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| linear mixed models for longitudinal data 2: Linear Mixed Models for Longitudinal Data Geert Verbeke, Geert Molenberghs, 2009-05-12 This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Most analyses were done with the MIXED procedure of the SAS software package, but the data analyses are presented in a software-independent fashion. |
| linear mixed models for longitudinal data 2: Methods and Applications of Longitudinal Data Analysis Xian Liu, 2015-09-01 Methods and Applications of Longitudinal Data Analysis describes methods for the analysis of longitudinal data in the medical, biological and behavioral sciences. It introduces basic concepts and functions including a variety of regression models, and their practical applications across many areas of research. Statistical procedures featured within the text include: - descriptive methods for delineating trends over time - linear mixed regression models with both fixed and random effects - covariance pattern models on correlated errors - generalized estimating equations - nonlinear regression models for categorical repeated measurements - techniques for analyzing longitudinal data with non-ignorable missing observations Emphasis is given to applications of these methods, using substantial empirical illustrations, designed to help users of statistics better analyze and understand longitudinal data. Methods and Applications of Longitudinal Data Analysis equips both graduate students and professionals to confidently apply longitudinal data analysis to their particular discipline. It also provides a valuable reference source for applied statisticians, demographers and other quantitative methodologists. - From novice to professional: this book starts with the introduction of basic models and ends with the description of some of the most advanced models in longitudinal data analysis - Enables students to select the correct statistical methods to apply to their longitudinal data and avoid the pitfalls associated with incorrect selection - Identifies the limitations of classical repeated measures models and describes newly developed techniques, along with real-world examples. |
| linear mixed models for longitudinal data 2: Longitudinal Data Analysis Garrett Fitzmaurice, Marie Davidian, Geert Verbeke, Geert Molenberghs, 2008-08-11 Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory |
| linear mixed models for longitudinal data 2: Mixed Effects Models for Complex Data Lang Wu, 2009-11-11 Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis. |
| linear mixed models for longitudinal data 2: Linear Mixed Models Brady T. West, Kathleen B. Welch, Andrzej T Galecki, 2014-07-17 Highly recommended by JASA, Technometrics, and other journals, the first edition of this bestseller showed how to easily perform complex linear mixed model (LMM) analyses via a variety of software programs. Linear Mixed Models: A Practical Guide Using Statistical Software, Second Edition continues to lead readers step by step through the process of fitting LMMs. This second edition covers additional topics on the application of LMMs that are valuable for data analysts in all fields. It also updates the case studies using the latest versions of the software procedures and provides up-to-date information on the options and features of the software procedures available for fitting LMMs in SAS, SPSS, Stata, R/S-plus, and HLM. New to the Second Edition A new chapter on models with crossed random effects that uses a case study to illustrate software procedures capable of fitting these models Power analysis methods for longitudinal and clustered study designs, including software options for power analyses and suggested approaches to writing simulations Use of the lmer() function in the lme4 R package New sections on fitting LMMs to complex sample survey data and Bayesian approaches to making inferences based on LMMs Updated graphical procedures in the software packages Substantially revised index to enable more efficient reading and easier location of material on selected topics or software options More practical recommendations on using the software for analysis A new R package (WWGbook) that contains all of the data sets used in the examples Ideal for anyone who uses software for statistical modeling, this book eliminates the need to read multiple software-specific texts by covering the most popular software programs for fitting LMMs in one handy guide. The authors illustrate the models and methods through real-world examples that enable comparisons of model-fitting options and results across the software procedures. |
| linear mixed models for longitudinal data 2: A Life Course Perspective on Health Trajectories and Transitions Claudine Burton-Jeangros, Stéphane Cullati, Amanda Sacker, David Blane, 2015-08-11 This open access book examines health trajectories and health transitions at different stages of the life course, including childhood, adulthood and later life. It provides findings that assess the role of biological and social transitions on health status over time. The essays examine a wide range of health issues, including the consequences of military service on body mass index, childhood obesity and cardiovascular health, socio-economic inequalities in preventive health care use, depression and anxiety during the child rearing period, health trajectories and transitions in people with cystic fibrosis and oral health over the life course. The book addresses theoretical, empirical and methodological issues as well as examines different national contexts, which help to identify factors of vulnerability and potential resources that support resilience available for specific groups and/or populations. Health reflects the ability of individuals to adapt to their social environment. This book analyzes health as a dynamic experience. It examines how different aspects of individual health unfold over time as a result of aging but also in relation to changing socioeconomic conditions. It also offers readers potential insights into public policies that affect the health status of a population. |
| linear mixed models for longitudinal data 2: Linear Mixed Models Brady T. West, Kathleen B. Welch, Andrzej T Galecki, 2006-11-22 Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementation, model interpretation, and visualization of clustered and longitudinal data. This easy-to-nav |
| linear mixed models for longitudinal data 2: Repeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled Trials Toshiro Tango, 2017-09-14 Repeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled Trials is the first book focused on the application of generalized linear mixed models and its related models in the statistical design and analysis of repeated measures from randomized controlled trials. The author introduces a new repeated measures design called S:T design combined with mixed models as a practical and useful framework of parallel group RCT design because of easy handling of missing data and sample size reduction. The book emphasizes practical, rather than theoretical, aspects of statistical analyses and the interpretation of results. It includes chapters in which the author describes some old-fashioned analysis designs that have been in the literature and compares the results with those obtained from the corresponding mixed models. The book will be of interest to biostatisticians, researchers, and graduate students in the medical and health sciences who are involved in clinical trials. Author Website:Data sets and programs used in the book are available at http://www.medstat.jp/downloadrepeatedcrc.html |
| linear mixed models for longitudinal data 2: Mixed-Effects Models in S and S-PLUS José C. Pinheiro, Douglas Bates, 2009-04-15 R, linear models, random, fixed, data, analysis, fit. |
| linear mixed models for longitudinal data 2: Models for Discrete Longitudinal Data Geert Molenberghs, Geert Verbeke, 2006-08-30 The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004. |
| linear mixed models for longitudinal data 2: Linear Mixed Models in Practice Geert Verbeke, Geert Molenberghs, 2012-12-06 A comprehensive treatment of linear mixed models, focusing on examples from designed experiments and longitudinal studies. Aimed at applied statisticians and biomedical researchers in industry, public health organisations, contract research organisations, and academia, this book is explanatory rather than mathematical rigorous. Although most analyses were done with the MIXED procedure of the SAS software package, and many of its features are clearly elucidated, considerable effort was put into presenting the data analyses in a software-independent fashion. |
| linear mixed models for longitudinal data 2: Linear Mixed-Effects Models Using R Andrzej Gałecki, Tomasz Burzykowski, 2013-02-05 Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text. |
| linear mixed models for longitudinal data 2: Generalized Linear Mixed Models Charles E. McCulloch, 2003 Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models |
| linear mixed models for longitudinal data 2: Applied Longitudinal Data Analysis Judith D. Singer, John B. Willett, 2003-03-27 By charting changes over time and investigating whether and when events occur, researchers reveal the temporal rhythms of our lives. |
| linear mixed models for longitudinal data 2: Mixed Models Eugene Demidenko, 2013-08-05 Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering. |
| linear mixed models for longitudinal data 2: Applied Mixed Model Analysis Jos W. R. Twisk, 2019-04-18 Emphasizing interpretation of results, this hands-on guide explains why, when, and how to use mixed models with your data. |
| linear mixed models for longitudinal data 2: SAS for Mixed Models Walter W. Stroup, George A. Milliken, Elizabeth A. Claassen, Russell D. Wolfinger, 2018-12-12 Discover the power of mixed models with SAS. Mixed models—now the mainstream vehicle for analyzing most research data—are part of the core curriculum in most master’s degree programs in statistics and data science. In a single volume, this book updates both SAS® for Linear Models, Fourth Edition, and SAS® for Mixed Models, Second Edition, covering the latest capabilities for a variety of applications featuring the SAS GLIMMIX and MIXED procedures. Written for instructors of statistics, graduate students, scientists, statisticians in business or government, and other decision makers, SAS® for Mixed Models is the perfect entry for those with a background in two-way analysis of variance, regression, and intermediate-level use of SAS. This book expands coverage of mixed models for non-normal data and mixed-model-based precision and power analysis, including the following topics: Random-effect-only and random-coefficients models Multilevel, split-plot, multilocation, and repeated measures models Hierarchical models with nested random effects Analysis of covariance models Generalized linear mixed models This book is part of the SAS Press program. |
| linear mixed models for longitudinal data 2: Joint Models for Longitudinal and Time-to-Event Data Dimitris Rizopoulos, 2012-06-22 In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest, e.g., prostate cancer studies where longitudinal PSA level measurements are collected in conjunction with the time-to-recurrence. Joint Models for Longitudinal and Time-to-Event Data: With Applications in R provides a full treatment of random effects joint models for longitudinal and time-to-event outcomes that can be utilized to analyze such data. The content is primarily explanatory, focusing on applications of joint modeling, but sufficient mathematical details are provided to facilitate understanding of the key features of these models. All illustrations put forward can be implemented in the R programming language via the freely available package JM written by the author. All the R code used in the book is available at: http://jmr.r-forge.r-project.org/ |
| linear mixed models for longitudinal data 2: Linear and Generalized Linear Mixed Models and Their Applications Jiming Jiang, 2007-05-30 This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis. |
| linear mixed models for longitudinal data 2: Contemporary Statistical Models for the Plant and Soil Sciences Oliver Schabenberger, Francis J. Pierce, 2001-11-13 Despite its many origins in agronomic problems, statistics today is often unrecognizable in this context. Numerous recent methodological approaches and advances originated in other subject-matter areas and agronomists frequently find it difficult to see their immediate relation to questions that their disciplines raise. On the other hand, statisticians often fail to recognize the riches of challenging data analytical problems contemporary plant and soil science provides. The first book to integrate modern statistics with crop, plant and soil science, Contemporary Statistical Models for the Plant and Soil Sciences bridges this gap. The breadth and depth of topics covered is unusual. Each of the main chapters could be a textbook in its own right on a particular class of data structures or models. The cogent presentation in one text allows research workers to apply modern statistical methods that otherwise are scattered across several specialized texts. The combination of theory and application orientation conveys ìwhyî a particular method works and ìhowî it is put in to practice. About the downloadable resources The accompanying downloadable resources are a key component of the book. For each of the main chapters additional sections of text are available that cover mathematical derivations, special topics, and supplementary applications. It supplies the data sets and SAS code for all applications and examples in the text, macros that the author developed, and SAS tutorials ranging from basic data manipulation to advanced programming techniques and publication quality graphics. Contemporary statistical models can not be appreciated to their full potential without a good understanding of theory. They also can not be applied to their full potential without the aid of statistical software. Contemporary Statistical Models for the Plant and Soil Science provides the essential mix of theory and applications of statistical methods pertinent to research in life sciences. |
| linear mixed models for longitudinal data 2: Multivariate Generalized Linear Mixed Models Using R Damon Mark Berridge, Robert Crouchley, 2011-04-25 Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R.A Un |
| linear mixed models for longitudinal data 2: Linear Mixed Models for Longitudinal Data Geert Verbeke, Geert Molenberghs, 2001-05-25 This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Most analyses were done with the MIXED procedure of the SAS software package, but the data analyses are presented in a software-independent fashion. |
| linear mixed models for longitudinal data 2: Longitudinal Analysis Lesa Hoffman, 2015-01-30 Longitudinal Analysis provides an accessible, application-oriented treatment of introductory and advanced linear models for within-person fluctuation and change. Organized by research design and data type, the text uses in-depth examples to provide a complete description of the model-building process. The core longitudinal models and their extensions are presented within a multilevel modeling framework, paying careful attention to the modeling concerns that are unique to longitudinal data. Written in a conversational style, the text provides verbal and visual interpretation of model equations to aid in their translation to empirical research results. Overviews and summaries, boldfaced key terms, and review questions will help readers synthesize the key concepts in each chapter. Written for non-mathematically-oriented readers, this text features: A description of the data manipulation steps required prior to model estimation so readers can more easily apply the steps to their own data An emphasis on how the terminology, interpretation, and estimation of familiar general linear models relates to those of more complex models for longitudinal data Integrated model comparisons, effect sizes, and statistical inference in each example to strengthen readers’ understanding of the overall model-building process Sample results sections for each example to provide useful templates for published reports Examples using both real and simulated data in the text, along with syntax and output for SPSS, SAS, STATA, and Mplus at www.PilesOfVariance.com to help readers apply the models to their own data The book opens with the building blocks of longitudinal analysis—general ideas, the general linear model for between-person analysis, and between- and within-person models for the variance and the options within repeated measures analysis of variance. Section 2 introduces unconditional longitudinal models including alternative covariance structure models to describe within-person fluctuation over time and random effects models for within-person change. Conditional longitudinal models are presented in section 3, including both time-invariant and time-varying predictors. Section 4 reviews advanced applications, including alternative metrics of time in accelerated longitudinal designs, three-level models for multiple dimensions of within-person time, the analysis of individuals in groups over time, and repeated measures designs not involving time. The book concludes with additional considerations and future directions, including an overview of sample size planning and other model extensions for non-normal outcomes and intensive longitudinal data. Class-tested at the University of Nebraska-Lincoln and in intensive summer workshops, this is an ideal text for graduate-level courses on longitudinal analysis or general multilevel modeling taught in psychology, human development and family studies, education, business, and other behavioral, social, and health sciences. The book’s accessible approach will also help those trying to learn on their own. Only familiarity with general linear models (regression, analysis of variance) is needed for this text. |
| linear mixed models for longitudinal data 2: Models for Intensive Longitudinal Data Theodore A. Walls, Joseph L. Schafer, 2006-01-19 Rapid technological advances in devices used for data collection have led to the emergence of a new class of longitudinal data: intensive longitudinal data (ILD). Behavioral scientific studies now frequently utilize handheld computers, beepers, web interfaces, and other technological tools for collecting many more data points over time than previously possible. Other protocols, such as those used in fMRI and monitoring of public safety, also produce ILD, hence the statistical models in this volume are applicable to a range of data. The volume features state-of-the-art statistical modeling strategies developed by leading statisticians and methodologists working on ILD in conjunction with behavioral scientists. Chapters present applications from across the behavioral and health sciences, including coverage of substantive topics such as stress, smoking cessation, alcohol use, traffic patterns, educational performance and intimacy. Models for Intensive Longitudinal Data (MILD) is designed for those who want to learn about advanced statistical models for intensive longitudinal data and for those with an interest in selecting and applying a given model. The chapters highlight issues of general concern in modeling these kinds of data, such as a focus on regulatory systems, issues of curve registration, variable frequency and spacing of measurements, complex multivariate patterns of change, and multiple independent series. The extraordinary breadth of coverage makes this an indispensable reference for principal investigators designing new studies that will introduce ILD, applied statisticians working on related models, and methodologists, graduate students, and applied analysts working in a range of fields. A companion Web site at www.oup.com/us/MILD contains program examples and documentation. |
| linear mixed models for longitudinal data 2: Longitudinal and Panel Data Edward W. Frees, 2004-08-16 An introduction to foundations and applications for quantitatively oriented graduate social-science students and individual researchers. |
| linear mixed models for longitudinal data 2: Dynamic Mixed Models for Familial Longitudinal Data Brajendra C. Sutradhar, 2011-01-27 This book provides a theoretical foundation for the analysis of discrete data such as count and binary data in the longitudinal setup. Unlike the existing books, this book uses a class of auto-correlation structures to model the longitudinal correlations for the repeated discrete data that accommodates all possible Gaussian type auto-correlation models as special cases including the equi-correlation models. This new dynamic modelling approach is utilized to develop theoretically sound inference techniques such as the generalized quasi-likelihood (GQL) technique for consistent and efficient estimation of the underlying regression effects involved in the model, whereas the existing ‘working’ correlations based GEE (generalized estimating equations) approach has serious theoretical limitations both for consistent and efficient estimation, and the existing random effects based correlations approach is not suitable to model the longitudinal correlations. The book has exploited the random effects carefully only to model the correlations of the familial data. Subsequently, this book has modelled the correlations of the longitudinal data collected from the members of a large number of independent families by using the class of auto-correlation structures conditional on the random effects. The book also provides models and inferences for discrete longitudinal data in the adaptive clinical trial set up. The book is mathematically rigorous and provides details for the development of estimation approaches under selected familial and longitudinal models. Further, while the book provides special cares for mathematics behind the correlation models, it also presents the illustrations of the statistical analysis of various real life data. This book will be of interest to the researchers including graduate students in biostatistics and econometrics, among other applied statistics research areas. Brajendra Sutradhar is a University Research Professor at Memorial University in St. John’s, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to the society including his special services for society’s annual meetings. |
| linear mixed models for longitudinal data 2: Modeling Intraindividual Variability With Repeated Measures Data Scott L. Hershberger, D.S. Moskowitz, 2013-06-17 This book examines how individuals behave across time and to what degree that behavior changes, fluctuates, or remains stable. It features the most current methods on modeling repeated measures data as reported by a distinguished group of experts in the field. The goal is to make the latest techniques used to assess intraindividual variability accessible to a wide range of researchers. Each chapter is written in a user-friendly style such that even the novice data analyst can easily apply the techniques. Each chapter features: a minimum discussion of mathematical detail; an empirical example applying the technique; and a discussion of the software related to that technique. Content highlights include analysis of mixed, multi-level, structural equation, and categorical data models. It is ideal for researchers, professionals, and students working with repeated measures data from the social and behavioral sciences, business, or biological sciences. |
| linear mixed models for longitudinal data 2: Fixed Effects Regression Methods for Longitudinal Data Using SAS Paul D. Allison, 2019-07-12 Fixed Effects Regression Methods for Longitudinal Data Using SAS, written by Paul Allison, is an invaluable resource for all researchers interested in adding fixed effects regression methods to their tool kit of statistical techniques. First introduced by economists, fixed effects methods are gaining widespread use throughout the social sciences. Designed to eliminate major biases from regression models with multiple observations (usually longitudinal) for each subject (usually a person), fixed effects methods essentially offer control for all stable characteristics of the subjects, even characteristics that are difficult or impossible to measure. This straightforward and thorough text shows you how to estimate fixed effects models with several SAS procedures that are appropriate for different kinds of outcome variables. The theoretical background of each model is explained, and the models are then illustrated with detailed examples using real data. The book contains thorough discussions of the following uses of SAS procedures: PROC GLM for estimating fixed effects linear models for quantitative outcomes, PROC LOGISTIC for estimating fixed effects logistic regression models, PROC PHREG for estimating fixed effects Cox regression models for repeated event data, PROC GENMOD for estimating fixed effects Poisson regression models for count data, and PROC CALIS for estimating fixed effects structural equation models. To gain the most benefit from this book, readers should be familiar with multiple linear regression, have practical experience using multiple regression on real data, and be comfortable interpreting the output from a regression analysis. An understanding of logistic regression and Poisson regression is a plus. Some experience with SAS is helpful, but not required. |
| linear mixed models for longitudinal data 2: Multilevel Modeling Using R W. Holmes Finch, Jocelyn E. Bolin, Ken Kelley, 2019-07-16 Like its bestselling predecessor, Multilevel Modeling Using R, Second Edition provides the reader with a helpful guide to conducting multilevel data modeling using the R software environment. After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single level and multilevel data. New in the Second Edition: Features the use of lmer (instead of lme) and including the most up to date approaches for obtaining confidence intervals for the model parameters. Discusses measures of R2 (the squared multiple correlation coefficient) and overall model fit. Adds a chapter on nonparametric and robust approaches to estimating multilevel models, including rank based, heavy tailed distributions, and the multilevel lasso. Includes a new chapter on multivariate multilevel models. Presents new sections on micro-macro models and multilevel generalized additive models. This thoroughly updated revision gives the reader state-of-the-art tools to launch their own investigations in multilevel modeling and gain insight into their research. About the Authors: W. Holmes Finch is the George and Frances Ball Distinguished Professor of Educational Psychology at Ball State University. Jocelyn E. Bolin is a Professor in the Department of Educational Psychology at Ball State University. Ken Kelley is the Edward F. Sorin Society Professor of IT, Analytics and Operations and the Associate Dean for Faculty and Research for the Mendoza College of Business at the University of Notre Dame. |
| linear mixed models for longitudinal data 2: Multivariate Statistical Machine Learning Methods for Genomic Prediction Osval Antonio Montesinos López, Abelardo Montesinos López, José Crossa, 2022-02-14 This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool. |
| linear mixed models for longitudinal data 2: Hierarchical Linear Models Stephen W. Raudenbush, Anthony S. Bryk, 2002 New edition of a text in which Raudenbush (U. of Michigan) and Bryk (sociology, U. of Chicago) provide examples, explanations, and illustrations of the theory and use of hierarchical linear models (HLM). New material in Part I (Logic) includes information on multivariate growth models and other topics. |
| linear mixed models for longitudinal data 2: Counting Processes and Survival Analysis Thomas R. Fleming, David P. Harrington, 2011-09-20 The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. The book is a valuable completion of the literature in this field. It is written in an ambitious mathematical style and can be recommended to statisticians as well as biostatisticians. -Biometrische Zeitschrift Not many books manage to combine convincingly topics from probability theory over mathematical statistics to applied statistics. This is one of them. The book has other strong points to recommend it: it is written with meticulous care, in a lucid style, general results being illustrated by examples from statistical theory and practice, and a bunch of exercises serve to further elucidate and elaborate on the text. -Mathematical Reviews This book gives a thorough introduction to martingale and counting process methods in survival analysis thereby filling a gap in the literature. -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts The authors have performed a valuable service to researchers in providing this material in [a] self-contained and accessible form. . . This text [is] essential reading for the probabilist or mathematical statistician working in the area of survival analysis. -Short Book Reviews, International Statistical Institute Counting Processes and Survival Analysis explores the martingale approach to the statistical analysis of counting processes, with an emphasis on the application of those methods to censored failure time data. This approach has proven remarkably successful in yielding results about statistical methods for many problems arising in censored data. A thorough treatment of the calculus of martingales as well as the most important applications of these methods to censored data is offered. Additionally, the book examines classical problems in asymptotic distribution theory for counting process methods and newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide practice in applying martingale methods and insight into the calculus itself. |
| linear mixed models for longitudinal data 2: Asymptotic Analysis of Mixed Effects Models Jiming Jiang, 2017-09-19 Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis. |
| linear mixed models for longitudinal data 2: Analysis of Longitudinal Data Peter Diggle, Patrick Heagerty, Kung-Yee Liang, Scott Zeger, 2013-03-14 This second edition has been completely revised and expanded to become the most up-to-date and thorough professional reference text in this fast-moving area of biostatistics. It contains an additional two chapters on fully parametric models for discrete repeated measures data and statistical models for time-dependent predictors. |
| linear mixed models for longitudinal data 2: Modelling Longitudinal and Spatially Correlated Data Timothy G. Gregoire, David R. Brillinger, Peter Diggle, Estelle Russek-Cohen, William G. Warren, Russell D. Wolfinger, 2012-12-06 Correlated data arise in numerous contexts across a wide spectrum of subject-matter disciplines. Modeling such data present special challenges and opportunities that have received increasing scrutiny by the statistical community in recent years. In October 1996 a group of 210 statisticians and other scientists assembled on the small island of Nantucket, U. S. A. , to present and discuss new developments relating to Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Direc tions. Its purpose was to provide a cross-disciplinary forum to explore the commonalities and meaningful differences in the source and treatment of such data. This volume is a compilation of some of the important invited and volunteered presentations made during that conference. The three days and evenings of oral and displayed presentations were arranged into six broad thematic areas. The session themes, the invited speakers and the topics they addressed were as follows: • Generalized Linear Models: Peter McCullagh-Residual Likelihood in Linear and Generalized Linear Models • Longitudinal Data Analysis: Nan Laird-Using the General Linear Mixed Model to Analyze Unbalanced Repeated Measures and Longi tudinal Data • Spatio---Temporal Processes: David R. Brillinger-Statistical Analy sis of the Tracks of Moving Particles • Spatial Data Analysis: Noel A. Cressie-Statistical Models for Lat tice Data • Modelling Messy Data: Raymond J. Carroll-Some Results on Gen eralized Linear Mixed Models with Measurement Error in Covariates • Future Directions: Peter J. |
| linear mixed models for longitudinal data 2: Theory of Statistical Inference Anthony Almudevar, 2021-12-30 Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory. |
| linear mixed models for longitudinal data 2: Regression and Time Series Model Selection Allan D. R. McQuarrie, Chih-Ling Tsai, 1998 This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of information-based model selection criteria, bootstrapping, and cross-validation selection methods over a wide range of models. |
| linear mixed models for longitudinal data 2: Statistical Inference for Models with Multivariate t-Distributed Errors A. K. Md. Ehsanes Saleh, Mohammad Arashi, S. M. M. Tabatabaey, 2014-10-01 This book summarizes the results of various models under normal theory with a brief review of the literature. Statistical Inference for Models with Multivariate t-Distributed Errors: Includes a wide array of applications for the analysis of multivariate observations Emphasizes the development of linear statistical models with applications to engineering, the physical sciences, and mathematics Contains an up-to-date bibliography featuring the latest trends and advances in the field to provide a collective source for research on the topic Addresses linear regression models with non-normal errors with practical real-world examples Uniquely addresses regression models in Student's t-distributed errors and t-models Supplemented with an Instructor's Solutions Manual, which is available via written request by the Publisher |
| linear mixed models for longitudinal data 2: Beyond Multiple Linear Regression Paul Roback, Julie Legler, 2021-01-14 Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner. The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling. A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR) |
| linear mixed models for longitudinal data 2: Data Mining With Decision Trees: Theory And Applications (2nd Edition) Oded Z Maimon, Lior Rokach, 2014-09-03 Decision trees have become one of the most powerful and popular approaches in knowledge discovery and data mining; it is the science of exploring large and complex bodies of data in order to discover useful patterns. Decision tree learning continues to evolve over time. Existing methods are constantly being improved and new methods introduced.This 2nd Edition is dedicated entirely to the field of decision trees in data mining; to cover all aspects of this important technique, as well as improved or new methods and techniques developed after the publication of our first edition. In this new edition, all chapters have been revised and new topics brought in. New topics include Cost-Sensitive Active Learning, Learning with Uncertain and Imbalanced Data, Using Decision Trees beyond Classification Tasks, Privacy Preserving Decision Tree Learning, Lessons Learned from Comparative Studies, and Learning Decision Trees for Big Data. A walk-through guide to existing open-source data mining software is also included in this edition.This book invites readers to explore the many benefits in data mining that decision trees offer: |
Module 11 Mixed-effects Models for Longitudinal Data Analysis
This module will overview statistical methods for the analysis of longitudinal data, with a focus on mixed-e ects models Focus will be on the practical application of appropriate analysis … See more
Mixed models in R using the lme4 package Part 2: Longitudinal …
Longitudinal data are repeated measures data in which the observations are taken over time. We wish to characterize the response over time within subjects and the variation in the time trends …
Longitudinal Data Analysis via Linear Mixed Models
Linear Mixed Models for Longitudinal Data. Springer. Purpose: Study change and the factors that effect change. Data: Longitudinal data consist of repeated measurements on the same unit …
Chapter 4 Models for Longitudinal Data
Based on our preliminary graphical exploration of these data, we t a mixed- e ects model with two xed-e ects parameters, the intercept and slope of the linear time trend for the population, and …
Mixed-effects modeling and longitudinal data analysis
Mixed Models Mixed-effects models provide a flexible and powerful tool for the analysis of grouped data, including: • blocked designs • repeated measures (each subject measured for …
Statistical models for longitudinal data : Linear Mixed Model
Summary: Principle of the linear mixed models I Random intercept measures heterogeneity at baseline I Random slope measures heterogeneity at the end of follow-up
Core Guide: Correlation Structures in Mixed Effects Models for ...
19 Sep 2017 · Longitudinal models with both a random intercept and a random slope for time induces a within-individual correlation matrix with correlations that decrease in magnitude the …
Linear mixed models for longitudinal data
A key feature of mixed models is that they can be used to model unbalanced data. In the context of longitudinal data, this includes situations where not all subjects have the same number of …
Linear Mixed Models for Longitudinal Data - external.dandelon.com
Linear Mixed Models for Longitudinal Data With 128 Illustrations Springer. Contents Preface vii Acknowledgments ix i 1 Introduction 1 2 Examples 7 ... 13.2 A Linear Mixed Model for the …
Linear Mixed Models for Longitudinal Data - Springer
In the following sections, we will use their data and their models to illustrate all features of linear mixed models in the context of longitudi nal data.
Bayesian model selection in linear mixed models for longitudinal …
We show in an extensive simulation study that the three marginal criteria are superior in choosing the appropriate longitudinal model. In addition, the marginal criteria selected most appropriate …
Deep mixture of linear mixed models for complex longitudinal data
14 Nov 2023 · Mixtures of linear mixed models (MLMMs) (e.g. Verbeke and Lesaffre (1996)) are widely used for the analysis of longitudinal data for which observation times differ by subject, …
ANALYZING LONGITUDINAL INTERVENTION STUDIES WITH …
To mitigate this issue, this paper proposes a linear mixed regression model (LMM) approach to the analysis of differences between multiple groups over multiple time points. After introducing …
Longitudinal Data and Linear Mixed Effects Models
Linear mixed effects models are popularly used for the analysis of longitudinal data of a continuous response variable. They are an exten-sion of linear models by including random …
Accessible Analysis of Longitudinal Data with Linear Mixed …
3 Dec 2020 · Summary Statement: Here, we show that linear mixed effects models are more appropriate for analyzing longitudinal data than ANOVA and we provide an accessible, web …
Statistical Modelling - University of Oxford
Abstract: Many approaches are available for the analysis of continuous longitudinal data. Over the last couple of decades, a lot of emphasis has been put on the linear mixed model. The current …
Advances in longitudinal data analysis: An historical perspective
The mixed-effects ANOVA model has a long history of use for analyzing longitudinal data, where it is often referred to as the univariate repeated-measures ANOVA. Statis-ticians recognized …
Longitudinal Data Analyses Using Linear Mixed Models in SPSS: …
Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear …
Mixed models in R using the lme4 package Part 2: Longitudinal …
Longitudinal data are repeated measures data in which the observations are taken over time. We wish to characterize the response over time within subjects and the variation in the time trends …
Models for Longitudinal Data: A Generalized Estimating Equation …
This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in …
Module 11 Mixed-effects Models for Longitudinal Data Analysis
I Generalized linear mixed-e ects models (GLMM): A conditional model for the mean response given subject-speci c random e ects, which induce a (possibly hierarchical) correlation structure
Mixed models in R using the lme4 package Part 2: Longitudinal data ...
Longitudinal data are repeated measures data in which the observations are taken over time. We wish to characterize the response over time within subjects and the variation in the time trends …
Longitudinal Data Analysis via Linear Mixed Models
Linear Mixed Models for Longitudinal Data. Springer. Purpose: Study change and the factors that effect change. Data: Longitudinal data consist of repeated measurements on the same unit …
Mixed-effects modeling and longitudinal data analysis
Mixed Models Mixed-effects models provide a flexible and powerful tool for the analysis of grouped data, including: • blocked designs • repeated measures (each subject measured for …
Chapter 4 Models for Longitudinal Data
Based on our preliminary graphical exploration of these data, we t a mixed- e ects model with two xed-e ects parameters, the intercept and slope of the linear time trend for the population, and …
Statistical models for longitudinal data : Linear Mixed Model
Summary: Principle of the linear mixed models I Random intercept measures heterogeneity at baseline I Random slope measures heterogeneity at the end of follow-up
Core Guide: Correlation Structures in Mixed Effects Models for ...
19 Sep 2017 · Longitudinal models with both a random intercept and a random slope for time induces a within-individual correlation matrix with correlations that decrease in magnitude the …
Linear mixed models for longitudinal data
A key feature of mixed models is that they can be used to model unbalanced data. In the context of longitudinal data, this includes situations where not all subjects have the same number of …
Linear Mixed Models for Longitudinal Data
Linear Mixed Models for Longitudinal Data With 128 Illustrations Springer. Contents Preface vii Acknowledgments ix i 1 Introduction 1 2 Examples 7 ... 13.2 A Linear Mixed Model for the …
Linear Mixed Models for Longitudinal Data - Springer
In the following sections, we will use their data and their models to illustrate all features of linear mixed models in the context of longitudi nal data.
Bayesian model selection in linear mixed models for longitudinal data
We show in an extensive simulation study that the three marginal criteria are superior in choosing the appropriate longitudinal model. In addition, the marginal criteria selected most appropriate …
Longitudinal Data and Linear Mixed Effects Models
Linear mixed effects models are popularly used for the analysis of longitudinal data of a continuous response variable. They are an exten-sion of linear models by including random …
Deep mixture of linear mixed models for complex longitudinal data
14 Nov 2023 · Mixtures of linear mixed models (MLMMs) (e.g. Verbeke and Lesaffre (1996)) are widely used for the analysis of longitudinal data for which observation times differ by subject, …
Accessible Analysis of Longitudinal Data with Linear Mixed Effects Models
3 Dec 2020 · Summary Statement: Here, we show that linear mixed effects models are more appropriate for analyzing longitudinal data than ANOVA and we provide an accessible, web …
ANALYZING LONGITUDINAL INTERVENTION STUDIES WITH LINEAR MIXED MODELS
To mitigate this issue, this paper proposes a linear mixed regression model (LMM) approach to the analysis of differences between multiple groups over multiple time points. After introducing …
Statistical Modelling - University of Oxford
Abstract: Many approaches are available for the analysis of continuous longitudinal data. Over the last couple of decades, a lot of emphasis has been put on the linear mixed model. The current …
Longitudinal Data Analyses Using Linear Mixed Models in SPSS: …
Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear …
Advances in longitudinal data analysis: An historical perspective
The mixed-effects ANOVA model has a long history of use for analyzing longitudinal data, where it is often referred to as the univariate repeated-measures ANOVA. Statis-ticians recognized …
Mixed models in R using the lme4 package Part 2: Longitudinal data ...
Longitudinal data are repeated measures data in which the observations are taken over time. We wish to characterize the response over time within subjects and the variation in the time trends …
Models for Longitudinal Data: A Generalized Estimating …
This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in …
