SAS® for Mixed Models: Introduction and Basic Applications

The first edition of SAS for Mixed Models published over two decades ago was a major revelation. The book totally changed my understanding of the theory and application of mixed models, leading me into several new research areas. As with many around the world, I enthusiastically welcomed and thoroughly studied the second edition that came out in 2006. The first edition dealt mostly with the use of PROC MIXED for linear mixed models (LMMs) and normal data, or data that can be assumed to be normal, with just a little on nonlinear mixed models and generalized linear mixed models (GLMMs), the latter for some non-normal distributions. The second edition expanded on many of the themes of the first, incorporating the new ODS graphics and tabular output, and adding several new topics, including power analysis, model diagnostics, and a little introductory material on Bayesian approaches to mixed-model analysis. The detailed presentation on the analysis of factorials (with multiple error terms) was most welcome. GLMMs and nonlinear mixed models received greatly expanded attention, with the brand new GLIMMIX procedure being used for the former and NLMIXED for much of the latter.

The 2006 edition has been the most important book on my bookshelf for over a decade; I probably came close to memorizing the volume. But the mixed-model-analysis field did not stand still during the past dozen years or so. SAS developers were adding many features to procedures, especially to GLIMMIX, while advances were made in statistical theory and methodology, especially for GLMMs. I know I was far from alone in eagerly awaiting the third edition of SAS for Mixed Models. It was worth the wait! Three of the original authors remain, with Walt Stroup now in the role of first author. His enjoyable, clear, and clever writing style can be found throughout the book (although the previous editions were also quite clear). In addition to George Milliken and Russ Wolfinger, Elizabeth Claassen has joined the team of authors. These authors have added a lot of material compared to the second edition. In fact, they have added so much that they broke up the new edition into two volumes; only the first one (“Introduction and Basic Applications”) is published so far. Hopefully we won’t have to wait too long for the second volume!

One way that the new edition grew in content was by incorporating parts of the other valuable book, the fourth edition of SAS for Linear Models. There is, therefore, increased coverage of experimental design and analysis of single and multiple-factor experiments, with clear presentation on the construction and testing of contrasts. Of course, there is a mixed-model flavor to everything that is covered. Two chapters are now dedicated to power, precision, sample sizes, and the planning of experiments, much welcomed expansions compared with the previous edition. Many clever ways of using GLIMMIX (or MIXED) to estimate power are provided; this is invaluable material because the many common power-analysis methods (such as those found in PROC POWER or GLMPOWER) do not directly apply to mixed models. There is very helpful material on inference for variances and covariances, with nice presentation on different ways of estimating confidence intervals. I really liked the discussion on how one translates study designs into plausible models by looking at the combination of the treatment and experimental design. The protocol previously advanced by Stroup called “What Would Fisher Do (WWFD)” provides a clever way of guiding researchers in search of the proper statistical model and choice of fixed and random effects. The WWFD is especially helpful when one takes the leap from LMMs to GLMMs.

The new edition truly shines in its coverage of GLMMs. Three chapters are devoted to the subject, which is a great expansion over the previous edition of the book. The coverage is justified, given the growing popularity of the field for analysis of non-normal data. There are excellent explanations of conditional and marginal models, and narrow and broad inference space, topics of great importance for GLMMs but which are often poorly or incorrectly understood by many. Implications of different parameter-estimation (model-fitting) methods are explained in detail for GLMMs. The authors correct the misconception that pseudo-likelihood is inferior to integral approximation methods; in fact, the best estimation method depends on circumstances, and this book gives a lot of guidance on how to make a reasoned choice for model fitting. It is clear that no software can compete with GLIMMIX for mixed-model analysis. It is only fitting that GLIMMIX is used for most analyses, even for LMMs.

The second edition had excellent material on model diagnostics, such as assessment of conditional and marginal residuals and the analysis of the influence of individual observations or clusters of observations on the model fit. The new edition expands on these concepts, especially for GLMMs, and adds a very helpful section on troubleshooting. There are many challenges in fitting LMMs and GLMMs to data, so the troubleshooting section will be one of the most valuable parts of the new book. Lots of web resources were cited.

The new SAS for Mixed Models edition should be read by everyone analyzing data. The book excels at combining instructional material on the meaning and uses of mixed models with specific instructions on how to use SAS software. I can’t wait for the second volume to come out, with coverage of spatial variability, nonlinear mixed modeling, heterogeneous variances, Bayesian analysis, and more. 

Laurence V. Madden
Distinguished Professor of Plant Protection
The Ohio State University