Multilevel and Longitudinal Modeling Using Stata, by Sophia Rabe-Hesketh and Anders Skrondal, looks specifically at Stata’s treatment of generalized linear mixed models, also known as multilevel or hierarchical models. These models are "mixed" because they allow fixed and random effects, and they are "generalized" because they are appropriate for continuous Gaussian responses as well as binary, count, and other types of limited dependent variables.

Beginning with the comparatively simple random-intercept linear model without covariates, Rabe-Hesketh and Skrondal develop the mixed model from principles, thereby familiarizing the reader with terminology, summarizing and relating the widely used estimating strategies, and providing historical perspective.

Once the authors have established the mixed-model foundation, they smoothly generalize to random-intercept models with covariates and then to random-coefficient models. The middle chapters of the book apply the concepts for Gaussian models to models for binary responses (e.g., logit and probit), ordinal responses (e.g., ordered logit and ordered probit), and count responses (e.g., Poisson). The authors then consider models with multiple levels of random variation and models with crossed (nonnested) random effects. In its examples and end-of-chapter exercises, the book contains real datasets and data from the medical, social, and behavioral sciences literature.

The book has several applications of generalized mixed models performed in Stata. Rabe-Hesketh and Skrondal developed gllamm, a Stata program that can fit many latent-variable models, of which the generalized linear mixed model is a special case. With the release of version 9, Stata introduced the xtmixed command for fitting linear (Gaussian) mixed models. Stata users can use gllamm and xtmixed in conjunction with the rest of the xt suite of commands to perform comparative mixed-model analyses for various response families. The type of models fit by these commands sometimes overlap; when this happens, the authors highlight the differences in syntax, data organization, and output for the two (or more) commands that can be used to fit the same model. The authors also point out the relative strengths and weaknesses of each command when used to fit the same model, based on considerations such as computational speed, accuracy, and available predictions and postestimation statistics. The book delineates the relationship between gllamm and xtmixed, clearly showing how they complement one another.

A reviewer for American Statistician commends Rabe-Hesketh and Skrondal for promoting the appropriate use of multilevel and longitudinal modeling. The reviewer writes in the August 2006 issue, “All too often computer manuals leave off ... important aspects of an analysis, but the authors have been careful to provide a well-rounded and complete approach to model fitting and interpretation.”

In summary, this book is the most complete, up-to-date depiction of Stata's capacity for fitting generalized linear mixed models. The authors provide an ideal introduction for Stata users wishing to learn about this powerful data