Linear Mixed Models: A Practical Guide Using Statistical Software (Second Edition)
Kathleen B. Welch, MS, MPH
Andrzej T. Galecki, M.D., Ph.D.

Note: The second edition is now available via online retailers. You can view a brief promotional video from the three authors here.

This book provides readers with a practical introduction to the theory and applications of linear mixed models, and introduces the fitting and interpretation of several types of linear mixed models using the statistical software packages SAS (PROC MIXED), SPSS (the MIXED and GENLINMIXED procedures), Stata (mixed / xtmixed), R (the lme() and lmer() functions), and HLM (Hierarchical Linear Models).

The book focuses on the statistical meaning behind linear mixed models. Why fit them? Why are they important? When are they applicable? What do they mean for research conclusions? The book also presents and compares practical, step-by-step analyses of real-world data sets in all of the aforementioned software packages, allowing readers to compare and contrast the packages in terms of their syntax/code, ease of use, available methods and options, and relative advantages.

Click on any of the following chapters for links to the data sets, updates to the software code in the book, and miscellaneous additional information:

Chapter 3 -> Two-level Models for Clustered Data: The Rat Pup Example
Chapter 4 -> Three-level Models for Clustered Data: The Classroom Example
Chapter 5 -> Models for Repeated Measures Data: The Rat Brain Example
Chapter 6 -> Random Coefficient Models for Longitudinal Data: The Autism Example
Chapter 7 -> Models for Clustered Longitudinal Data: The Dental Veneer Example
Chapter 8 -> Models for Data with Crossed Random Factors: The Sat Score Example

Notes on Shrinkage Estimators
SPSS White Paper on the MIXED Procedure, with instructions on data preparation and use of the MIXED Procedure via the SPSS menus

1. Technometrics
2. Biometrical Journal
3. Stata

1. Journal of Statistical Theory and Practice
2. Journal of the American Statistical Association
3. Stata
4. Technometrics (Nominated for the 2009 Ziegel Prize)
5. Biometrics
6. Statistics in Medicine
7. Journal of Quality Technology
8. Journal of the Royal Statistical Society-Series A
9. Biometrical Journal

The book was nominated for the 2009 Ziegel Prize, sponsored by the Journal Technometrics and honoring a first edition with clearly discussed statistical methodology that "brings together in one volume a body of material previously only available in scattered research articles and having the potential to significantly improve practice in engineering and science."

1. BAYESIAN ANALYSIS: For examples of Bayesian approaches to the analysis of the data sets in each chapter in SAS and R, click on our Bayesian Analysis in SAS page or our Bayesian Analysis in R page. You should also check out the Stan web page, and the web page for "The BUGS Book" (forthcoming). A new R package named brms is now available as well, which makes it very easy to use the Stan machinery in the background to fit mixed-effects models using Bayesian methodology. We strongly encourage readers to take advantage of this package's features and work with Stan to fit these models, especially when your research objectives involve making inference about variance components.

2. POWER ANALYSIS: Those interested in power analysis and sample size calculations for study designs that are multilevel and/or longitudinal in nature can check out this site for some very helpful free software and documentation (the Optimal Design software package) developed at the University of Michigan. Additional free simulation-based software and documentation for power analysis in multilevel designs can be found here. We have also prepared an example of a simulation program in SAS for the second edition of the book that can be downloaded here for example power calculations.

3. An R package containing the data sets for the book, WWGbook, has been posted on CRAN. Please visit the R Project site for links to CRAN mirrors.

4. Use of the lmerTest package in R should be properly cited as follows: Alexandra Kuznetsova, Per Bruun Brockhoff, Rune Haubo, and Bojesen Christensen (2014). lmerTest: Tests for random and fixed effects for linear mixed effect models (lmer objects of lme4 package). R package version 2.0-13/r71. http://R-Forge.R-project.org/projects/lmertest/.