Sophia Rabe-Hesketh, Anders Skrondal
Stata Press (12 August 2005)
This book is a Stata-specific treatment of generalised linear mixed models, also known as multilevel or hierarchical models. These models are 'mixed' in the sense that they allow fixed and random effects and are 'generalized' in the sense that they are appropriate not only for continuous Gaussian responses, but also for binary, count, and other types of limited dependent variables.
Beginning with the comparatively simple random-intercept linear model without covariates, the text develops the mixed model from first principles, familiarizing the reader with terminology, summarizing and relating the widely-used estimating strategies, and providing historical perspective.
Once this mixed-model foundation has been established, the text smoothly generalizes to random-intercept models with covariates and then to random-coefficient models. The middle chapters of the text apply the concepts defined earlier for Gaussian models to models for binary responses (eg., logit and probit), ordinal responses (eg. ordered logit and ordered probit), and count responses (eg. Poisson). Models with multiple levels of random variation are then considered, as well as models with crossed (nonnested) random effects. The datasets used are real data from the medical, social, and behavioural sciences literature, and several thought-provoking exercises are included at the end of each chapter.
The text is loaded with applications of generalized mixed models performed in Stata. The authors are the developers of gllamm, a Stata program that can fit a vast array of 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. These two commands, combined with the rest of the xt suite of Stata commands (e.g., xtlogit, xtprobit, etc.), can be used in conjunction in order to perform comparative mixed-model analyses for various response families. The types of models fit by these commands sometimes overlap, and when this occurs 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 text also points out the relative strengths and weaknesses of each command when used to fit the same model, based on issues such as computational speed, accuracy, and available predictions and postestimation statistics. In particular, the relationship between gllamm and xtmixed and how they complement each other is made very clear.
In summary, this text is the most complete and up-to-date depiction of Stata's capacity for fitting generalized linear mixed models and an ideal introduction for Stata users wishing to learn about this powerful data-analysis tool.