Linear Mixed Models

Linear Mixed Models: A Practical Guide Using Statistical Software

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Features

  • Dedicates an entire chapter to the key theories underlying LMMs for clustered, longitudinal, and repeated measures data
  • Provides descriptions, explanations, and examples of software code necessary to fit LMMs in SAS, SPSS, R, Stata, and HLM
  • Contains detailed tables of estimates and results, allowing for easy comparisons across software procedures
  • Presents step-by-step analyses of real-world data sets that arise from a variety of research settings and study designs, including hypothesis testing, interpretation of results, and model diagnostics
  • Supplies software code in each chapter to compare the relative advantages and disadvantages of each package
  • Includes a supporting website that features many of the data sets used in the examples as well as the most up-to-date versions of selected portions of the syntax associated with the examples
  • Summary

    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-navigate reference details the use of procedures for fitting LMMs in five popular statistical software packages: SAS, SPSS, Stata, R/S-plus, and HLM.

    The authors introduce basic theoretical concepts, present a heuristic approach to fitting LMMs based on both general and hierarchical model specifications, develop the model-building process step-by-step, and demonstrate the estimation, testing, and interpretation of fixed-effect parameters and covariance parameters associated with random effects. These concepts are illustrated through examples using real-world data sets that enable comparisons of model fitting options and results across the software procedures. The book also gives an overview of important options and features available in each procedure.

    Making popular software procedures for fitting LMMs easy-to-use, this valuable resource shows how to perform LMM analyses and provides a clear explanation of mixed modeling techniques and theories.

    Table of Contents

    PREFACE
    INTRODUCTION
    What Are Linear Mixed Models (LMMs)?
    A Brief History of Linear Mixed Models
    LINEAR MIXED MODELS: AN OVERVIEW
    Introduction
    Specification of LMMs
    The Marginal Linear Model
    Estimation in LMMs
    Computational Issues
    Tools for Model Selection
    Model Building Strategies
    Checking Model Assumptions (Diagnostics)
    Other Aspects of LMMs
    Chapter Summary
    TWO-LEVEL MODELS FOR CLUSTERED DATA: THE RAT PUP EXAMPLE
    Introduction
    The Rat Pup Study
    Overview of the Rat Pup Data Analysis
    Analysis Steps in the Software Procedures
    Results of Hypothesis Tests
    Comparing Results across the Software Procedures
    Interpreting Parameter Estimates in the Final Model
    Estimating the Intraclass Correlation Coefficients (ICCs)
    Calculating Predicted Values
    Diagnostics for the Final Model
    Software Notes
    THREE-LEVEL MODELS FOR CLUSTERED DATA; THE CLASSROOM EXAMPLE
    Introduction
    The Classroom Study
    Overview of the Classroom Data Analysis
    Analysis Steps in the Software Procedures
    Results of Hypothesis Tests
    Comparing Results across the Software Procedures
    Interpreting Parameter Estimates in the Final Model
    Estimating the Intraclass Correlation Coefficients (ICCs)
    Calculating Predicted Values
    Diagnostics for the Final Model
    Software Notes
    MODELS FOR REPEATED MEASURES DATA: THE RAT BRAIN EXAMPLE
    Introduction
    The Rat Brain Study
    Overview of the Rat Brain Data Analysis
    Analysis Steps in the Software Procedures
    Results of Hypothesis Tests            
    Comparing Results across the Software Procedures
    Interpreting Parameter Estimates in the Final Model
    The Implied Marginal Variance-Covariance Matrix for the Final Model
    Diagnostics for the Final Model
    Software Notes
    Other Analytic Approaches
    RANDOM COEFFICIENT MODELS FOR LONGITUDINAL DATA: THE AUTISM EXAMPLE
    Introduction
    The Autism Study
    Overview of the Autism Data Analysis
    Analysis Steps in the Software Procedures
    Results of Hypothesis Tests
    Comparing Results across the Software Procedures
    Interpreting Parameter Estimates in the Final Model
    Calculating Predicted Values
    Diagnostics for the Final Model
    Software Note: Computational Problems with the D Matrix
    An Alternative Approach: Fitting the Marginal Model with an Unstructured Covariance Matrix
    MODELS FOR CLUSTERED LONGITUDINAL DATA: THE DENTAL VENEER EXAMPLE
    Introduction
    The Dental Veneer Study
    Overview of the Dental Veneer Data Analysis
    Analysis Steps in the Software Procedures
    Results of Hypothesis Tests
    Comparing Results across the Software Procedures
    Interpreting Parameter Estimates in the Final Model
    The Implied Marginal Variance-Covariance Matrix for the Final Model
    Diagnostics for the Final Model
    Software Notes
    Other Analytic Approaches
    REFERENCES
    APPENDIX A: STATISTICAL SOFTWARE RESOURCES
    APPENDIX B: CALCULATION OF THE MARGINAL VARIANCE-COVARIANCE MATRIX
    APPENDIX C: ACRONYMS/ABBREVIATIONS
    INDEX

    Author Bio(s)

    Editorial Reviews

    "… a good overview of the main types or variants of LMMs available. Furthermore, the book also gives a very well-balanced treatment to five mainstream software packages used to fit the LMMs used in each example. The treatment of the examples is done in a rather thorough way, very useful for practitioners. This book is thus highly recommended to all those who are mainly interested in learning how to fit a specific LMM to their data or willing to learn what kinds of data and for what kind of situations LMMs may be fit and adequate. It may also be a very good starting point for those willing to get a more in-depth knowledge of LMMs … a very useful manual for the application of LMMs, which will contribute beyond any doubt to the development of work in this and related areas."
    —Carlos A. Coelho and Abel M. Rodrigues, Journal of Statistical Theory and Practice, 2012

    "In this book the authors take on the herculean task of demonstrating how to perform complex LMM analyses with five programs: HLM, R/S–PLUS, SAS, SPSS, and Stata. It is much more than a software manual; through the use of excellent introductory material and details given throughout, it provides a solid introduction to LMM analysis. … Software-oriented books can quickly become dated, but the [book’s] website http://www-personal.umich.edu/~bwest/almmussp.html appears to keep up with new developments … this book is a tremendous contribution to the field of applied mixed modeling. It is much more than a software manual. It is well organized, has minimal typographical errors, and contains a complete index. It could easily serve as a reference guide. Anyone working with LMMs should seriously consider obtaining this book."
    Technometrics, May 2009, Vol. 51, No. 2

    "… the book is very useful for the well-informed practitioner, who wants to fit LMMs and needs to make a choice about the specific statistical software to use."
    Biometrical Journal, Vol. 51, 2009

    "… useful to someone who wanted to understand the process of setting up, conducting, and evaluating a mixed model analysis. West et al. [is] appropriate for a researcher with problems where model selection is a major component of the analysis. ... would also be useful to a practicing statistician who is familiar with mixed models and wishes to use a new statistical package."
    Biometrics, December 2008

    "This text is a most welcome addition to the literature on regression models. … It is one of those rare texts with no glaring omissions or obvious shortcomings. The book consolidates syntax germane to LMMs for most major software packages, obviating the need to consult multiple platform-specific texts. Most importantly, the material is presented in an easy-to-read, sensibly organized fashion … a must buy for the applied statistician and researcher alike."
    —Gregory E. Gilbert, Medical University of South Carolina, Journal of the American Statistical Association

    "I commend this book to anyone who is using software for statistical modelling, either for a detailed account of specific linear models or an exemplar of how to gather the information to compare software."
    Journal of the Royal Statistical Society

    "… a good reference for any practicing statisticians and researchers who want a basic introduction to the topic ... also useful for researchers who need to compare their analysis to existing works done using different software packages. Because the basic concept is well summarized and presented through examples and tables ... I would recommend this textbook as a special topic for teaching an advanced undergraduate or introductory graduate course on linear models."
    Journal of Quality Technology

    "... an excellent first course in the theory and methods of linear mixed models … also provides a thorough and up-to-date guide through the major software applications for linear mixed models, namely, Stata, SAS, R, SPSS, and HLM. Each of five middle chapters highlights a different software package and teaches you the basics of fitting mixed models therein. Tables comparing each package show the results obtained from fitting identical models, ... . If you wish to fit linear mixed models, whether in Stata or elsewhere, we recommend this text."
    —Stata Technical Group

    Downloads / Updates

    Resource OS Platform Updated Description Instructions
    Cross Platform February 24, 2006 Download datasets and software code atwww-personal.umich.edu/~bwest/almmussp.html

     
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