E.; Tilak, N.; Radov, A.

2016-12-01

In this paper, a classical computer implementation of RBM is compared to a quantum annealing based RBM running on a D-Wave 2X (an adiabatic quantum computer). The codes for both are essentially identical. Only a flag is set to change the activation function from a classically computed logistic function to the D-Wave. To obtain greater understanding of the behavior of the D-Wave, a study of the stochastic properties of a virtual qubit (a 12 qubit chain) and a cell of qubits (an 8 qubit cell) was performed. We will present the results of comparing the D-Wave implementation with a theoretically errorless adiabatic quantum computer. The main purpose of this study is to develop a generic RBM regression tool in order to infer CO2 fluxes from the NASA satellite OCO-2 observed CO2 concentrations and predicted atmospheric states using regression models. The carbon fluxes will then be assimilated into a land surface model to predict the Net Ecosystem Exchange at globally distributed regional sites.

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Scoring and staging systems using cox linear regression modeling and recursive partitioning.

PubMed

Lee, J W; Um, S H; Lee, J B; Mun, J; Cho, H

2006-01-01

Scoring and staging systems are used to determine the order and class of data according to predictors. Systems used for medical data, such as the Child-Turcotte-Pugh scoring and staging systems for ordering and classifying patients with liver disease, are often derived strictly from physicians' experience and intuition. We construct objective and data-based scoring/staging systems using statistical methods. We consider Cox linear regression modeling and recursive partitioning techniques for censored survival data. In particular, to obtain a target number of stages we propose cross-validation and amalgamation algorithms. We also propose an algorithm for constructing scoring and staging systems by integrating local Cox linear regression models into recursive partitioning, so that we can retain the merits of both methods such as superior predictive accuracy, ease of use, and detection of interactions between predictors. The staging system construction algorithms are compared by cross-validation evaluation of real data. The data-based cross-validation comparison shows that Cox linear regression modeling is somewhat better than recursive partitioning when there are only continuous predictors, while recursive partitioning is better when there are significant categorical predictors. The proposed local Cox linear recursive partitioning has better predictive accuracy than Cox linear modeling and simple recursive partitioning. This study indicates that integrating local linear modeling into recursive partitioning can significantly improve prediction accuracy in constructing scoring and staging systems.

Factors associated to quality of life in active elderly.

PubMed

Alexandre, Tiago da Silva; Cordeiro, Renata Cereda; Ramos, Luiz Roberto

2009-08-01

To analyze whether quality of life in active, healthy elderly individuals is influenced by functional status and sociodemographic characteristics, as well as psychological parameters. Study conducted in a sample of 120 active elderly subjects recruited from two open universities of the third age in the cities of São Paulo and São José dos Campos (Southeastern Brazil) between May 2005 and April 2006. Quality of life was measured using the abbreviated Brazilian version of the World Health Organization Quality of Live (WHOQOL-bref) questionnaire. Sociodemographic, clinical and functional variables were measured through crossculturally validated assessments by the Mini Mental State Examination, Geriatric Depression Scale, Functional Reach, One-Leg Balance Test, Timed Up and Go Test, Six-Minute Walk Test, Human Activity Profile and a complementary questionnaire. Simple descriptive analyses, Pearson's correlation coefficient, Student's t-test for non-related samples, analyses of variance, linear regression analyses and variance inflation factor were performed. The significance level for all statistical tests was set at 0.05. Linear regression analysis showed an independent correlation without colinearity between depressive symptoms measured by the Geriatric Depression Scale and four domains of the WHOQOL-bref. Not having a conjugal life implied greater perception in the social domain; developing leisure activities and having an income over five minimum wages implied greater perception in the environment domain. Functional status had no influence on the Quality of Life variable in the analysis models in active elderly. In contrast, psychological factors, as assessed by the Geriatric Depression Scale, and sociodemographic characteristics, such as marital status, income and leisure activities, had an impact on quality of life.

Association of sweat chloride concentration at time of diagnosis and CFTR genotype with mortality and cystic fibrosis phenotype.

PubMed

McKone, Edward F; Velentgas, Priscilla; Swenson, Anna J; Goss, Christopher H

2015-09-01

The extent to which sweat chloride concentration predicts survival and clinical phenotype independently of CFTR genotype in cystic fibrosis is not well understood. We analyzed the US Cystic Fibrosis Foundation Patient Registry data using Cox regression to examine the relationship between sweat chloride concentration (<60, 60-<80, ≥80mmol/L), CFTR genotype (high and lower risk for lung function decline), and survival and mixed linear regression to examine the relationship between sweat chloride, CFTR genotype, and measures of lung function and growth. When included in the same model, CFTR genotype, but not sweat chloride, was independently associated with survival and with lung function, height, and BMI. Among patients with unclassified CFTR genotype, sweat chloride was an independent predictor of survival (<60 HR 0.53 [0.37, 0.77], 60-<80 0.51 [0.42, 0.63]). Sweat chloride concentration may be a useful predictor of mortality and clinical phenotype when CFTR genotype functional class is unclassified. Copyright © 2015 European Cystic Fibrosis Society. Published by Elsevier B.V. All rights reserved.

Preoperative determinant of early postoperative renal function following radical cystectomy and intestinal urinary diversion.

PubMed

Gondo, Tatsuo; Ohno, Yoshio; Nakashima, Jun; Hashimoto, Takeshi; Nakagami, Yoshihiro; Tachibana, Masaaki

2017-02-01

To identify preoperative factors correlated with postoperative early renal function in patients who had undergone radical cystectomy (RC) and intestinal urinary diversion. We retrospectively identified 201 consecutive bladder cancer patients without distant metastasis who had undergone RC at our institution between 2003 and 2012. The estimated glomerular filtration rate (eGFR) was calculated using the modified Chronic Kidney Disease Epidemiology equation before RC and 3 months following RC. Univariate and stepwise multiple linear regression analyses were applied to estimate postoperative renal function and to identify significant preoperative predictors of postoperative renal function. Patients who had undergone intestinal urinary diversion and were available for the collection of follow-up data (n = 164) were eligible for the present study. Median preoperative and postoperative eGFRs were 69.7 (interquartile range [IQR] 56.3-78.0) and 70.7 (IQR 57.3-78.1), respectively. In univariate analyses, age, preoperative proteinuria, thickness of abdominal subcutaneous fat tissue (TSF), preoperative serum creatinine level, preoperative eGFR, and urinary diversion type were significantly associated with postoperative eGFR. In a stepwise multiple linear regression analysis, preoperative eGFR, age, and TSF were significant factors for predicting postoperative eGFR (p < 0.001, p = 0.02, and p = 0.046, respectively). The estimated postoperative eGFRs correlated well with the actual postoperative eGFRs (r = 0.65, p < 0.001). Preoperative eGFR, age, and TSF were independent preoperative factors for determining postoperative renal function in patients who had undergone RC and intestinal urinary diversion. These results may be used for patient counseling before surgery, including the planning of perioperative chemotherapy administration.

SOME STATISTICAL ISSUES RELATED TO MULTIPLE LINEAR REGRESSION MODELING OF BEACH BACTERIA CONCENTRATIONS

EPA Science Inventory

As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those is...

A simplified competition data analysis for radioligand specific activity determination.

PubMed

Venturino, A; Rivera, E S; Bergoc, R M; Caro, R A

1990-01-01

Non-linear regression and two-step linear fit methods were developed to determine the actual specific activity of 125I-ovine prolactin by radioreceptor self-displacement analysis. The experimental results obtained by the different methods are superposable. The non-linear regression method is considered to be the most adequate procedure to calculate the specific activity, but if its software is not available, the other described methods are also suitable.

Height and Weight Estimation From Anthropometric Measurements Using Machine Learning Regressions

PubMed Central

Fernandes, Bruno J. T.; Roque, Alexandre

2018-01-01

Height and weight are measurements explored to tracking nutritional diseases, energy expenditure, clinical conditions, drug dosages, and infusion rates. Many patients are not ambulant or may be unable to communicate, and a sequence of these factors may not allow accurate estimation or measurements; in those cases, it can be estimated approximately by anthropometric means. Different groups have proposed different linear or non-linear equations which coefficients are obtained by using single or multiple linear regressions. In this paper, we present a complete study of the application of different learning models to estimate height and weight from anthropometric measurements: support vector regression, Gaussian process, and artificial neural networks. The predicted values are significantly more accurate than that obtained with conventional linear regressions. In all the cases, the predictions are non-sensitive to ethnicity, and to gender, if more than two anthropometric parameters are analyzed. The learning model analysis creates new opportunities for anthropometric applications in industry, textile technology, security, and health care. PMID:29651366

Molecular markers of neuropsychological functioning and Alzheimer's disease.

PubMed

Edwards, Melissa; Balldin, Valerie Hobson; Hall, James; O'Bryant, Sid

2015-03-01

The current project sought to examine molecular markers of neuropsychological functioning among elders with and without Alzheimer's disease (AD) and determine the predictive ability of combined molecular markers and select neuropsychological tests in detecting disease presence. Data were analyzed from 300 participants (n = 150, AD and n = 150, controls) enrolled in the Texas Alzheimer's Research and Care Consortium. Linear regression models were created to examine the link between the top five molecular markers from our AD blood profile and neuropsychological test scores. Logistical regressions were used to predict AD presence using serum biomarkers in combination with select neuropsychological measures. Using the neuropsychological test with the least amount of variance overlap with the molecular markers, the combined neuropsychological test and molecular markers was highly accurate in detecting AD presence. This work provides the foundation for the generation of a point-of-care device that can be used to screen for AD.

Least square regularized regression in sum space.

PubMed

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Simple method for quick estimation of aquifer hydrogeological parameters

NASA Astrophysics Data System (ADS)

Ma, C.; Li, Y. Y.

2017-08-01

Development of simple and accurate methods to determine the aquifer hydrogeological parameters was of importance for groundwater resources assessment and management. Aiming at the present issue of estimating aquifer parameters based on some data of the unsteady pumping test, a fitting function of Theis well function was proposed using fitting optimization method and then a unitary linear regression equation was established. The aquifer parameters could be obtained by solving coefficients of the regression equation. The application of the proposed method was illustrated, using two published data sets. By the error statistics and analysis on the pumping drawdown, it showed that the method proposed in this paper yielded quick and accurate estimates of the aquifer parameters. The proposed method could reliably identify the aquifer parameters from long distance observed drawdowns and early drawdowns. It was hoped that the proposed method in this paper would be helpful for practicing hydrogeologists and hydrologists.

Using the Ridge Regression Procedures to Estimate the Multiple Linear Regression Coefficients

NASA Astrophysics Data System (ADS)

Gorgees, HazimMansoor; Mahdi, FatimahAssim

2018-05-01

This article concerns with comparing the performance of different types of ordinary ridge regression estimators that have been already proposed to estimate the regression parameters when the near exact linear relationships among the explanatory variables is presented. For this situations we employ the data obtained from tagi gas filling company during the period (2008-2010). The main result we reached is that the method based on the condition number performs better than other methods since it has smaller mean square error (MSE) than the other stated methods.

Compensatory selection for roads over natural linear features by wolves in northern Ontario: Implications for caribou conservation

PubMed Central

Patterson, Brent R.; Anderson, Morgan L.; Rodgers, Arthur R.; Vander Vennen, Lucas M.; Fryxell, John M.

2017-01-01

Woodland caribou (Rangifer tarandus caribou) in Ontario are a threatened species that have experienced a substantial retraction of their historic range. Part of their decline has been attributed to increasing densities of anthropogenic linear features such as trails, roads, railways, and hydro lines. These features have been shown to increase the search efficiency and kill rate of wolves. However, it is unclear whether selection for anthropogenic linear features is additive or compensatory to selection for natural (water) linear features which may also be used for travel. We studied the selection of water and anthropogenic linear features by 52 resident wolves (Canis lupus x lycaon) over four years across three study areas in northern Ontario that varied in degrees of forestry activity and human disturbance. We used Euclidean distance-based resource selection functions (mixed-effects logistic regression) at the seasonal range scale with random coefficients for distance to water linear features, primary/secondary roads/railways, and hydro lines, and tertiary roads to estimate the strength of selection for each linear feature and for several habitat types, while accounting for availability of each feature. Next, we investigated the trade-off between selection for anthropogenic and water linear features. Wolves selected both anthropogenic and water linear features; selection for anthropogenic features was stronger than for water during the rendezvous season. Selection for anthropogenic linear features increased with increasing density of these features on the landscape, while selection for natural linear features declined, indicating compensatory selection of anthropogenic linear features. These results have implications for woodland caribou conservation. Prey encounter rates between wolves and caribou seem to be strongly influenced by increasing linear feature densities. This behavioral mechanism–a compensatory functional response to anthropogenic linear feature density resulting in decreased use of natural travel corridors–has negative consequences for the viability of woodland caribou. PMID:29117234

Compensatory selection for roads over natural linear features by wolves in northern Ontario: Implications for caribou conservation.

PubMed

Newton, Erica J; Patterson, Brent R; Anderson, Morgan L; Rodgers, Arthur R; Vander Vennen, Lucas M; Fryxell, John M

2017-01-01

Woodland caribou (Rangifer tarandus caribou) in Ontario are a threatened species that have experienced a substantial retraction of their historic range. Part of their decline has been attributed to increasing densities of anthropogenic linear features such as trails, roads, railways, and hydro lines. These features have been shown to increase the search efficiency and kill rate of wolves. However, it is unclear whether selection for anthropogenic linear features is additive or compensatory to selection for natural (water) linear features which may also be used for travel. We studied the selection of water and anthropogenic linear features by 52 resident wolves (Canis lupus x lycaon) over four years across three study areas in northern Ontario that varied in degrees of forestry activity and human disturbance. We used Euclidean distance-based resource selection functions (mixed-effects logistic regression) at the seasonal range scale with random coefficients for distance to water linear features, primary/secondary roads/railways, and hydro lines, and tertiary roads to estimate the strength of selection for each linear feature and for several habitat types, while accounting for availability of each feature. Next, we investigated the trade-off between selection for anthropogenic and water linear features. Wolves selected both anthropogenic and water linear features; selection for anthropogenic features was stronger than for water during the rendezvous season. Selection for anthropogenic linear features increased with increasing density of these features on the landscape, while selection for natural linear features declined, indicating compensatory selection of anthropogenic linear features. These results have implications for woodland caribou conservation. Prey encounter rates between wolves and caribou seem to be strongly influenced by increasing linear feature densities. This behavioral mechanism-a compensatory functional response to anthropogenic linear feature density resulting in decreased use of natural travel corridors-has negative consequences for the viability of woodland caribou.

Is serum zinc level associated with prediabetes and diabetes?: a cross-sectional study from Bangladesh.

PubMed

Islam, Md Rafiqul; Arslan, Iqbal; Attia, John; McEvoy, Mark; McElduff, Patrick; Basher, Ariful; Rahman, Waliur; Peel, Roseanne; Akhter, Ayesha; Akter, Shahnaz; Vashum, Khanrin P; Milton, Abul Hasnat

2013-01-01

To determine serum zinc level and other relevant biological markers in normal, prediabetic and diabetic individuals and their association with Homeostasis Model Assessment (HOMA) parameters. This cross-sectional study was conducted between March and December 2009. Any patient aged ≥ 30 years attending the medicine outpatient department of a medical university hospital in Dhaka, Bangladesh and who had a blood glucose level ordered by a physician was eligible to participate. A total of 280 participants were analysed. On fasting blood sugar results, 51% were normal, 13% had prediabetes and 36% had diabetes. Mean serum zinc level was lowest in prediabetic compared to normal and diabetic participants (mean differences were approximately 65 ppb/L and 33 ppb/L, respectively). In multiple linear regression, serum zinc level was found to be significantly lower in prediabetes than in those with normoglycemia. Beta cell function was significantly lower in prediabetes than normal participants. Adjusted linear regression for HOMA parameters did not show a statistically significant association between serum zinc level, beta cell function (P = 0.07) and insulin resistance (P = 0.08). Low serum zinc accentuated the increase in insulin resistance seen with increasing BMI. Participants with prediabetes have lower zinc levels than controls and zinc is significantly associated with beta cell function and insulin resistance. Further longitudinal population based studies are warranted and controlled trials would be valuable for establishing whether zinc supplementation in prediabetes could be a useful strategy in preventing progression to Type 2 diabetes.

Association between resting-state brain network topological organization and creative ability: Evidence from a multiple linear regression model.

PubMed

Jiao, Bingqing; Zhang, Delong; Liang, Aiying; Liang, Bishan; Wang, Zengjian; Li, Junchao; Cai, Yuxuan; Gao, Mengxia; Gao, Zhenni; Chang, Song; Huang, Ruiwang; Liu, Ming

2017-10-01

Previous studies have indicated a tight linkage between resting-state functional connectivity of the human brain and creative ability. This study aimed to further investigate the association between the topological organization of resting-state brain networks and creativity. Therefore, we acquired resting-state fMRI data from 22 high-creativity participants and 22 low-creativity participants (as determined by their Torrance Tests of Creative Thinking scores). We then constructed functional brain networks for each participant and assessed group differences in network topological properties before exploring the relationships between respective network topological properties and creative ability. We identified an optimized organization of intrinsic brain networks in both groups. However, compared with low-creativity participants, high-creativity participants exhibited increased global efficiency and substantially decreased path length, suggesting increased efficiency of information transmission across brain networks in creative individuals. Using a multiple linear regression model, we further demonstrated that regional functional integration properties (i.e., the betweenness centrality and global efficiency) of brain networks, particularly the default mode network (DMN) and sensorimotor network (SMN), significantly predicted the individual differences in creative ability. Furthermore, the associations between network regional properties and creative performance were creativity-level dependent, where the difference in the resource control component may be important in explaining individual difference in creative performance. These findings provide novel insights into the neural substrate of creativity and may facilitate objective identification of creative ability. Copyright © 2017 Elsevier B.V. All rights reserved.

Multi-frame linear regressive filter for the measurement of infrared pixel spatial response and MTF from sparse data.

PubMed

Huard, Edouard; Derelle, Sophie; Jaeck, Julien; Nghiem, Jean; Haïdar, Riad; Primot, Jérôme

2018-03-05

A challenging point in the prediction of the image quality of infrared imaging systems is the evaluation of the detector modulation transfer function (MTF). In this paper, we present a linear method to get a 2D continuous MTF from sparse spectral data. Within the method, an object with a predictable sparse spatial spectrum is imaged by the focal plane array. The sparse data is then treated to return the 2D continuous MTF with the hypothesis that all the pixels have an identical spatial response. The linearity of the treatment is a key point to estimate directly the error bars of the resulting detector MTF. The test bench will be presented along with measurement tests on a 25 μm pitch InGaAs detector.

Resistance of nickel-chromium-aluminum alloys to cyclic oxidation at 1100 C and 1200 C

NASA Technical Reports Server (NTRS)

Barrett, C. A.; Lowell, C. E.

1976-01-01

Nickel-rich alloys in the Ni-Cr-Al system were evaluated for cyclic oxidation resistance in still air at 1,100 and 1,200 C. A first approximation oxidation attack parameter Ka was derived from specific weight change data involving both a scaling growth constant and a spalling constant. An estimating equation was derived with Ka as a function of the Cr and Al content by multiple linear regression and translated into countour ternary diagrams showing regions of minimum attack. An additional factor inferred from the regression analysis was that alloys melted in zirconia crucibles had significantly greater oxidation resistance than comparable alloys melted otherwise.

Alzheimer's Disease Detection by Pseudo Zernike Moment and Linear Regression Classification.

PubMed

Wang, Shui-Hua; Du, Sidan; Zhang, Yin; Phillips, Preetha; Wu, Le-Nan; Chen, Xian-Qing; Zhang, Yu-Dong

2017-01-01

This study presents an improved method based on "Gorji et al. Neuroscience. 2015" by introducing a relatively new classifier-linear regression classification. Our method selects one axial slice from 3D brain image, and employed pseudo Zernike moment with maximum order of 15 to extract 256 features from each image. Finally, linear regression classification was harnessed as the classifier. The proposed approach obtains an accuracy of 97.51%, a sensitivity of 96.71%, and a specificity of 97.73%. Our method performs better than Gorji's approach and five other state-of-the-art approaches. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Cellulose microfibril orientation of Picea abies and its variability at the micron-level determined by Raman imaging.

PubMed

Gierlinger, Notburga; Luss, Saskia; König, Christian; Konnerth, Johannes; Eder, Michaela; Fratzl, Peter

2010-01-01

The functional characteristics of plant cell walls depend on the composition of the cell wall polymers, as well as on their highly ordered architecture at scales from a few nanometres to several microns. Raman spectra of wood acquired with linear polarized laser light include information about polymer composition as well as the alignment of cellulose microfibrils with respect to the fibre axis (microfibril angle). By changing the laser polarization direction in 3 degrees steps, the dependency between cellulose and laser orientation direction was investigated. Orientation-dependent changes of band height ratios and spectra were described by quadratic linear regression and partial least square regressions, respectively. Using the models and regressions with high coefficients of determination (R(2) > 0.99) microfibril orientation was predicted in the S1 and S2 layers distinguished by the Raman imaging approach in cross-sections of spruce normal, opposite, and compression wood. The determined microfibril angle (MFA) in the different S2 layers ranged from 0 degrees to 49.9 degrees and was in coincidence with X-ray diffraction determination. With the prerequisite of geometric sample and laser alignment, exact MFA prediction can complete the picture of the chemical cell wall design gained by the Raman imaging approach at the micron level in all plant tissues.

Estimation of Energy Expenditure Using a Patch-Type Sensor Module with an Incremental Radial Basis Function Neural Network

PubMed Central

Li, Meina; Kwak, Keun-Chang; Kim, Youn Tae

2016-01-01

Conventionally, indirect calorimetry has been used to estimate oxygen consumption in an effort to accurately measure human body energy expenditure. However, calorimetry requires the subject to wear a mask that is neither convenient nor comfortable. The purpose of our study is to develop a patch-type sensor module with an embedded incremental radial basis function neural network (RBFNN) for estimating the energy expenditure. The sensor module contains one ECG electrode and a three-axis accelerometer, and can perform real-time heart rate (HR) and movement index (MI) monitoring. The embedded incremental network includes linear regression (LR) and RBFNN based on context-based fuzzy c-means (CFCM) clustering. This incremental network is constructed by building a collection of information granules through CFCM clustering that is guided by the distribution of error of the linear part of the LR model. PMID:27669249

A simple bias correction in linear regression for quantitative trait association under two-tail extreme selection.

PubMed

Kwan, Johnny S H; Kung, Annie W C; Sham, Pak C

2011-09-01

Selective genotyping can increase power in quantitative trait association. One example of selective genotyping is two-tail extreme selection, but simple linear regression analysis gives a biased genetic effect estimate. Here, we present a simple correction for the bias.

Random regression analyses using B-spline functions to model growth of Nellore cattle.

PubMed

Boligon, A A; Mercadante, M E Z; Lôbo, R B; Baldi, F; Albuquerque, L G

2012-02-01

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

A Common Mechanism for Resistance to Oxime Reactivation of Acetylcholinesterase Inhibited by Organophosphorus Compounds

DTIC Science & Technology

2013-01-01

application of the Hammett equation with the constants rph in the chemistry of organophosphorus compounds, Russ. Chem. Rev. 38 (1969) 795–811. [13...of oximes and OP compounds and the ability of oximes to reactivate OP- inhibited AChE. Multiple linear regression equations were analyzed using...phosphonate pairs, 21 oxime/ phosphoramidate pairs and 12 oxime/phosphate pairs. The best linear regression equation resulting from multiple regression anal

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Spectral Regression Discriminant Analysis for Hyperspectral Image Classification

NASA Astrophysics Data System (ADS)

Pan, Y.; Wu, J.; Huang, H.; Liu, J.

2012-08-01

Dimensionality reduction algorithms, which aim to select a small set of efficient and discriminant features, have attracted great attention for Hyperspectral Image Classification. The manifold learning methods are popular for dimensionality reduction, such as Locally Linear Embedding, Isomap, and Laplacian Eigenmap. However, a disadvantage of many manifold learning methods is that their computations usually involve eigen-decomposition of dense matrices which is expensive in both time and memory. In this paper, we introduce a new dimensionality reduction method, called Spectral Regression Discriminant Analysis (SRDA). SRDA casts the problem of learning an embedding function into a regression framework, which avoids eigen-decomposition of dense matrices. Also, with the regression based framework, different kinds of regularizes can be naturally incorporated into our algorithm which makes it more flexible. It can make efficient use of data points to discover the intrinsic discriminant structure in the data. Experimental results on Washington DC Mall and AVIRIS Indian Pines hyperspectral data sets demonstrate the effectiveness of the proposed method.

Optimal Estimation of Clock Values and Trends from Finite Data

NASA Technical Reports Server (NTRS)

Greenhall, Charles

2005-01-01

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

Specialization Agreements in the Council for Mutual Economic Assistance

DTIC Science & Technology

1988-02-01

proportions to stabilize variance (S. Weisberg, Applied Linear Regression , 2nd ed., John Wiley & Sons, New York, 1985, p. 134). If the dependent...27, 1986, p. 3. Weisberg, S., Applied Linear Regression , 2nd ed., John Wiley & Sons, New York, 1985, p. 134. Wiles, P. J., Communist International

Radio Propagation Prediction Software for Complex Mixed Path Physical Channels

DTIC Science & Technology

2006-08-14

63 4.4.6. Applied Linear Regression Analysis in the Frequency Range 1-50 MHz 69 4.4.7. Projected Scaling to...4.4.6. Applied Linear Regression Analysis in the Frequency Range 1-50 MHz In order to construct a comprehensive numerical algorithm capable of

INTRODUCTION TO A COMBINED MULTIPLE LINEAR REGRESSION AND ARMA MODELING APPROACH FOR BEACH BACTERIA PREDICTION

EPA Science Inventory

Due to the complexity of the processes contributing to beach bacteria concentrations, many researchers rely on statistical modeling, among which multiple linear regression (MLR) modeling is most widely used. Despite its ease of use and interpretation, there may be time dependence...

Data Transformations for Inference with Linear Regression: Clarifications and Recommendations

ERIC Educational Resources Information Center

Pek, Jolynn; Wong, Octavia; Wong, C. M.

2017-01-01

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

USING LINEAR AND POLYNOMIAL MODELS TO EXAMINE THE ENVIRONMENTAL STABILITY OF VIRUSES

EPA Science Inventory

The article presents the development of model equations for describing the fate of viral infectivity in environmental samples. Most of the models were based upon the use of a two-step linear regression approach. The first step employs regression of log base 10 transformed viral t...

Identifying the Factors That Influence Change in SEBD Using Logistic Regression Analysis

ERIC Educational Resources Information Center

Camilleri, Liberato; Cefai, Carmel

2013-01-01

Multiple linear regression and ANOVA models are widely used in applications since they provide effective statistical tools for assessing the relationship between a continuous dependent variable and several predictors. However these models rely heavily on linearity and normality assumptions and they do not accommodate categorical dependent…

Simple and multiple linear regression: sample size considerations.

PubMed

Hanley, James A

2016-11-01

The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression. This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates. By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres. Copyright © 2016 Elsevier Inc. All rights reserved.

A Cross-Domain Collaborative Filtering Algorithm Based on Feature Construction and Locally Weighted Linear Regression

PubMed Central

Jiang, Feng; Han, Ji-zhong

2018-01-01

Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods. PMID:29623088

A Cross-Domain Collaborative Filtering Algorithm Based on Feature Construction and Locally Weighted Linear Regression.

PubMed

Yu, Xu; Lin, Jun-Yu; Jiang, Feng; Du, Jun-Wei; Han, Ji-Zhong

2018-01-01

Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods.

Validity of linear encoder measurement of sit-to-stand performance power in older people.

PubMed

Lindemann, U; Farahmand, P; Klenk, J; Blatzonis, K; Becker, C

2015-09-01

To investigate construct validity of linear encoder measurement of sit-to-stand performance power in older people by showing associations with relevant functional performance and physiological parameters. Cross-sectional study. Movement laboratory of a geriatric rehabilitation clinic. Eighty-eight community-dwelling, cognitively unimpaired older women (mean age 78 years). Sit-to-stand performance power and leg power were assessed using a linear encoder and the Nottingham Power Rig, respectively. Gait speed was measured on an instrumented walkway. Maximum quadriceps and hand grip strength were assessed using dynamometers. Mid-thigh muscle cross-sectional area of both legs was measured using magnetic resonance imaging. Associations of sit-to-stand performance power with power assessed by the Nottingham Power Rig, maximum gait speed and muscle cross-sectional area were r=0.646, r=0.536 and r=0.514, respectively. A linear regression model explained 50% of the variance in sit-to-stand performance power including muscle cross-sectional area (p=0.001), maximum gait speed (p=0.002), and power assessed by the Nottingham Power Rig (p=0.006). Construct validity of linear encoder measurement of sit-to-stand power was shown at functional level and morphological level for older women. This measure could be used in routine clinical practice as well as in large-scale studies. DRKS00003622. Copyright © 2015 Chartered Society of Physiotherapy. Published by Elsevier Ltd. All rights reserved.

Soiling of window glass of building façades: a new Dose-Response Function based on the mass of deposited particles

NASA Astrophysics Data System (ADS)

Ionescu, Anda; Lefèvre, Roger

2017-04-01

Materials used in building façades are subject to different types of weathering, an important one being soiling. The material studied here is the silica-soda-lime glass, used for windows and contemporaneous façades. Glass weathering in a polluted environment, sheltered from rain, is dominated by soiling. This phenomenon can be expressed either by an optical parameter, the haze, or by the mass of Deposited and Neoformed Particles by unit of glass surface (DNPs). By contrast to the haze, which is an optical parameter requiring an expensive technology (spectrophotometry), measuring DNPs is much simpler: the glass sample is weighed before and after exposure and the result, divided by the sample surface. After the development of a previous Dose-Response Function (DRF) expressing soiling evolution through haze, this study focuses on the development of a new DRF for soiling expressed in terms of DNPs mass, sheltered from rain. The development of this DRF follows a statistical approach. The general form proposed for the DRF is: DNPs=A(dose1, dose2, …., dosen).g(t) where g(t) represents the temporal trend obtained from standardized data. Data standardization has been employed in order to obtain a general trend independent of the environmental characteristics of the monitoring site. According to previous studies and physical considerations, the analytical form of the temporal trend g(t) was expressed by a function admitting an horizontal asymptote: the saturation level of soling. Ten monitoring campaigns (performed at different European sites) were used; the longest one runs up to 2102 days and the shortest ones, up to 365 days, with 14 to 5 records, respectively. Two different models were fitted by a non-linear regression: the Hill's model and a decreasing exponential model. Both models performed well (R2 ranging from 0.73 to 0.76) and they were further tested in order to get the final form of the DRF. The amplitude function A was considered as a linear combination of the different doses. A multiple linear regression was then applied to doses multiplied by the temporal trend function g permitting to obtain the regression coefficients of the amplitude function A. Another database was used, containing the monitoring values for SO2, NO2 and PM10 concentrations, as well as temperature and relative humidity, monitored at 19 European sites. The correlation between pollution concentrations was taken into account and led to a selection of pollutants in order to avoid numerical instability in the regression procedure. The meteorological parameters didn't have a statistical impact, so they were not considered as doses. A DRF for DNPs could be established using SO2 and PM10 concentrations and the Hill model for the g(t) trend with a determination coefficient of 0.7. This DRF was then used to plot the annual DNPs evolution from 1500 to 2100 in Paris and compared to the same curve expressed in terms of Haze for the same period. The obtained evolution is comparable and reveals an important peak corresponding to the industrial period.

Analysis of Binary Adherence Data in the Setting of Polypharmacy: A Comparison of Different Approaches

PubMed Central

Esserman, Denise A.; Moore, Charity G.; Roth, Mary T.

2009-01-01

Older community dwelling adults often take multiple medications for numerous chronic diseases. Non-adherence to these medications can have a large public health impact. Therefore, the measurement and modeling of medication adherence in the setting of polypharmacy is an important area of research. We apply a variety of different modeling techniques (standard linear regression; weighted linear regression; adjusted linear regression; naïve logistic regression; beta-binomial (BB) regression; generalized estimating equations (GEE)) to binary medication adherence data from a study in a North Carolina based population of older adults, where each medication an individual was taking was classified as adherent or non-adherent. In addition, through simulation we compare these different methods based on Type I error rates, bias, power, empirical 95% coverage, and goodness of fit. We find that estimation and inference using GEE is robust to a wide variety of scenarios and we recommend using this in the setting of polypharmacy when adherence is dichotomously measured for multiple medications per person. PMID:20414358

Genetic Programming Transforms in Linear Regression Situations

NASA Astrophysics Data System (ADS)

Castillo, Flor; Kordon, Arthur; Villa, Carlos

The chapter summarizes the use of Genetic Programming (GP) inMultiple Linear Regression (MLR) to address multicollinearity and Lack of Fit (LOF). The basis of the proposed method is applying appropriate input transforms (model respecification) that deal with these issues while preserving the information content of the original variables. The transforms are selected from symbolic regression models with optimal trade-off between accuracy of prediction and expressional complexity, generated by multiobjective Pareto-front GP. The chapter includes a comparative study of the GP-generated transforms with Ridge Regression, a variant of ordinary Multiple Linear Regression, which has been a useful and commonly employed approach for reducing multicollinearity. The advantages of GP-generated model respecification are clearly defined and demonstrated. Some recommendations for transforms selection are given as well. The application benefits of the proposed approach are illustrated with a real industrial application in one of the broadest empirical modeling areas in manufacturing - robust inferential sensors. The chapter contributes to increasing the awareness of the potential of GP in statistical model building by MLR.

Linear and nonlinear stiffness and friction in biological rhythmic movements.

PubMed

Beek, P J; Schmidt, R C; Morris, A W; Sim, M Y; Turvey, M T

1995-11-01

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.

A comparison of methods to handle skew distributed cost variables in the analysis of the resource consumption in schizophrenia treatment.

PubMed

Kilian, Reinhold; Matschinger, Herbert; Löeffler, Walter; Roick, Christiane; Angermeyer, Matthias C

2002-03-01

Transformation of the dependent cost variable is often used to solve the problems of heteroscedasticity and skewness in linear ordinary least square regression of health service cost data. However, transformation may cause difficulties in the interpretation of regression coefficients and the retransformation of predicted values. The study compares the advantages and disadvantages of different methods to estimate regression based cost functions using data on the annual costs of schizophrenia treatment. Annual costs of psychiatric service use and clinical and socio-demographic characteristics of the patients were assessed for a sample of 254 patients with a diagnosis of schizophrenia (ICD-10 F 20.0) living in Leipzig. The clinical characteristics of the participants were assessed by means of the BPRS 4.0, the GAF, and the CAN for service needs. Quality of life was measured by WHOQOL-BREF. A linear OLS regression model with non-parametric standard errors, a log-transformed OLS model and a generalized linear model with a log-link and a gamma distribution were used to estimate service costs. For the estimation of robust non-parametric standard errors, the variance estimator by White and a bootstrap estimator based on 2000 replications were employed. Models were evaluated by the comparison of the R2 and the root mean squared error (RMSE). RMSE of the log-transformed OLS model was computed with three different methods of bias-correction. The 95% confidence intervals for the differences between the RMSE were computed by means of bootstrapping. A split-sample-cross-validation procedure was used to forecast the costs for the one half of the sample on the basis of a regression equation computed for the other half of the sample. All three methods showed significant positive influences of psychiatric symptoms and met psychiatric service needs on service costs. Only the log- transformed OLS model showed a significant negative impact of age, and only the GLM shows a significant negative influences of employment status and partnership on costs. All three models provided a R2 of about.31. The Residuals of the linear OLS model revealed significant deviances from normality and homoscedasticity. The residuals of the log-transformed model are normally distributed but still heteroscedastic. The linear OLS model provided the lowest prediction error and the best forecast of the dependent cost variable. The log-transformed model provided the lowest RMSE if the heteroscedastic bias correction was used. The RMSE of the GLM with a log link and a gamma distribution was higher than those of the linear OLS model and the log-transformed OLS model. The difference between the RMSE of the linear OLS model and that of the log-transformed OLS model without bias correction was significant at the 95% level. As result of the cross-validation procedure, the linear OLS model provided the lowest RMSE followed by the log-transformed OLS model with a heteroscedastic bias correction. The GLM showed the weakest model fit again. None of the differences between the RMSE resulting form the cross- validation procedure were found to be significant. The comparison of the fit indices of the different regression models revealed that the linear OLS model provided a better fit than the log-transformed model and the GLM, but the differences between the models RMSE were not significant. Due to the small number of cases in the study the lack of significance does not sufficiently proof that the differences between the RSME for the different models are zero and the superiority of the linear OLS model can not be generalized. The lack of significant differences among the alternative estimators may reflect a lack of sample size adequate to detect important differences among the estimators employed. Further studies with larger case number are necessary to confirm the results. Specification of an adequate regression models requires a careful examination of the characteristics of the data. Estimation of standard errors and confidence intervals by nonparametric methods which are robust against deviations from the normal distribution and the homoscedasticity of residuals are suitable alternatives to the transformation of the skew distributed dependent variable. Further studies with more adequate case numbers are needed to confirm the results.

Ranibizumab treatment in age-related macular degeneration: a meta-analysis of one-year results.

PubMed

Gerding, H

2014-04-01

Although ranibizumab is widely used in age-related macular degeneration there is no systematic data available on the relation between treatment frequency and functional efficacy within the first 12 months of follow-up. A meta-analysis was performed on available MEDLINE literature. 47 relevant clinical studies (54 case series) could be identified covering 11706 treated eyes. Non-linear and linear regressions were calculated for the relation between treatment frequency and functional outcome (average gain in visual acuity, % of eyes losing less than 15 letters of visual acuity, % of eyes gaining ≥ 15 letters) within the first year of care. Mean improvement of average visual gain was +4.9 ± 3.6 (mean ± 1 standard deviation) letters (case-weighted: 3.3 letters). The average number of ranibizumab injections until month 12 was 6.3 ± 2.0 (case-weighted: 5.9). 92.4 ± 3.9% of eyes (case-weighted: 91.9%) lost less than three lines of visual acuity and 24.5 ± 8.2% (case-weighted: 23.3) gained more than 3 lines within the first year. Analysis of the relation between the number of injections and functional improvement indicated best fit for non-linear equations. A nearly stepwise improvement of functional gain occurred between 6.8 and 7.2 injections/year. A saturation effect of treatment occurred at higher injection frequency. The results of this meta-analysis clearly indicate a non-linear relation between the number of injections and functional gain of ranibizumab within the first 12 months of treatment. Treatment saturation seems to occur at a treatment frequency >7.2 injections within the first 12 months. Georg Thieme Verlag KG Stuttgart · New York.

Sexual Response Models: Toward a More Flexible Pattern of Women's Sexuality.

PubMed

Ferenidou, Fotini; Kirana, Paraskevi-Sofia; Fokas, Konstantinos; Hatzichristou, Dimitrios; Athanasiadis, Loukas

2016-09-01

Recent research suggests that none of the current theoretical models can sufficiently describe women's sexual response, because several factors and situations can influence this. To explore individual variations of a sexual model that describes women's sexual responses and to assess the association of endorsement of that model with sexual dysfunctions and reasons to engage in sexual activity. A sample of 157 randomly selected hospital employees completed self-administered questionnaires. Two models were developed: one merged the Master and Johnson model with the Kaplan model (linear) and the other was the Basson model (circular). Sexual function was evaluated by the Female Sexual Function Index and the Brief Sexual Symptom Checklist for Women. The Reasons for Having Sex Questionnaire was administered to investigate the reasons for which women have sex. Women reported that their current sexual experiences were at times consistent with the linear and circular models (66.9%), only the linear model (27%), only the circular model (5.4%), and neither model (0.7%). When the groups were reconfigured to the group that endorsed more than 5 of 10 sexual experiences, 64.3% of women endorsed the linear model, 20.4% chose the linear and circular models, 14.6% chose the circular model, and 0.7% selected neither. The Female Sexual Function Index, demographic factors, having sex for insecurity reasons, and sexual satisfaction correlated with the endorsement of a sexual response model. When these factors were entered in a stepwise logistic regression analysis, only the Female Sexual Function Index and having sex for insecurity reasons maintained a significant association with the sexual response model. The present study emphasizes the heterogeneity of female sexuality, with most of the sample reporting alternating between the linear and circular models. Sexual dysfunctions and having sex for insecurity reasons were associated with the Basson model. Copyright © 2016 International Society for Sexual Medicine. Published by Elsevier Inc. All rights reserved.

Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

In several biological contexts, parameter inference often relies on computationally-intensive techniques. "Approximate Bayesian Computation", or ABC, methods based on summary statistics have become increasingly popular. A particular flavor of ABC based on using a linear regression to approximate the posterior distribution of the parameters, conditional on the summary statistics, is computationally appealing, yet no standalone tool exists to automate the procedure. Here, I describe a program to implement the method. The software package ABCreg implements the local linear-regression approach to ABC. The advantages are: 1. The code is standalone, and fully-documented. 2. The program will automatically process multiple data sets, and create unique output files for each (which may be processed immediately in R), facilitating the testing of inference procedures on simulated data, or the analysis of multiple data sets. 3. The program implements two different transformation methods for the regression step. 4. Analysis options are controlled on the command line by the user, and the program is designed to output warnings for cases where the regression fails. 5. The program does not depend on any particular simulation machinery (coalescent, forward-time, etc.), and therefore is a general tool for processing the results from any simulation. 6. The code is open-source, and modular.Examples of applying the software to empirical data from Drosophila melanogaster, and testing the procedure on simulated data, are shown. In practice, the ABCreg simplifies implementing ABC based on local-linear regression.

Multivariate Linear Regression and CART Regression Analysis of TBM Performance at Abu Hamour Phase-I Tunnel

NASA Astrophysics Data System (ADS)

Jakubowski, J.; Stypulkowski, J. B.; Bernardeau, F. G.

2017-12-01

The first phase of the Abu Hamour drainage and storm tunnel was completed in early 2017. The 9.5 km long, 3.7 m diameter tunnel was excavated with two Earth Pressure Balance (EPB) Tunnel Boring Machines from Herrenknecht. TBM operation processes were monitored and recorded by Data Acquisition and Evaluation System. The authors coupled collected TBM drive data with available information on rock mass properties, cleansed, completed with secondary variables and aggregated by weeks and shifts. Correlations and descriptive statistics charts were examined. Multivariate Linear Regression and CART regression tree models linking TBM penetration rate (PR), penetration per revolution (PPR) and field penetration index (FPI) with TBM operational and geotechnical characteristics were performed for the conditions of the weak/soft rock of Doha. Both regression methods are interpretable and the data were screened with different computational approaches allowing enriched insight. The primary goal of the analysis was to investigate empirical relations between multiple explanatory and responding variables, to search for best subsets of explanatory variables and to evaluate the strength of linear and non-linear relations. For each of the penetration indices, a predictive model coupling both regression methods was built and validated. The resultant models appeared to be stronger than constituent ones and indicated an opportunity for more accurate and robust TBM performance predictions.

Locomotive syndrome is associated not only with physical capacity but also degree of depression.

PubMed

Ikemoto, Tatsunori; Inoue, Masayuki; Nakata, Masatoshi; Miyagawa, Hirofumi; Shimo, Kazuhiro; Wakabayashi, Toshiko; Arai, Young-Chang P; Ushida, Takahiro

2016-05-01

Reports of locomotive syndrome (LS) have recently been increasing. Although physical performance measures for LS have been well investigated to date, studies including psychiatric assessment are still scarce. Hence, the aim of this study was to investigate both physical and mental parameters in relation to presence and severity of LS using a 25-question geriatric locomotive function scale (GLFS-25) questionnaire. 150 elderly people aged over 60 years who were members of our physical-fitness center and displayed well-being were enrolled in this study. Firstly, using the previously determined GLFS-25 cutoff value (=16 points), subjects were divided into two groups accordingly: an LS and non-LS group in order to compare each parameter (age, grip strength, timed-up-and-go test (TUG), one-leg standing with eye open, back muscle and leg muscle strength, degree of depression and cognitive impairment) between the groups using the Mann-Whitney U-test followed by multiple logistic regression analysis. Secondly, a multiple linear regression was conducted to determine which variables showed the strongest correlation with severity of LS. We confirmed 110 people for non-LS (73%) and 40 people for LS using the GLFS-25 cutoff value. Comparative analysis between LS and non-LS revealed significant differences in parameters in age, grip strength, TUG, one-leg standing, back muscle strength and degree of depression (p < 0.006, after Bonferroni correction). Multiple logistic regression revealed that functional decline in grip strength, TUG and one-leg standing and degree of depression were significantly associated with LS. On the other hand, we observed that the significant contributors towards the GLFS-25 score were TUG and degree of depression in multiple linear regression analysis. The results indicate that LS is associated with not only the capacity of physical performance but also the degree of depression although most participants fell under the criteria of LS. Copyright © 2016 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.

Analysis and selection of magnitude relations for the Working Group on Utah Earthquake Probabilities

USGS Publications Warehouse

Duross, Christopher; Olig, Susan; Schwartz, David

2015-01-01

Prior to calculating time-independent and -dependent earthquake probabilities for faults in the Wasatch Front region, the Working Group on Utah Earthquake Probabilities (WGUEP) updated a seismic-source model for the region (Wong and others, 2014) and evaluated 19 historical regressions on earthquake magnitude (M). These regressions relate M to fault parameters for historical surface-faulting earthquakes, including linear fault length (e.g., surface-rupture length [SRL] or segment length), average displacement, maximum displacement, rupture area, seismic moment (Mo ), and slip rate. These regressions show that significant epistemic uncertainties complicate the determination of characteristic magnitude for fault sources in the Basin and Range Province (BRP). For example, we found that M estimates (as a function of SRL) span about 0.3–0.4 units (figure 1) owing to differences in the fault parameter used; age, quality, and size of historical earthquake databases; and fault type and region considered.

Spectral-Spatial Shared Linear Regression for Hyperspectral Image Classification.

PubMed

Haoliang Yuan; Yuan Yan Tang

2017-04-01

Classification of the pixels in hyperspectral image (HSI) is an important task and has been popularly applied in many practical applications. Its major challenge is the high-dimensional small-sized problem. To deal with this problem, lots of subspace learning (SL) methods are developed to reduce the dimension of the pixels while preserving the important discriminant information. Motivated by ridge linear regression (RLR) framework for SL, we propose a spectral-spatial shared linear regression method (SSSLR) for extracting the feature representation. Comparing with RLR, our proposed SSSLR has the following two advantages. First, we utilize a convex set to explore the spatial structure for computing the linear projection matrix. Second, we utilize a shared structure learning model, which is formed by original data space and a hidden feature space, to learn a more discriminant linear projection matrix for classification. To optimize our proposed method, an efficient iterative algorithm is proposed. Experimental results on two popular HSI data sets, i.e., Indian Pines and Salinas demonstrate that our proposed methods outperform many SL methods.

Simple linear and multivariate regression models.

PubMed

Rodríguez del Águila, M M; Benítez-Parejo, N

2011-01-01

In biomedical research it is common to find problems in which we wish to relate a response variable to one or more variables capable of describing the behaviour of the former variable by means of mathematical models. Regression techniques are used to this effect, in which an equation is determined relating the two variables. While such equations can have different forms, linear equations are the most widely used form and are easy to interpret. The present article describes simple and multiple linear regression models, how they are calculated, and how their applicability assumptions are checked. Illustrative examples are provided, based on the use of the freely accessible R program. Copyright © 2011 SEICAP. Published by Elsevier Espana. All rights reserved.

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

The relationship between victimization and mental health functioning in homeless youth and adults.

PubMed

Rattelade, Stephanie; Farrell, Susan; Aubry, Tim; Klodawsky, Fran

2014-06-01

This study examined the relationship between victimization and mental health functioning in homeless individuals. Homeless populations experience higher levels of victimization than the general population, which in turn have a detrimental effect on their mental health. A sample of 304 homeless adults and youth completed one-on-one interviews, answering questions on mental health, past victimization, and recent victimization experiences. A hierarchical linear regression showed that experiences of childhood sexual abuse predicted lower mental health functioning after controlling for the sex and age of individuals. The study findings are applicable to current support programs for victims in the homeless population and are relevant to future research on homelessness and victimization.

Models of subjective response to in-flight motion data

NASA Technical Reports Server (NTRS)

Rudrapatna, A. N.; Jacobson, I. D.

1973-01-01

Mathematical relationships between subjective comfort and environmental variables in an air transportation system are investigated. As a first step in model building, only the motion variables are incorporated and sensitivities are obtained using stepwise multiple regression analysis. The data for these models have been collected from commercial passenger flights. Two models are considered. In the first, subjective comfort is assumed to depend on rms values of the six-degrees-of-freedom accelerations. The second assumes a Rustenburg type human response function in obtaining frequency weighted rms accelerations, which are used in a linear model. The form of the human response function is examined and the results yield a human response weighting function for different degrees of freedom.

Anxiety Levels Are Independently Associated With Cognitive Performance in an Australian Multiple Sclerosis Patient Cohort.

PubMed

Ribbons, Karen; Lea, Rodney; Schofield, Peter W; Lechner-Scott, Jeannette

2017-01-01

Neurological and psychological symptoms in multiple sclerosis can affect cognitive function. The objective of this study was to explore the relationship between psychological measures and cognitive performance in a patient cohort. In 322 multiple sclerosis patients, psychological symptoms were measured using the Depression Anxiety and Stress Scale, and cognitive function was evaluated using Audio Recorded Cognitive Screen. Multifactor linear regression analysis, accounting for all clinical covariates, found that anxiety was the only psychological measure to remain a significant predictor of cognitive performance (p<0.001), particularly memory function (p<0.001). Further prospective studies are required to determine whether treatment of anxiety improves cognitive impairment.

Optimization of isotherm models for pesticide sorption on biopolymer-nanoclay composite by error analysis.

PubMed

Narayanan, Neethu; Gupta, Suman; Gajbhiye, V T; Manjaiah, K M

2017-04-01

A carboxy methyl cellulose-nano organoclay (nano montmorillonite modified with 35-45 wt % dimethyl dialkyl (C 14 -C 18 ) amine (DMDA)) composite was prepared by solution intercalation method. The prepared composite was characterized by infrared spectroscopy (FTIR), X-Ray diffraction spectroscopy (XRD) and scanning electron microscopy (SEM). The composite was utilized for its pesticide sorption efficiency for atrazine, imidacloprid and thiamethoxam. The sorption data was fitted into Langmuir and Freundlich isotherms using linear and non linear methods. The linear regression method suggested best fitting of sorption data into Type II Langmuir and Freundlich isotherms. In order to avoid the bias resulting from linearization, seven different error parameters were also analyzed by non linear regression method. The non linear error analysis suggested that the sorption data fitted well into Langmuir model rather than in Freundlich model. The maximum sorption capacity, Q 0 (μg/g) was given by imidacloprid (2000) followed by thiamethoxam (1667) and atrazine (1429). The study suggests that the degree of determination of linear regression alone cannot be used for comparing the best fitting of Langmuir and Freundlich models and non-linear error analysis needs to be done to avoid inaccurate results. Copyright © 2017 Elsevier Ltd. All rights reserved.

London Measure of Unplanned Pregnancy: guidance for its use as an outcome measure

PubMed Central

Hall, Jennifer A; Barrett, Geraldine; Copas, Andrew; Stephenson, Judith

2017-01-01

Background The London Measure of Unplanned Pregnancy (LMUP) is a psychometrically validated measure of the degree of intention of a current or recent pregnancy. The LMUP is increasingly being used worldwide, and can be used to evaluate family planning or preconception care programs. However, beyond recommending the use of the full LMUP scale, there is no published guidance on how to use the LMUP as an outcome measure. Ordinal logistic regression has been recommended informally, but studies published to date have all used binary logistic regression and dichotomized the scale at different cut points. There is thus a need for evidence-based guidance to provide a standardized methodology for multivariate analysis and to enable comparison of results. This paper makes recommendations for the regression method for analysis of the LMUP as an outcome measure. Materials and methods Data collected from 4,244 pregnant women in Malawi were used to compare five regression methods: linear, logistic with two cut points, and ordinal logistic with either the full or grouped LMUP score. The recommendations were then tested on the original UK LMUP data. Results There were small but no important differences in the findings across the regression models. Logistic regression resulted in the largest loss of information, and assumptions were violated for the linear and ordinal logistic regression. Consequently, robust standard errors were used for linear regression and a partial proportional odds ordinal logistic regression model attempted. The latter could only be fitted for grouped LMUP score. Conclusion We recommend the linear regression model with robust standard errors to make full use of the LMUP score when analyzed as an outcome measure. Ordinal logistic regression could be considered, but a partial proportional odds model with grouped LMUP score may be required. Logistic regression is the least-favored option, due to the loss of information. For logistic regression, the cut point for un/planned pregnancy should be between nine and ten. These recommendations will standardize the analysis of LMUP data and enhance comparability of results across studies. PMID:28435343

SOCR Analyses – an Instructional Java Web-based Statistical Analysis Toolkit

PubMed Central

Chu, Annie; Cui, Jenny; Dinov, Ivo D.

2011-01-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test. The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website. In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models. PMID:21546994

Using Parametric Cost Models to Estimate Engineering and Installation Costs of Selected Electronic Communications Systems

DTIC Science & Technology

1994-09-01

Institute of Technology, Wright- Patterson AFB OH, January 1994. 4. Neter, John and others. Applied Linear Regression Models. Boston: Irwin, 1989. 5...Technology, Wright-Patterson AFB OH 5 April 1994. 29. Neter, John and others. Applied Linear Regression Models. Boston: Irwin, 1989. 30. Office of

An Evaluation of the Automated Cost Estimating Integrated Tools (ACEIT) System

DTIC Science & Technology

1989-09-01

residual and it is described as the residual divided by its standard deviation (13:App A,17). Neter, Wasserman, and Kutner, in Applied Linear Regression Models...others. Applied Linear Regression Models. Homewood IL: Irwin, 1983. 19. Raduchel, William J. "A Professional’s Perspective on User-Friendliness," Byte

Conjoint Analysis: A Study of the Effects of Using Person Variables.

ERIC Educational Resources Information Center

Fraas, John W.; Newman, Isadore

Three statistical techniques--conjoint analysis, a multiple linear regression model, and a multiple linear regression model with a surrogate person variable--were used to estimate the relative importance of five university attributes for students in the process of selecting a college. The five attributes include: availability and variety of…

Fitting program for linear regressions according to Mahon (1996)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trappitsch, Reto G.

2018-01-09

This program takes the users' Input data and fits a linear regression to it using the prescription presented by Mahon (1996). Compared to the commonly used York fit, this method has the correct prescription for measurement error propagation. This software should facilitate the proper fitting of measurements with a simple Interface.

How Robust Is Linear Regression with Dummy Variables?

ERIC Educational Resources Information Center

Blankmeyer, Eric

2006-01-01

Researchers in education and the social sciences make extensive use of linear regression models in which the dependent variable is continuous-valued while the explanatory variables are a combination of continuous-valued regressors and dummy variables. The dummies partition the sample into groups, some of which may contain only a few observations.…

Revisiting the Scale-Invariant, Two-Dimensional Linear Regression Method

ERIC Educational Resources Information Center

Patzer, A. Beate C.; Bauer, Hans; Chang, Christian; Bolte, Jan; Su¨lzle, Detlev

2018-01-01

The scale-invariant way to analyze two-dimensional experimental and theoretical data with statistical errors in both the independent and dependent variables is revisited by using what we call the triangular linear regression method. This is compared to the standard least-squares fit approach by applying it to typical simple sets of example data…

An Introduction to Graphical and Mathematical Methods for Detecting Heteroscedasticity in Linear Regression.

ERIC Educational Resources Information Center

Thompson, Russel L.

Homoscedasticity is an important assumption of linear regression. This paper explains what it is and why it is important to the researcher. Graphical and mathematical methods for testing the homoscedasticity assumption are demonstrated. Sources of homoscedasticity and types of homoscedasticity are discussed, and methods for correction are…

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Common pitfalls in statistical analysis: Linear regression analysis

PubMed Central

Aggarwal, Rakesh; Ranganathan, Priya

2017-01-01

In a previous article in this series, we explained correlation analysis which describes the strength of relationship between two continuous variables. In this article, we deal with linear regression analysis which predicts the value of one continuous variable from another. We also discuss the assumptions and pitfalls associated with this analysis. PMID:28447022

Explaining ethnic disparities in lung function among young adults: A pilot investigation

PubMed Central

Patel, Jaymini; Minelli, Cosetta; Burney, Peter G. J.

2017-01-01

Background Ethnic disparities in lung function have been linked mainly to anthropometric factors but have not been fully explained. We conducted a cross-sectional pilot study to investigate how best to study ethnic differences in lung function in young adults and evaluate whether these could be explained by birth weight and socio-economic factors. Methods We recruited 112 university students of White and South Asian British ethnicity, measured post-bronchodilator lung function, obtained information on respiratory symptoms and socio-economic factors through questionnaires, and acquired birth weight through data linkage. We regressed lung function against ethnicity and candidate predictors defined a priori using linear regression, and used penalised regression to examine a wider range of factors. We reviewed the implications of our findings for the feasibility of a larger study. Results There was a similar parental socio-economic environment and no difference in birth weight between the two ethnic groups, but the ethnic difference in FVC adjusted for sex, age, height, demi-span, father’s occupation, birth weight, maternal educational attainment and maternal upbringing was 0.81L (95%CI: -1.01 to -0.54L). Difference in body proportions did not explain the ethnic differences although parental immigration was an important predictor of FVC independent of ethnic group. Participants were comfortable with study procedures and we were able to link birth weight data to clinical measurements. Conclusion Studies of ethnic disparities in lung function among young adults are feasible. Future studies should recruit a socially more diverse sample and investigate the role of markers of acculturation in explaining such differences. PMID:28575113

Mental ability and psychological work performance in Chinese workers.

PubMed

Zhong, Fei; Yano, Eiji; Lan, Yajia; Wang, Mianzhen; Wang, Zhiming; Wang, Xiaorong

2006-10-01

This study was to explore the relationship among mental ability, occupational stress, and psychological work performance in Chinese workers, and to identify relevant modifiers of mental ability and psychological work performance. Psychological Stress Intensity (PSI), psychological work performance, and mental ability (Mental Function Index, MFI) were determined among 485 Chinese workers (aged 33 to 62 yr, 65% of men) with varied work occupations. Occupational Stress Questionnaire (OSQ) and mental ability with 3 tests (including immediate memory, digit span, and cipher decoding) were used. The relationship between mental ability and psychological work performance was analyzed with multiple linear regression approach. PSI, MFI, or psychological work performance were significantly different among different work types and educational level groups (p<0.01). Multiple linear regression analysis showed that MFI was significantly related to gender, age, educational level, and work type. Higher MFI and lower PSI predicted a better psychological work performance, even after adjusted for gender, age, educational level, and work type. The study suggests that occupational stress and low mental ability are important predictors for poor psychological work performance, which is modified by both gender and educational level.

Microbial Transformation of Esters of Chlorinated Carboxylic Acids

PubMed Central

Paris, D. F.; Wolfe, N. L.; Steen, W. C.

1984-01-01

Two groups of compounds were selected for microbial transformation studies. In the first group were carboxylic acid esters having a fixed aromatic moiety and an increasing length of the alkyl component. Ethyl esters of chlorine-substituted carboxylic acids were in the second group. Microorganisms from environmental waters and a pure culture of Pseudomonas putida U were used. The bacterial populations were monitored by plate counts, and disappearance of the parent compound was followed by gas-liquid chromatography as a function of time. The products of microbial hydrolysis were the respective carboxylic acids. Octanol-water partition coefficients (Kow) for the compounds were measured. These values spanned three orders of magnitude, whereas microbial transformation rate constants (kb) varied only 50-fold. The microbial rate constants of the carboxylic acid esters with a fixed aromatic moiety increased with an increasing length of alkyl substituents. The regression coefficient for the linear relationships between log kb and log Kow was high for group 1 compounds, indicating that these parameters correlated well. The regression coefficient for the linear relationships for group 2 compounds, however, was low, indicating that these parameters correlated poorly. PMID:16346459

Prediction of octanol-water partition coefficients of organic compounds by multiple linear regression, partial least squares, and artificial neural network.

PubMed

Golmohammadi, Hassan

2009-11-30

A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structure of 141 organic compounds to their octanol-water partition coefficients (log P(o/w)). A genetic algorithm was applied as a variable selection tool. Modeling of log P(o/w) of these compounds as a function of theoretically derived descriptors was established by multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN). The best selected descriptors that appear in the models are: atomic charge weighted partial positively charged surface area (PPSA-3), fractional atomic charge weighted partial positive surface area (FPSA-3), minimum atomic partial charge (Qmin), molecular volume (MV), total dipole moment of molecule (mu), maximum antibonding contribution of a molecule orbital in the molecule (MAC), and maximum free valency of a C atom in the molecule (MFV). The result obtained showed the ability of developed artificial neural network to prediction of partition coefficients of organic compounds. Also, the results revealed the superiority of ANN over the MLR and PLS models. Copyright 2009 Wiley Periodicals, Inc.

Developing a dengue forecast model using machine learning: A case study in China.

PubMed

Guo, Pi; Liu, Tao; Zhang, Qin; Wang, Li; Xiao, Jianpeng; Zhang, Qingying; Luo, Ganfeng; Li, Zhihao; He, Jianfeng; Zhang, Yonghui; Ma, Wenjun

2017-10-01

In China, dengue remains an important public health issue with expanded areas and increased incidence recently. Accurate and timely forecasts of dengue incidence in China are still lacking. We aimed to use the state-of-the-art machine learning algorithms to develop an accurate predictive model of dengue. Weekly dengue cases, Baidu search queries and climate factors (mean temperature, relative humidity and rainfall) during 2011-2014 in Guangdong were gathered. A dengue search index was constructed for developing the predictive models in combination with climate factors. The observed year and week were also included in the models to control for the long-term trend and seasonality. Several machine learning algorithms, including the support vector regression (SVR) algorithm, step-down linear regression model, gradient boosted regression tree algorithm (GBM), negative binomial regression model (NBM), least absolute shrinkage and selection operator (LASSO) linear regression model and generalized additive model (GAM), were used as candidate models to predict dengue incidence. Performance and goodness of fit of the models were assessed using the root-mean-square error (RMSE) and R-squared measures. The residuals of the models were examined using the autocorrelation and partial autocorrelation function analyses to check the validity of the models. The models were further validated using dengue surveillance data from five other provinces. The epidemics during the last 12 weeks and the peak of the 2014 large outbreak were accurately forecasted by the SVR model selected by a cross-validation technique. Moreover, the SVR model had the consistently smallest prediction error rates for tracking the dynamics of dengue and forecasting the outbreaks in other areas in China. The proposed SVR model achieved a superior performance in comparison with other forecasting techniques assessed in this study. The findings can help the government and community respond early to dengue epidemics.

Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows.

PubMed

Bohmanova, J; Miglior, F; Jamrozik, J; Misztal, I; Sullivan, P G

2008-09-01

A random regression model with both random and fixed regressions fitted by Legendre polynomials of order 4 was compared with 3 alternative models fitting linear splines with 4, 5, or 6 knots. The effects common for all models were a herd-test-date effect, fixed regressions on days in milk (DIM) nested within region-age-season of calving class, and random regressions for additive genetic and permanent environmental effects. Data were test-day milk, fat and protein yields, and SCS recorded from 5 to 365 DIM during the first 3 lactations of Canadian Holstein cows. A random sample of 50 herds consisting of 96,756 test-day records was generated to estimate variance components within a Bayesian framework via Gibbs sampling. Two sets of genetic evaluations were subsequently carried out to investigate performance of the 4 models. Models were compared by graphical inspection of variance functions, goodness of fit, error of prediction of breeding values, and stability of estimated breeding values. Models with splines gave lower estimates of variances at extremes of lactations than the model with Legendre polynomials. Differences among models in goodness of fit measured by percentages of squared bias, correlations between predicted and observed records, and residual variances were small. The deviance information criterion favored the spline model with 6 knots. Smaller error of prediction and higher stability of estimated breeding values were achieved by using spline models with 5 and 6 knots compared with the model with Legendre polynomials. In general, the spline model with 6 knots had the best overall performance based upon the considered model comparison criteria.

AucPR: an AUC-based approach using penalized regression for disease prediction with high-dimensional omics data.

PubMed

Yu, Wenbao; Park, Taesung

2014-01-01

It is common to get an optimal combination of markers for disease classification and prediction when multiple markers are available. Many approaches based on the area under the receiver operating characteristic curve (AUC) have been proposed. Existing works based on AUC in a high-dimensional context depend mainly on a non-parametric, smooth approximation of AUC, with no work using a parametric AUC-based approach, for high-dimensional data. We propose an AUC-based approach using penalized regression (AucPR), which is a parametric method used for obtaining a linear combination for maximizing the AUC. To obtain the AUC maximizer in a high-dimensional context, we transform a classical parametric AUC maximizer, which is used in a low-dimensional context, into a regression framework and thus, apply the penalization regression approach directly. Two kinds of penalization, lasso and elastic net, are considered. The parametric approach can avoid some of the difficulties of a conventional non-parametric AUC-based approach, such as the lack of an appropriate concave objective function and a prudent choice of the smoothing parameter. We apply the proposed AucPR for gene selection and classification using four real microarray and synthetic data. Through numerical studies, AucPR is shown to perform better than the penalized logistic regression and the nonparametric AUC-based method, in the sense of AUC and sensitivity for a given specificity, particularly when there are many correlated genes. We propose a powerful parametric and easily-implementable linear classifier AucPR, for gene selection and disease prediction for high-dimensional data. AucPR is recommended for its good prediction performance. Beside gene expression microarray data, AucPR can be applied to other types of high-dimensional omics data, such as miRNA and protein data.

Using Remote Sensing Data to Evaluate Surface Soil Properties in Alabama Ultisols

NASA Technical Reports Server (NTRS)

Sullivan, Dana G.; Shaw, Joey N.; Rickman, Doug; Mask, Paul L.; Luvall, Jeff

2005-01-01

Evaluation of surface soil properties via remote sensing could facilitate soil survey mapping, erosion prediction and allocation of agrochemicals for precision management. The objective of this study was to evaluate the relationship between soil spectral signature and surface soil properties in conventionally managed row crop systems. High-resolution RS data were acquired over bare fields in the Coastal Plain, Appalachian Plateau, and Ridge and Valley provinces of Alabama using the Airborne Terrestrial Applications Sensor multispectral scanner. Soils ranged from sandy Kandiudults to fine textured Rhodudults. Surface soil samples (0-1 cm) were collected from 163 sampling points for soil organic carbon, particle size distribution, and citrate dithionite extractable iron content. Surface roughness, soil water content, and crusting were also measured during sampling. Two methods of analysis were evaluated: 1) multiple linear regression using common spectral band ratios, and 2) partial least squares regression. Our data show that thermal infrared spectra are highly, linearly related to soil organic carbon, sand and clay content. Soil organic carbon content was the most difficult to quantify in these highly weathered systems, where soil organic carbon was generally less than 1.2%. Estimates of sand and clay content were best using partial least squares regression at the Valley site, explaining 42-59% of the variability. In the Coastal Plain, sandy surfaces prone to crusting limited estimates of sand and clay content via partial least squares and regression with common band ratios. Estimates of iron oxide content were a function of mineralogy and best accomplished using specific band ratios, with regression explaining 36-65% of the variability at the Valley and Coastal Plain sites, respectively.

Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

NASA Astrophysics Data System (ADS)

Wu, Cheng; Zhen Yu, Jian

2018-03-01

Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

A novel simple QSAR model for the prediction of anti-HIV activity using multiple linear regression analysis.

PubMed

Afantitis, Antreas; Melagraki, Georgia; Sarimveis, Haralambos; Koutentis, Panayiotis A; Markopoulos, John; Igglessi-Markopoulou, Olga

2006-08-01

A quantitative-structure activity relationship was obtained by applying Multiple Linear Regression Analysis to a series of 80 1-[2-hydroxyethoxy-methyl]-6-(phenylthio) thymine (HEPT) derivatives with significant anti-HIV activity. For the selection of the best among 37 different descriptors, the Elimination Selection Stepwise Regression Method (ES-SWR) was utilized. The resulting QSAR model (R (2) (CV) = 0.8160; S (PRESS) = 0.5680) proved to be very accurate both in training and predictive stages.

Conditional parametric models for storm sewer runoff

NASA Astrophysics Data System (ADS)

Jonsdottir, H.; Nielsen, H. Aa; Madsen, H.; Eliasson, J.; Palsson, O. P.; Nielsen, M. K.

2007-05-01

The method of conditional parametric modeling is introduced for flow prediction in a sewage system. It is a well-known fact that in hydrological modeling the response (runoff) to input (precipitation) varies depending on soil moisture and several other factors. Consequently, nonlinear input-output models are needed. The model formulation described in this paper is similar to the traditional linear models like final impulse response (FIR) and autoregressive exogenous (ARX) except that the parameters vary as a function of some external variables. The parameter variation is modeled by local lines, using kernels for local linear regression. As such, the method might be referred to as a nearest neighbor method. The results achieved in this study were compared to results from the conventional linear methods, FIR and ARX. The increase in the coefficient of determination is substantial. Furthermore, the new approach conserves the mass balance better. Hence this new approach looks promising for various hydrological models and analysis.

Wavelet regression model in forecasting crude oil price

NASA Astrophysics Data System (ADS)

Hamid, Mohd Helmie; Shabri, Ani

2017-05-01

This study presents the performance of wavelet multiple linear regression (WMLR) technique in daily crude oil forecasting. WMLR model was developed by integrating the discrete wavelet transform (DWT) and multiple linear regression (MLR) model. The original time series was decomposed to sub-time series with different scales by wavelet theory. Correlation analysis was conducted to assist in the selection of optimal decomposed components as inputs for the WMLR model. The daily WTI crude oil price series has been used in this study to test the prediction capability of the proposed model. The forecasting performance of WMLR model were also compared with regular multiple linear regression (MLR), Autoregressive Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) using root mean square errors (RMSE) and mean absolute errors (MAE). Based on the experimental results, it appears that the WMLR model performs better than the other forecasting technique tested in this study.

Early Changes in Clinical, Functional, and Laboratory Biomarkers in Workers at Risk of Indium Lung Disease

PubMed Central

Virji, M. Abbas; Trapnell, Bruce C.; Carey, Brenna; Healey, Terrance; Kreiss, Kathleen

2014-01-01

Rationale: Occupational exposure to indium compounds, including indium–tin oxide, can result in potentially fatal indium lung disease. However, the early effects of exposure on the lungs are not well understood. Objectives: To determine the relationship between short-term occupational exposures to indium compounds and the development of early lung abnormalities. Methods: Among indium–tin oxide production and reclamation facility workers, we measured plasma indium, respiratory symptoms, pulmonary function, chest computed tomography, and serum biomarkers of lung disease. Relationships between plasma indium concentration and health outcome variables were evaluated using restricted cubic spline and linear regression models. Measurements and Main Results: Eighty-seven (93%) of 94 indium–tin oxide facility workers (median tenure, 2 yr; median plasma indium, 1.0 μg/l) participated in the study. Spirometric abnormalities were not increased compared with the general population, and few subjects had radiographic evidence of alveolar proteinosis (n = 0), fibrosis (n = 2), or emphysema (n = 4). However, in internal comparisons, participants with plasma indium concentrations ≥ 1.0 μg/l had more dyspnea, lower mean FEV1 and FVC, and higher median serum Krebs von den Lungen-6 and surfactant protein-D levels. Spline regression demonstrated nonlinear exposure response, with significant differences occurring at plasma indium concentrations as low as 1.0 μg/l compared with the reference. Associations between health outcomes and the natural log of plasma indium concentration were evident in linear regression models. Associations were not explained by age, smoking status, facility tenure, or prior occupational exposures. Conclusions: In indium–tin oxide facility workers with short-term, low-level exposure, plasma indium concentrations lower than previously reported were associated with lung symptoms, decreased spirometric parameters, and increased serum biomarkers of lung disease. PMID:25295756

Comparison of the COPD Assessment Test (CAT) and the Clinical COPD Questionnaire (CCQ) in a Clinical Population.

PubMed

Sundh, Josefin; Ställberg, Björn; Lisspers, Karin; Kämpe, Mary; Janson, Christer; Montgomery, Scott

2016-01-01

The COPD Assessment Test (CAT) and the Clinical COPD Questionnaire (CCQ) are both clinically useful health status instruments. The main objective was to compare CAT and CCQ measurement instruments. CAT and CCQ forms were completed by 432 randomly selected primary and secondary care patients with a COPD diagnosis. Correlation and linear regression analyses of CAT and CCQ were performed. Standardised scores were created for the CAT and CCQ scores, and separate multiple linear regression analyses for CAT and CCQ examined associations with sex, age (≤ 60, 61-70 and >70 years), exacerbations (≥ 1 vs 0 in the previous year), body mass index (BMI), heart disease, anxiety/depression and lung function (subgroup with n = 246). CAT and CCQ correlated well (r = 0.88, p < 0.0001), as did CAT ≥ 10 and CCQ ≥ 1 (r = 0.78, p < 0.0001). CCQ 1.0 corresponded to CAT 9.93 and CAT 10 to CCQ 1.29. Both instruments were associated with BMI < 20 (standardised adjusted regression coefficient (95%CI) for CAT 0.56 (0.18 to 0.93) and CCQ 0.56 (0.20 to 0.92)), exacerbations (CAT 0.77 (0.58 to 0.95) and CCQ 0.94 (0.76 to 1.12)), heart disease (CAT 0.38 (0.17 to 0.59) and CCQ 0.23 (0.03 to 0.43)), anxiety/depression (CAT 0.35 (0.15 to 0.56) and CCQ 0.41 (0.21 to 0.60)) and COPD stage (CAT 0.19 (0.05 to 0.34) and CCQ 0.22 (0.07 to 0.36)). CAT and CCQ correlate well with each other. Heart disease, anxiety/depression, underweight, exacerbations, and low lung function are associated with worse health status assessed by both instruments.

Associations between maternal long-chain polyunsaturated fatty acid concentrations and child cognition at 7 years of age: The MEFAB birth cohort.

PubMed

Brouwer-Brolsma, E M; van de Rest, O; Godschalk, R; Zeegers, M P A; Gielen, M; de Groot, R H M

2017-11-01

Concentrations of the fish fatty acids EPA and DHA are low among Dutch women of reproductive age. As the human brain incorporates high concentrations of these fatty acids in utero, particularly during third trimester of gestation, these low EPA and DHA concentrations may have adverse consequences for fetal brain development and functioning. Analyses were conducted using longitudinal observational data of 292 mother-child pairs participating in the MEFAB cohort. Maternal AA, DHA, and EPA were determined in plasma phospholipids - obtained in three trimesters - by gas-liquid chromatography. Cognitive function was assessed at 7 years of age, using the Kaufman Assessment Battery for Children, resulting in three main outcome parameters: sequential processing (short-term memory), simultaneous processing (problem-solving skills), and the mental processing composite score. Spline regression and linear regression analyses were used to analyse the data, while adjusting for potential relevant covariates. Only 2% of the children performed more than one SD below the mental processing composite norm score. Children with lower test scores (<25%) were more likely to have a younger mother with a higher pre-gestational BMI, less likely to be breastfed, and more likely to be born with a lower birth weight, compared to children with higher test scores (≥25%). Fully-adjusted linear regression models did not show associations of maternal AA, DHA, or EPA status during any of the pregnancy trimesters with childhood sequential and simultaneous processing. Maternal fatty acid status during pregnancy was not associated with cognitive performance in Dutch children at age 7. Copyright © 2017 Elsevier Ltd. All rights reserved.

VoxelStats: A MATLAB Package for Multi-Modal Voxel-Wise Brain Image Analysis.

PubMed

Mathotaarachchi, Sulantha; Wang, Seqian; Shin, Monica; Pascoal, Tharick A; Benedet, Andrea L; Kang, Min Su; Beaudry, Thomas; Fonov, Vladimir S; Gauthier, Serge; Labbe, Aurélie; Rosa-Neto, Pedro

2016-01-01

In healthy individuals, behavioral outcomes are highly associated with the variability on brain regional structure or neurochemical phenotypes. Similarly, in the context of neurodegenerative conditions, neuroimaging reveals that cognitive decline is linked to the magnitude of atrophy, neurochemical declines, or concentrations of abnormal protein aggregates across brain regions. However, modeling the effects of multiple regional abnormalities as determinants of cognitive decline at the voxel level remains largely unexplored by multimodal imaging research, given the high computational cost of estimating regression models for every single voxel from various imaging modalities. VoxelStats is a voxel-wise computational framework to overcome these computational limitations and to perform statistical operations on multiple scalar variables and imaging modalities at the voxel level. VoxelStats package has been developed in Matlab(®) and supports imaging formats such as Nifti-1, ANALYZE, and MINC v2. Prebuilt functions in VoxelStats enable the user to perform voxel-wise general and generalized linear models and mixed effect models with multiple volumetric covariates. Importantly, VoxelStats can recognize scalar values or image volumes as response variables and can accommodate volumetric statistical covariates as well as their interaction effects with other variables. Furthermore, this package includes built-in functionality to perform voxel-wise receiver operating characteristic analysis and paired and unpaired group contrast analysis. Validation of VoxelStats was conducted by comparing the linear regression functionality with existing toolboxes such as glim_image and RMINC. The validation results were identical to existing methods and the additional functionality was demonstrated by generating feature case assessments (t-statistics, odds ratio, and true positive rate maps). In summary, VoxelStats expands the current methods for multimodal imaging analysis by allowing the estimation of advanced regional association metrics at the voxel level.

Masticatory performance and oral health-related quality of life before and after complete denture treatment.

PubMed

Yamamoto, Saori; Shiga, Hiroshi

2018-03-13

To clarify the relationship between masticatory performance and oral health-related quality of life (OHRQoL) before and after complete denture treatment. Thirty patients wearing complete dentures were asked to chew a gummy jelly on their habitual chewing side, and the amount of glucose extraction during chewing was measured as the parameter of masticatory performance. Subjects were asked to answer the Oral Health Impact Profile (OHIP-J49) questionnaire, which consists of 49 questions related to oral problems. The total score of 49 question items along with individual domain scores within the seven domains (functional limitation, pain, psychological discomfort, physical disability, psychological disability, social disability and handicap) were calculated and used as the parameters of OHRQoL. These records were obtained before treatment and 3 months after treatment. Each parameter of masticatory performance and OHRQoL was compared before treatment and after treatment. The relationship between masticatory performance and OHRQoL was investigated, and a stepwise multiple linear regression analysis was performed. Both masticatory performance and OHRQoL were significantly improved after treatment. Furthermore, masticatory performance was significantly correlated with some parameters of OHRQoL. The stepwise multiple linear regression analysis showed functional limitation and pain as important factors affecting masticatory performance before treatment and functional limitation as important factors affecting masticatory performance after treatment. These results suggested that masticatory performance and OHRQoL are significantly improved after treatment and that there is a close relationship between the two. Moreover, functional limitation was found to be the most important factor affecting masticatory performance. Copyright © 2018 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved.

Depressive symptoms, handgrip strength, and weight status in US older adults.

PubMed

Smith, Lee; White, Stephanie; Stubbs, Brendon; Hu, Liang; Veronese, Nicola; Vancampfort, Davy; Hamer, Mark; Gardner, Benjamin; Yang, Lin

2018-06-05

Handgrip strength is a valid indicator of broader physical functioning. Handgrip strength and weight status have been independently associated with depressive symptoms in older adults, but no study has yet investigated the relationships between all three in older US adults. This study investigated the relationship between physical function and depressive symptoms by weight status in older US adults. Cross-sectional data were analysed from the National Health and Nutrition Examination Survey waves 2011 to 2012 and 2013 to 2014. Physical function was assessed using a grip strength dynamometer. Depressive symptoms were assessed using the self-reported Patient Health Questionnaire-9. Weight status was assessed using Body Mass Index (BMI) and participants were categorised as normal weight (< 25 kg/m 2 ), overweight (25 to < 30 kg/m 2 ), and obese (≥ 30.0 kg/m 2 ). Associations between depressive symptoms and hand grip strength were estimated by gender-specific multiple linear regressions and BMI stratified multivariable linear regression. A total of 2,812 adults (54% female, mean age 69.2 years, mean BMI 29.2 kg/m 2 ) were included. Women with moderate to severe depressive symptoms had 1.60 kg (95% CI: 0.91 to 2.30) lower hand grip strength compared to women with minimal or no depressive symptoms. No such association was observed in men. Among those with obesity, men (-3.72 kg, 95% CI: -7.00 to -0.43) and women (-1.83 kg, 95% CI: -2.87 to -0.78) with moderate to severe depressive symptoms both had lower handgrip strength. Among older US adults, women and people who are obese and depressed are at the greatest risk of decline in physical function. Copyright © 2018 Elsevier B.V. All rights reserved.

High Right Ventricular Stroke Work Index Is Associated with Worse Kidney Function in Patients with Heart Failure with Preserved Ejection Fraction.

PubMed

Kanjanahattakij, Napatt; Sirinvaravong, Natee; Aguilar, Francisco; Agrawal, Akanksha; Krishnamoorthy, Parasuram; Gupta, Shuchita

2018-01-01

In patients with heart failure with preserved ejection fraction (HFpEF), worse kidney function is associated with worse overall cardiac mechanics. Right ventricular stroke work index (RVSWI) is a parameter of right ventricular function. The aim of our study was to determine the relationship between RVSWI and glomerular filtration rate (GFR) in patients with HFpEF. This was a single-center cross-sectional study. HFpEF is defined as patients with documented heart failure with ejection fraction > 50% and pulmonary wedge pressure > 15 mm Hg from right heart catheterization. RVSWI (normal value 8-12 g/m/beat/m2) was calculated using the formula: RVSWI = 0.0136 × stroke volume index × (mean pulmonary artery pressure - mean right atrial pressure). Univariate and multivariate linear regression analysis was performed to study the correlation between RVSWI and GFR. Ninety-one patients were included in the study. The patients were predominantly female (n = 64, 70%) and African American (n = 61, 67%). Mean age was 66 ± 12 years. Mean GFR was 59 ± 35 mL/min/1.73 m2. Mean RVSWI was 11 ± 6 g/m/beat/m2. Linear regression analysis showed that there was a significant independent inverse relationship between RVSWI and GFR (unstandardized coefficient = -1.3, p = 0.029). In the subgroup with combined post and precapillary pulmonary hypertension (Cpc-PH) the association remained significant (unstandardized coefficient = -1.74, 95% CI -3.37 to -0.11, p = 0.04). High right ventricular workload indicated by high RVSWI is associated with worse renal function in patients with Cpc-PH. Further prospective studies are needed to better understand this association. © 2018 S. Karger AG, Basel.

Partitioning sources of variation in vertebrate species richness

USGS Publications Warehouse

Boone, R.B.; Krohn, W.B.

2000-01-01

Aim: To explore biogeographic patterns of terrestrial vertebrates in Maine, USA using techniques that would describe local and spatial correlations with the environment. Location: Maine, USA. Methods: We delineated the ranges within Maine (86,156 km2) of 275 species using literature and expert review. Ranges were combined into species richness maps, and compared to geomorphology, climate, and woody plant distributions. Methods were adapted that compared richness of all vertebrate classes to each environmental correlate, rather than assessing a single explanatory theory. We partitioned variation in species richness into components using tree and multiple linear regression. Methods were used that allowed for useful comparisons between tree and linear regression results. For both methods we partitioned variation into broad-scale (spatially autocorrelated) and fine-scale (spatially uncorrelated) explained and unexplained components. By partitioning variance, and using both tree and linear regression in analyses, we explored the degree of variation in species richness for each vertebrate group that Could be explained by the relative contribution of each environmental variable. Results: In tree regression, climate variation explained richness better (92% of mean deviance explained for all species) than woody plant variation (87%) and geomorphology (86%). Reptiles were highly correlated with environmental variation (93%), followed by mammals, amphibians, and birds (each with 84-82% deviance explained). In multiple linear regression, climate was most closely associated with total vertebrate richness (78%), followed by woody plants (67%) and geomorphology (56%). Again, reptiles were closely correlated with the environment (95%), followed by mammals (73%), amphibians (63%) and birds (57%). Main conclusions: Comparing variation explained using tree and multiple linear regression quantified the importance of nonlinear relationships and local interactions between species richness and environmental variation, identifying the importance of linear relationships between reptiles and the environment, and nonlinear relationships between birds and woody plants, for example. Conservation planners should capture climatic variation in broad-scale designs; temperatures may shift during climate change, but the underlying correlations between the environment and species richness will presumably remain.

Investigation of absolute and relative response for three different liquid chromatography/tandem mass spectrometry systems; the impact of ionization and detection saturation.

PubMed

Nilsson, Lars B; Skansen, Patrik

2012-06-30

The investigations in this article were triggered by two observations in the laboratory; for some liquid chromatography/tandem mass spectrometry (LC/MS/MS) systems it was possible to obtain linear calibration curves for extreme concentration ranges and for some systems seemingly linear calibration curves gave good accuracy at low concentrations only when using a quadratic regression function. The absolute and relative responses were tested for three different LC/MS/MS systems by injecting solutions of a model compound and a stable isotope labeled internal standard. The analyte concentration range for the solutions was 0.00391 to 500 μM (128,000×), giving overload of the chromatographic column at the highest concentrations. The stable isotope labeled internal standard concentration was 0.667 μM in all samples. The absolute response per concentration unit decreased rapidly as higher concentrations were injected. The relative response, the ratio for the analyte peak area to the internal standard peak area, per concentration unit was calculated. For system 1, the ionization process was found to limit the response and the relative response per concentration unit was constant. For systems 2 and 3, the ion detection process was the limiting factor resulting in decreasing relative response at increasing concentrations. For systems behaving like system 1, simple linear regression can be used for any concentration range while, for systems behaving like systems 2 and 3, non-linear regression is recommended for all concentration ranges. Another consequence is that the ionization capacity limited systems will be insensitive to matrix ion suppression when an ideal internal standard is used while the detection capacity limited systems are at risk of giving erroneous results at high concentrations if the matrix ion suppression varies for different samples in a run. Copyright © 2012 John Wiley & Sons, Ltd.

Kinesiophobia, Pain, Muscle Functions, and Functional Performances among Older Persons with Low Back Pain.

PubMed

Ishak, Nor Azizah; Zahari, Zarina; Justine, Maria

2017-01-01

This study aims (1) to determine the association between kinesiophobia and pain, muscle functions, and functional performances and (2) to determine whether kinesiophobia predicts pain, muscle functions, and functional performance among older persons with low back pain (LBP). This is a correlational study, involving 63 institutionalized older persons (age = 70.98 ± 7.90 years) diagnosed with LBP. Anthropometric characteristics (BMI) and functional performances (lower limb function, balance and mobility, and hand grip strength) were measured. Muscle strength (abdominal and back muscle strength) was assessed using the Baseline® Mechanical Push/Pull Dynamometer, while muscle control (transverse abdominus and multifidus) was measured by using the Pressure Biofeedback Unit. The pain intensity and the level of kinesiophobia were measured using Numerical Rating Scale and Tampa Scale of Kinesiophobia, respectively. Data were analyzed using Pearson's correlation coefficients and multivariate linear regressions. No significant correlations were found between kinesiophobia and pain and muscle functions (all p > 0.05). Kinesiophobia was significantly correlated with mobility and balance ( p = 0.038, r = 0.263). Regressions analysis showed that kinesiophobia was a significant predictor of mobility and balance ( p = 0.038). We can conclude that kinesiophobia predicted mobility and balance in older persons with LBP. Kinesiophobia should be continuously assessed in clinical settings to recognize the obstacles that may affect patient's compliance towards a rehabilitation program in older persons with LBP.

Kinesiophobia, Pain, Muscle Functions, and Functional Performances among Older Persons with Low Back Pain

PubMed Central

2017-01-01

Objectives This study aims (1) to determine the association between kinesiophobia and pain, muscle functions, and functional performances and (2) to determine whether kinesiophobia predicts pain, muscle functions, and functional performance among older persons with low back pain (LBP). Methods This is a correlational study, involving 63 institutionalized older persons (age = 70.98 ± 7.90 years) diagnosed with LBP. Anthropometric characteristics (BMI) and functional performances (lower limb function, balance and mobility, and hand grip strength) were measured. Muscle strength (abdominal and back muscle strength) was assessed using the Baseline® Mechanical Push/Pull Dynamometer, while muscle control (transverse abdominus and multifidus) was measured by using the Pressure Biofeedback Unit. The pain intensity and the level of kinesiophobia were measured using Numerical Rating Scale and Tampa Scale of Kinesiophobia, respectively. Data were analyzed using Pearson's correlation coefficients and multivariate linear regressions. Results No significant correlations were found between kinesiophobia and pain and muscle functions (all p > 0.05). Kinesiophobia was significantly correlated with mobility and balance (p = 0.038, r = 0.263). Regressions analysis showed that kinesiophobia was a significant predictor of mobility and balance (p = 0.038). Conclusion We can conclude that kinesiophobia predicted mobility and balance in older persons with LBP. Kinesiophobia should be continuously assessed in clinical settings to recognize the obstacles that may affect patient's compliance towards a rehabilitation program in older persons with LBP. PMID:28634547

Global and System-Specific Resting-State fMRI Fluctuations Are Uncorrelated: Principal Component Analysis Reveals Anti-Correlated Networks

PubMed Central

Carbonell, Felix; Bellec, Pierre

2011-01-01

Abstract The influence of the global average signal (GAS) on functional-magnetic resonance imaging (fMRI)–based resting-state functional connectivity is a matter of ongoing debate. The global average fluctuations increase the correlation between functional systems beyond the correlation that reflects their specific functional connectivity. Hence, removal of the GAS is a common practice for facilitating the observation of network-specific functional connectivity. This strategy relies on the implicit assumption of a linear-additive model according to which global fluctuations, irrespective of their origin, and network-specific fluctuations are super-positioned. However, removal of the GAS introduces spurious negative correlations between functional systems, bringing into question the validity of previous findings of negative correlations between fluctuations in the default-mode and the task-positive networks. Here we present an alternative method for estimating global fluctuations, immune to the complications associated with the GAS. Principal components analysis was applied to resting-state fMRI time-series. A global-signal effect estimator was defined as the principal component (PC) that correlated best with the GAS. The mean correlation coefficient between our proposed PC-based global effect estimator and the GAS was 0.97±0.05, demonstrating that our estimator successfully approximated the GAS. In 66 out of 68 runs, the PC that showed the highest correlation with the GAS was the first PC. Since PCs are orthogonal, our method provides an estimator of the global fluctuations, which is uncorrelated to the remaining, network-specific fluctuations. Moreover, unlike the regression of the GAS, the regression of the PC-based global effect estimator does not introduce spurious anti-correlations beyond the decrease in seed-based correlation values allowed by the assumed additive model. After regressing this PC-based estimator out of the original time-series, we observed robust anti-correlations between resting-state fluctuations in the default-mode and the task-positive networks. We conclude that resting-state global fluctuations and network-specific fluctuations are uncorrelated, supporting a Resting-State Linear-Additive Model. In addition, we conclude that the network-specific resting-state fluctuations of the default-mode and task-positive networks show artifact-free anti-correlations. PMID:22444074

Silicone Foul Release Coatings: Effect of the Interaction of Oil and Coating Functionalities on the Magnitude of Macrofouling Attachment Strengths

DTIC Science & Technology

2003-01-01

Hawaii) is described. The response of tubeworms (Hydroides elegans, Hydroides dianthus ), oysters (Ostrea sp., Crassostrea sp.) and barnacles (Balanus...8 and Hydroides dianthus ) and oysters (Ostrea sp. and Crassostrea sp.) to the silicone coatings were measured using ASTM D 5618-94 (1994), in which...Oyster (Crassostrea sp.) and tubeworm (H. dianthus ) attachment strengths at the Indian River Lagoon site Linear regression analyses of the adhesion

Resting-State Functional Connectivity Predicts Cognitive Impairment Related to Alzheimer's Disease.

PubMed

Lin, Qi; Rosenberg, Monica D; Yoo, Kwangsun; Hsu, Tiffany W; O'Connell, Thomas P; Chun, Marvin M

2018-01-01

Resting-state functional connectivity (rs-FC) is a promising neuromarker for cognitive decline in aging population, based on its ability to reveal functional differences associated with cognitive impairment across individuals, and because rs-fMRI may be less taxing for participants than task-based fMRI or neuropsychological tests. Here, we employ an approach that uses rs-FC to predict the Alzheimer's Disease Assessment Scale (11 items; ADAS11) scores, which measure overall cognitive functioning, in novel individuals. We applied this technique, connectome-based predictive modeling, to a heterogeneous sample of 59 subjects from the Alzheimer's Disease Neuroimaging Initiative, including normal aging, mild cognitive impairment, and AD subjects. First, we built linear regression models to predict ADAS11 scores from rs-FC measured with Pearson's r correlation. The positive network model tested with leave-one-out cross validation (LOOCV) significantly predicted individual differences in cognitive function from rs-FC. In a second analysis, we considered other functional connectivity features, accordance and discordance, which disentangle the correlation and anticorrelation components of activity timecourses between brain areas. Using partial least square regression and LOOCV, we again built models to successfully predict ADAS11 scores in novel individuals. Our study provides promising evidence that rs-FC can reveal cognitive impairment in an aging population, although more development is needed for clinical application.

Self-rated and observer-rated measures of well-being and distress in adolescence: an exploratory study.

PubMed

Vescovelli, Francesca; Albieri, Elisa; Ruini, Chiara

2014-01-01

The evaluation of eudaimonic well-being in adolescence is hampered by the lack of specific assessment tools. Moreover, with younger populations, the assessment of positive functioning may be biased by self-report data only, and may be more accurate by adding significant adults' evaluations. The objective of this research was to measure adolescents' well-being and prosocial behaviours using self-rated and observer-rated instruments, and their pattern of associations. The sample included 150 Italian high school adolescents. Observed-evaluation was performed by their school teachers using the Strengths and Difficulties Questionnaire. Adolescents completed Ryff's Psychological Well-being Scales and Symptom Questionnaire. Pearson' r correlations and Linear regression were performed. Self-rated dimensions of psychological well-being significantly correlated with all observer-rated dimensions, but Strengths and Difficulties Emotional symptom scale. Multiple linear regression showed that the self-rated dimensions Environmental Mastery and Personal Growth, and surprisingly not Positive Relations, are related to the observer-rated dimension Prosocial Behaviour. Adolescents with higher levels of well-being in specific dimensions tend to be perceived as less problematic by their teachers. However, some dimensions of positive functioning present discrepancies between self and observer-rated instruments. Thus, the conjunct use of self-reports and observer-rated tools for a more comprehensive assessment of students' eudaimonic well-being is recommended.

Relationship between fear of falling and outcomes of an inpatient geriatric rehabilitation population--fear of the fear of falling.

PubMed

Denkinger, Michael D; Igl, Wilmar; Lukas, Albert; Bader, Anne; Bailer, Stefanie; Franke, Sebastian; Denkinger, Claudia M; Nikolaus, Thorsten; Jamour, Michael

2010-04-01

To examine the effects of various risk factors on three functional outcomes during rehabilitation. Geriatric inpatient rehabilitation unit. Observational longitudinal study. One hundred sixty-one geriatric rehabilitation inpatients (men, women), mean age 82, who were capable of walking at baseline. Functional status was assessed weekly between admission and discharge and at a follow-up 4 months later at home using the function component of the Short Form-Late Life Function and Disability Instrument, the Barthel Index, and Habitual Gait Speed. Various risk factors, such as falls-related self-efficacy (Falls Efficacy Scale-International), were measured. Associations between predictors and functional status at discharge and follow-up were analyzed using linear regression models and bivariate plots. Fear of falling predicted functioning across all outcomes except for habitual gait speed at discharge and follow-up. Visual comparison of functional trajectories between subgroups confirmed these findings, with different levels of fear of falling across time in linear plots. Thus, superior ability of this measure to discriminate between functional status at baseline across all outcomes and to discriminate between functional change especially with regard to the performance-based outcome was demonstrated. Falls-related self-efficacy is the only parameter that significantly predicts rehabilitation outcome at discharge and follow-up across all outcomes. Therefore, it should be routinely assessed in future studies in (geriatric) rehabilitation and considered to be an important treatment goal.

Post-processing through linear regression

NASA Astrophysics Data System (ADS)

van Schaeybroeck, B.; Vannitsem, S.

2011-03-01

Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

Linear regression metamodeling as a tool to summarize and present simulation model results.

PubMed

Jalal, Hawre; Dowd, Bryan; Sainfort, François; Kuntz, Karen M

2013-10-01

Modelers lack a tool to systematically and clearly present complex model results, including those from sensitivity analyses. The objective was to propose linear regression metamodeling as a tool to increase transparency of decision analytic models and better communicate their results. We used a simplified cancer cure model to demonstrate our approach. The model computed the lifetime cost and benefit of 3 treatment options for cancer patients. We simulated 10,000 cohorts in a probabilistic sensitivity analysis (PSA) and regressed the model outcomes on the standardized input parameter values in a set of regression analyses. We used the regression coefficients to describe measures of sensitivity analyses, including threshold and parameter sensitivity analyses. We also compared the results of the PSA to deterministic full-factorial and one-factor-at-a-time designs. The regression intercept represented the estimated base-case outcome, and the other coefficients described the relative parameter uncertainty in the model. We defined simple relationships that compute the average and incremental net benefit of each intervention. Metamodeling produced outputs similar to traditional deterministic 1-way or 2-way sensitivity analyses but was more reliable since it used all parameter values. Linear regression metamodeling is a simple, yet powerful, tool that can assist modelers in communicating model characteristics and sensitivity analyses.

Support vector regression to predict porosity and permeability: Effect of sample size

NASA Astrophysics Data System (ADS)

Al-Anazi, A. F.; Gates, I. D.

2012-02-01

Porosity and permeability are key petrophysical parameters obtained from laboratory core analysis. Cores, obtained from drilled wells, are often few in number for most oil and gas fields. Porosity and permeability correlations based on conventional techniques such as linear regression or neural networks trained with core and geophysical logs suffer poor generalization to wells with only geophysical logs. The generalization problem of correlation models often becomes pronounced when the training sample size is small. This is attributed to the underlying assumption that conventional techniques employing the empirical risk minimization (ERM) inductive principle converge asymptotically to the true risk values as the number of samples increases. In small sample size estimation problems, the available training samples must span the complexity of the parameter space so that the model is able both to match the available training samples reasonably well and to generalize to new data. This is achieved using the structural risk minimization (SRM) inductive principle by matching the capability of the model to the available training data. One method that uses SRM is support vector regression (SVR) network. In this research, the capability of SVR to predict porosity and permeability in a heterogeneous sandstone reservoir under the effect of small sample size is evaluated. Particularly, the impact of Vapnik's ɛ-insensitivity loss function and least-modulus loss function on generalization performance was empirically investigated. The results are compared to the multilayer perception (MLP) neural network, a widely used regression method, which operates under the ERM principle. The mean square error and correlation coefficients were used to measure the quality of predictions. The results demonstrate that SVR yields consistently better predictions of the porosity and permeability with small sample size than the MLP method. Also, the performance of SVR depends on both kernel function type and loss functions used.

The Evolution of Self-Reported Urinary and Sexual Dysfunction over the Last Two Decades: Implications for Comparative Effectiveness Research.

PubMed

Resnick, Matthew J; Barocas, Daniel A; Morgans, Alicia K; Phillips, Sharon E; Koyama, Tatsuki; Albertsen, Peter C; Cooperberg, Matthew R; Goodman, Michael; Greenfield, Sheldon; Hamilton, Ann S; Hoffman, Karen E; Hoffman, Richard M; Kaplan, Sherrie H; McCollum, Dan; Paddock, Lisa E; Stanford, Janet L; Stroup, Antoinette M; Wu, Xiao-Cheng; Penson, David F

2015-06-01

Despite the paramount importance of patient-reported outcomes, little is known about the evolution of patient-reported urinary and sexual function over time. To evaluate differences in pretreatment urinary and sexual function in two population-based cohorts of men with prostate cancer enrolled nearly 20 yr apart. Patients were enrolled in the Prostate Cancer Outcomes Study (PCOS) or the Comparative Effectiveness Analysis of Surgery and Radiation (CEASAR) study, two population-based cohorts that enrolled patients with incident prostate cancer from 1994 to 1995 and from 2011 to 2012, respectively. Participants completed surveys at baseline and various time points thereafter. We performed multivariable logistic and linear regression analysis to investigate differences in pretreatment function between studies. The study comprised 5469 men of whom 2334 (43%) were enrolled in PCOS and 3135 (57%) were enrolled in CEASAR. Self-reported urinary incontinence was higher in CEASAR compared with PCOS (7.7% vs 4.7%; adjusted odds ratio [OR]: 1.83; 95% confidence interval [CI], 1.39-2.43). Similarly, self-reported erectile dysfunction was more common among CEASAR participants (44.7% vs 24.0%) with an adjusted OR of 3.12 (95% CI, 2.68-3.64). Multivariable linear regression models revealed less favorable self-reported baseline function among CEASAR participants in the urinary incontinence and sexual function domains. The study is limited by its observational design and possibility of unmeasured confounding. Reporting of pretreatment urinary incontinence and erectile dysfunction has increased over the past two decades. These findings may reflect sociological changes including heightened media attention and direct-to-consumer marketing, among other potential explanations. Patient reporting of urinary and sexual function has evolved and is likely contingent on continually changing societal norms. Recognizing the evolving nature of patient reporting is essential in efforts to conduct high-quality, impactful comparative effectiveness research. Copyright © 2014 European Association of Urology. All rights reserved.

A Simulation-Based Comparison of Several Stochastic Linear Regression Methods in the Presence of Outliers.

ERIC Educational Resources Information Center

Rule, David L.

Several regression methods were examined within the framework of weighted structural regression (WSR), comparing their regression weight stability and score estimation accuracy in the presence of outlier contamination. The methods compared are: (1) ordinary least squares; (2) WSR ridge regression; (3) minimum risk regression; (4) minimum risk 2;…

Unit Cohesion and the Surface Navy: Does Cohesion Affect Performance

DTIC Science & Technology

1989-12-01

v. 68, 1968. Neter, J., Wasserman, W., and Kutner, M. H., Applied Linear Regression Models, 2d ed., Boston, MA: Irwin, 1989. Rand Corporation R-2607...Neter, J., Wasserman, W., and Kutner, M. H., Applied Linear Regression Models, 2d ed., Boston, MA: Irwin, 1989. SAS User’s Guide: Basics, Version 5 ed

Comparison of Selection Procedures and Validation of Criterion Used in Selection of Significant Control Variates of a Simulation Model

DTIC Science & Technology

1990-03-01

and M.H. Knuter. Applied Linear Regression Models. Homewood IL: Richard D. Erwin Inc., 1983. Pritsker, A. Alan B. Introduction to Simulation and SLAM...Control Variates in Simulation," European Journal of Operational Research, 42: (1989). Neter, J., W. Wasserman, and M.H. Xnuter. Applied Linear Regression Models

Comparing Regression Coefficients between Nested Linear Models for Clustered Data with Generalized Estimating Equations

ERIC Educational Resources Information Center

Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer

2013-01-01

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Calibrated Peer Review for Interpreting Linear Regression Parameters: Results from a Graduate Course

ERIC Educational Resources Information Center

Enders, Felicity B.; Jenkins, Sarah; Hoverman, Verna

2010-01-01

Biostatistics is traditionally a difficult subject for students to learn. While the mathematical aspects are challenging, it can also be demanding for students to learn the exact language to use to correctly interpret statistical results. In particular, correctly interpreting the parameters from linear regression is both a vital tool and a…

What Is Wrong with ANOVA and Multiple Regression? Analyzing Sentence Reading Times with Hierarchical Linear Models

ERIC Educational Resources Information Center

Richter, Tobias

2006-01-01

Most reading time studies using naturalistic texts yield data sets characterized by a multilevel structure: Sentences (sentence level) are nested within persons (person level). In contrast to analysis of variance and multiple regression techniques, hierarchical linear models take the multilevel structure of reading time data into account. They…

Some Applied Research Concerns Using Multiple Linear Regression Analysis.

ERIC Educational Resources Information Center

Newman, Isadore; Fraas, John W.

The intention of this paper is to provide an overall reference on how a researcher can apply multiple linear regression in order to utilize the advantages that it has to offer. The advantages and some concerns expressed about the technique are examined. A number of practical ways by which researchers can deal with such concerns as…

Using Simple Linear Regression to Assess the Success of the Montreal Protocol in Reducing Atmospheric Chlorofluorocarbons

ERIC Educational Resources Information Center

Nelson, Dean

2009-01-01

Following the Guidelines for Assessment and Instruction in Statistics Education (GAISE) recommendation to use real data, an example is presented in which simple linear regression is used to evaluate the effect of the Montreal Protocol on atmospheric concentration of chlorofluorocarbons. This simple set of data, obtained from a public archive, can…

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Subjective cognitive complaints and neuropsychological performance in former smokers with and without chronic obstructive pulmonary disease.

PubMed

Brunette, Amanda M; Holm, Kristen E; Wamboldt, Frederick S; Kozora, Elizabeth; Moser, David J; Make, Barry J; Crapo, James D; Meschede, Kimberly; Weinberger, Howard D; Moreau, Kerrie L; Bowler, Russell P; Hoth, Karin F

2018-05-01

This study examined the association of perceived cognitive difficulties with objective cognitive performance in former smokers. We hypothesized that greater perceived cognitive difficulties would be associated with poorer performance on objective executive and memory tasks. Participants were 95 former smokers recruited from the COPDGene study. They completed questionnaires (including the Cognitive Difficulties Scale [CDS] and the Hospital Anxiety and Depression Scale [HADS]), neuropsychological assessment, and pulmonary function testing. Pearson correlations and t-tests were conducted to examine the bivariate association of the CDS (total score and subscales for attention/concentration, praxis, delayed recall, orientation for persons, temporal orientation, and prospective memory) with each domain of objective cognitive functioning (memory recall, executive functioning/processing speed, visuospatial processing, and language). Simultaneous multiple linear regression was used to further examine all statistically significant bivariate associations. The following covariates were included in all regression models: age, sex, pack-years, premorbid functioning (WRAT-IV Reading), HADS total score, and chronic obstructive pulmonary disease (COPD) status (yes/no based on GOLD criteria). In regression models, greater perceived cognitive difficulties overall (using CDS total score) were associated with poorer performance on executive functioning/processing speed tasks (b = -0.07, SE = 0.03, p = .037). Greater perceived cognitive difficulties on the CDS praxis subscale were associated with poorer performance on executive functioning/processing speed tasks (b = -3.65, SE = 1.25, p = .005), memory recall tasks (b = -4.60, SE = 1.75, p = .010), and language tasks (b = -3.89, SE = 1.39, p = .006). Clinicians should be aware that cognitive complaints may be indicative of problems with the executive functioning/processing speed and memory of former smokers with and without COPD.

Physical Function, Hyperuricemia, and Gout in Older Adults.

PubMed

Burke, Bridget Teevan; Köttgen, Anna; Law, Andrew; Windham, Beverly Gwen; Segev, Dorry; Baer, Alan N; Coresh, Josef; McAdams-DeMarco, Mara A

2015-12-01

Gout prevalence is high in older adults and those affected are at risk of physical disability, yet it is unclear whether they have worse physical function. We studied gout, hyperuricemia, and physical function in 5,819 older adults (age ≥65 years) attending the 2011-2013 Atherosclerosis Risk in Communities Study visit, a prospective US population-based cohort. Differences in lower extremity function (Short Physical Performance Battery [SPPB] and 4-meter walking speed) and upper extremity function (grip strength) by gout status and by hyperuricemia prevalence were estimated in adjusted ordinal logistic regression (SPPB) and linear regression (walking speed and grip strength) models. Lower scores or times signify worse function. The prevalence of poor physical performance (first quartile) by gout and hyperuricemia was estimated using adjusted modified Poisson regression. Ten percent of participants reported a history of gout and 21% had hyperuricemia. There was no difference in grip strength by history of gout (P = 0.77). Participants with gout performed worse on the SPPB test; they had 0.77 times (95% confidence interval [95% CI] 0.65, 0.90, P = 0.001) the prevalence odds of a 1-unit increase in SPPB score and were 1.18 times (95% CI 1.07, 1.32, P = 0.002) more likely to have poor SPPB performance. Participants with a history of gout had slower walking speed (mean difference -0.03; 95% CI -0.05, -0.01, P < 0.001) and were 1.19 times (95% CI 1.06, 1.34, P = 0.003) more likely to have poor walking speed. Similarly, SPPB score and walking speed, but not grip strength, were worse in participants with hyperuricemia. Older adults with gout and hyperuricemia are more likely to have worse lower extremity, but not upper extremity, function. © 2015, American College of Rheumatology.

Is Serum Zinc Level Associated with Prediabetes and Diabetes?: A Cross-Sectional Study from Bangladesh

PubMed Central

Islam, Md. Rafiqul; Arslan, Iqbal; Attia, John; McEvoy, Mark; McElduff, Patrick; Basher, Ariful; Rahman, Waliur; Peel, Roseanne; Akhter, Ayesha; Akter, Shahnaz; Vashum, Khanrin P.; Milton, Abul Hasnat

2013-01-01

Aims To determine serum zinc level and other relevant biological markers in normal, prediabetic and diabetic individuals and their association with Homeostasis Model Assessment (HOMA) parameters. Methods This cross-sectional study was conducted between March and December 2009. Any patient aged ≥30 years attending the medicine outpatient department of a medical university hospital in Dhaka, Bangladesh and who had a blood glucose level ordered by a physician was eligible to participate. Results A total of 280 participants were analysed. On fasting blood sugar results, 51% were normal, 13% had prediabetes and 36% had diabetes. Mean serum zinc level was lowest in prediabetic compared to normal and diabetic participants (mean differences were approximately 65 ppb/L and 33 ppb/L, respectively). In multiple linear regression, serum zinc level was found to be significantly lower in prediabetes than in those with normoglycemia. Beta cell function was significantly lower in prediabetes than normal participants. Adjusted linear regression for HOMA parameters did not show a statistically significant association between serum zinc level, beta cell function (P = 0.07) and insulin resistance (P = 0.08). Low serum zinc accentuated the increase in insulin resistance seen with increasing BMI. Conclusion Participants with prediabetes have lower zinc levels than controls and zinc is significantly associated with beta cell function and insulin resistance. Further longitudinal population based studies are warranted and controlled trials would be valuable for establishing whether zinc supplementation in prediabetes could be a useful strategy in preventing progression to Type 2 diabetes. PMID:23613929

An increase in visceral fat is associated with a decrease in the taste and olfactory capacity

PubMed Central

Fernandez-Garcia, Jose Carlos; Alcaide, Juan; Santiago-Fernandez, Concepcion; Roca-Rodriguez, MM.; Aguera, Zaida; Baños, Rosa; Botella, Cristina; de la Torre, Rafael; Fernandez-Real, Jose M.; Fruhbeck, Gema; Gomez-Ambrosi, Javier; Jimenez-Murcia, Susana; Menchon, Jose M.; Casanueva, Felipe F.; Fernandez-Aranda, Fernando; Tinahones, Francisco J.; Garrido-Sanchez, Lourdes

2017-01-01

Introduction Sensory factors may play an important role in the determination of appetite and food choices. Also, some adipokines may alter or predict the perception and pleasantness of specific odors. We aimed to analyze differences in smell–taste capacity between females with different weights and relate them with fat and fat-free mass, visceral fat, and several adipokines. Materials and methods 179 females with different weights (from low weight to morbid obesity) were studied. We analyzed the relation between fat, fat-free mass, visceral fat (indirectly estimated by bioelectrical impedance analysis with visceral fat rating (VFR)), leptin, adiponectin and visfatin. The smell and taste assessments were performed through the "Sniffin’ Sticks" and "Taste Strips" respectively. Results We found a lower score in the measurement of smell (TDI-score (Threshold, Discrimination and Identification)) in obese subjects. All the olfactory functions measured, such as threshold, discrimination, identification and the TDI-score, correlated negatively with age, body mass index (BMI), leptin, fat mass, fat-free mass and VFR. In a multiple linear regression model, VFR mainly predicted the TDI-score. With regard to the taste function measurements, the normal weight subjects showed a higher score of taste functions. However a tendency to decrease was observed in the groups with greater or lesser BMI. In a multiple linear regression model VFR and age mainly predicted the total taste scores. Discussion We show for the first time that a reverse relationship exists between visceral fat and sensory signals, such as smell and taste, across a population with different body weight conditions. PMID:28158237

Applications of statistics to medical science, III. Correlation and regression.

PubMed

Watanabe, Hiroshi

2012-01-01

In this third part of a series surveying medical statistics, the concepts of correlation and regression are reviewed. In particular, methods of linear regression and logistic regression are discussed. Arguments related to survival analysis will be made in a subsequent paper.

Locally Weighted Score Estimation for Quantile Classification in Binary Regression Models

PubMed Central

Rice, John D.; Taylor, Jeremy M. G.

2016-01-01

One common use of binary response regression methods is classification based on an arbitrary probability threshold dictated by the particular application. Since this is given to us a priori, it is sensible to incorporate the threshold into our estimation procedure. Specifically, for the linear logistic model, we solve a set of locally weighted score equations, using a kernel-like weight function centered at the threshold. The bandwidth for the weight function is selected by cross validation of a novel hybrid loss function that combines classification error and a continuous measure of divergence between observed and fitted values; other possible cross-validation functions based on more common binary classification metrics are also examined. This work has much in common with robust estimation, but diers from previous approaches in this area in its focus on prediction, specifically classification into high- and low-risk groups. Simulation results are given showing the reduction in error rates that can be obtained with this method when compared with maximum likelihood estimation, especially under certain forms of model misspecification. Analysis of a melanoma data set is presented to illustrate the use of the method in practice. PMID:28018492

Regression of non-linear coupling of noise in LIGO detectors

NASA Astrophysics Data System (ADS)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.

QSRR modeling for diverse drugs using different feature selection methods coupled with linear and nonlinear regressions.

PubMed

Goodarzi, Mohammad; Jensen, Richard; Vander Heyden, Yvan

2012-12-01

A Quantitative Structure-Retention Relationship (QSRR) is proposed to estimate the chromatographic retention of 83 diverse drugs on a Unisphere poly butadiene (PBD) column, using isocratic elutions at pH 11.7. Previous work has generated QSRR models for them using Classification And Regression Trees (CART). In this work, Ant Colony Optimization is used as a feature selection method to find the best molecular descriptors from a large pool. In addition, several other selection methods have been applied, such as Genetic Algorithms, Stepwise Regression and the Relief method, not only to evaluate Ant Colony Optimization as a feature selection method but also to investigate its ability to find the important descriptors in QSRR. Multiple Linear Regression (MLR) and Support Vector Machines (SVMs) were applied as linear and nonlinear regression methods, respectively, giving excellent correlation between the experimental, i.e. extrapolated to a mobile phase consisting of pure water, and predicted logarithms of the retention factors of the drugs (logk(w)). The overall best model was the SVM one built using descriptors selected by ACO. Copyright © 2012 Elsevier B.V. All rights reserved.

The association of genetic variants of type 2 diabetes with kidney function.

PubMed

Franceschini, Nora; Shara, Nawar M; Wang, Hong; Voruganti, V Saroja; Laston, Sandy; Haack, Karin; Lee, Elisa T; Best, Lyle G; Maccluer, Jean W; Cochran, Barbara J; Dyer, Thomas D; Howard, Barbara V; Cole, Shelley A; North, Kari E; Umans, Jason G

2012-07-01

Type 2 diabetes is highly prevalent and is the major cause of progressive chronic kidney disease in American Indians. Genome-wide association studies identified several loci associated with diabetes but their impact on susceptibility to diabetic complications is unknown. We studied the association of 18 type 2 diabetes genome-wide association single-nucleotide polymorphisms (SNPs) with estimated glomerular filtration rate (eGFR; MDRD equation) and urine albumin-to-creatinine ratio in 6958 Strong Heart Study family and cohort participants. Center-specific residuals of eGFR and log urine albumin-to-creatinine ratio, obtained from linear regression models adjusted for age, sex, and body mass index, were regressed onto SNP dosage using variance component models in family data and linear regression in unrelated individuals. Estimates were then combined across centers. Four diabetic loci were associated with eGFR and one locus with urine albumin-to-creatinine ratio. A SNP in the WFS1 gene (rs10010131) was associated with higher eGFR in younger individuals and with increased albuminuria. SNPs in the FTO, KCNJ11, and TCF7L2 genes were associated with lower eGFR, but not albuminuria, and were not significant in prospective analyses. Our findings suggest a shared genetic risk for type 2 diabetes and its kidney complications, and a potential role for WFS1 in early-onset diabetic nephropathy in American Indian populations.

Cellulose microfibril orientation of Picea abies and its variability at the micron-level determined by Raman imaging

PubMed Central

Gierlinger, Notburga; Luss, Saskia; König, Christian; Konnerth, Johannes; Eder, Michaela; Fratzl, Peter

2010-01-01

The functional characteristics of plant cell walls depend on the composition of the cell wall polymers, as well as on their highly ordered architecture at scales from a few nanometres to several microns. Raman spectra of wood acquired with linear polarized laser light include information about polymer composition as well as the alignment of cellulose microfibrils with respect to the fibre axis (microfibril angle). By changing the laser polarization direction in 3° steps, the dependency between cellulose and laser orientation direction was investigated. Orientation-dependent changes of band height ratios and spectra were described by quadratic linear regression and partial least square regressions, respectively. Using the models and regressions with high coefficients of determination (R2 > 0.99) microfibril orientation was predicted in the S1 and S2 layers distinguished by the Raman imaging approach in cross-sections of spruce normal, opposite, and compression wood. The determined microfibril angle (MFA) in the different S2 layers ranged from 0° to 49.9° and was in coincidence with X-ray diffraction determination. With the prerequisite of geometric sample and laser alignment, exact MFA prediction can complete the picture of the chemical cell wall design gained by the Raman imaging approach at the micron level in all plant tissues. PMID:20007198

Effects of integration time on in-water radiometric profiles.

PubMed

D'Alimonte, Davide; Zibordi, Giuseppe; Kajiyama, Tamito

2018-03-05

This work investigates the effects of integration time on in-water downward irradiance E d , upward irradiance E u and upwelling radiance L u profile data acquired with free-fall hyperspectral systems. Analyzed quantities are the subsurface value and the diffuse attenuation coefficient derived by applying linear and non-linear regression schemes. Case studies include oligotrophic waters (Case-1), as well as waters dominated by Colored Dissolved Organic Matter (CDOM) and Non-Algal Particles (NAP). Assuming a 24-bit digitization, measurements resulting from the accumulation of photons over integration times varying between 8 and 2048ms are evaluated at depths corresponding to: 1) the beginning of each integration interval (Fst); 2) the end of each integration interval (Lst); 3) the averages of Fst and Lst values (Avg); and finally 4) the values weighted accounting for the diffuse attenuation coefficient of water (Wgt). Statistical figures show that the effects of integration time can bias results well above 5% as a function of the depth definition. Results indicate the validity of the Wgt depth definition and the fair applicability of the Avg one. Instead, both the Fst and Lst depths should not be adopted since they may introduce pronounced biases in E u and L u regression products for highly absorbing waters. Finally, the study reconfirms the relevance of combining multiple radiometric casts into a single profile to increase precision of regression products.

Job stress models, depressive disorders and work performance of engineers in microelectronics industry.

PubMed

Chen, Sung-Wei; Wang, Po-Chuan; Hsin, Ping-Lung; Oates, Anthony; Sun, I-Wen; Liu, Shen-Ing

2011-01-01

Microelectronic engineers are considered valuable human capital contributing significantly toward economic development, but they may encounter stressful work conditions in the context of a globalized industry. The study aims at identifying risk factors of depressive disorders primarily based on job stress models, the Demand-Control-Support and Effort-Reward Imbalance models, and at evaluating whether depressive disorders impair work performance in microelectronics engineers in Taiwan. The case-control study was conducted among 678 microelectronics engineers, 452 controls and 226 cases with depressive disorders which were defined by a score 17 or more on the Beck Depression Inventory and a psychiatrist's diagnosis. The self-administered questionnaires included the Job Content Questionnaire, Effort-Reward Imbalance Questionnaire, demography, psychosocial factors, health behaviors and work performance. Hierarchical logistic regression was applied to identify risk factors of depressive disorders. Multivariate linear regressions were used to determine factors affecting work performance. By hierarchical logistic regression, risk factors of depressive disorders are high demands, low work social support, high effort/reward ratio and low frequency of physical exercise. Combining the two job stress models may have better predictive power for depressive disorders than adopting either model alone. Three multivariate linear regressions provide similar results indicating that depressive disorders are associated with impaired work performance in terms of absence, role limitation and social functioning limitation. The results may provide insight into the applicability of job stress models in a globalized high-tech industry considerably focused in non-Western countries, and the design of workplace preventive strategies for depressive disorders in Asian electronics engineering population.

Evaluating Differential Effects Using Regression Interactions and Regression Mixture Models

ERIC Educational Resources Information Center

Van Horn, M. Lee; Jaki, Thomas; Masyn, Katherine; Howe, George; Feaster, Daniel J.; Lamont, Andrea E.; George, Melissa R. W.; Kim, Minjung

2015-01-01

Research increasingly emphasizes understanding differential effects. This article focuses on understanding regression mixture models, which are relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their…

Residential Mobility and Cognitive Function Among Middle-Aged and Older Adults in China.

PubMed

Xu, Hanzhang; Dupre, Matthew E; Østbye, Truls; Vorderstrasse, Allison A; Wu, Bei

2018-01-01

To assess the association between rural and urban residential mobility and cognitive function among middle-aged and older adults in China. We used data from the World Health Organization Study on global AGEing and adult health that included adults age 50+ from China ( N = 12,410). We used multivariate linear regressions to examine how residential mobility and age at migration were associated with cognitive function. Urban and urban-to-urban residents had the highest level of cognitive function, whereas rural and rural-to-rural residents had the poorest cognitive function. Persons who migrated to/within rural areas before age 20 had poorer cognitive function than those who migrated during later adulthood. Socioeconomic factors played a major role in accounting for the disparities in cognition; however, the association remained significant after inclusion of all covariates. Residential mobility and age at migration have significant implications for cognitive function among middle-aged and older adults in China.

A biocultural perspective on fictive kinship in the Andes: social support and women's immune function in El Alto, Bolivia.

PubMed

Hicks, Kathryn

2014-09-01

This article examines the influence of emotional and instrumental support on women's immune function, a biomarker of stress, in the city of El Alto, Bolivia. It tests the prediction that instrumental support is protective of immune function for women living in this marginal environment. Qualitative and quantitative ethnographic methods were employed to assess perceived emotional and instrumental support and common sources of support; multiple linear regression analysis was used to model the relationship between social support and antibodies to the Epstein-Barr virus. These analyses provided no evidence that instrumental social support is related to women's health, but there is some evidence that emotional support from compadres helps protect immune function. © 2014 by the American Anthropological Association.

General functioning predicts reward and punishment learning in schizophrenia.

PubMed

Somlai, Zsuzsanna; Moustafa, Ahmed A; Kéri, Szabolcs; Myers, Catherine E; Gluck, Mark A

2011-04-01

Previous studies investigating feedback-driven reinforcement learning in patients with schizophrenia have provided mixed results. In this study, we explored the clinical predictors of reward and punishment learning using a probabilistic classification learning task. Patients with schizophrenia (n=40) performed similarly to healthy controls (n=30) on the classification learning task. However, more severe negative and general symptoms were associated with lower reward-learning performance, whereas poorer general psychosocial functioning was correlated with both lower reward- and punishment-learning performances. Multiple linear regression analyses indicated that general psychosocial functioning was the only significant predictor of reinforcement learning performance when education, antipsychotic dose, and positive, negative and general symptoms were included in the analysis. These results suggest a close relationship between reinforcement learning and general psychosocial functioning in schizophrenia. Published by Elsevier B.V.