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## Multilevel and Longitudinal Modeling Using Stata, 2nd Edition

 Multilevel and Longitudinal Modeling Using Stata, Second Edition, 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. The second edition has much to offer for readers of the first edition, reading more like a sequel than an update. The text has almost doubled in length from the original, coming in at 562 pages. This second edition incorporates three new chapters: a chapter on standard linear regression, a chapter on discrete-time survival analysis, and a chapter on longitudinal and panel data containing an expanded discussion of random-coefficient and growth-curve models. The authors have updated this edition for Stata 10, expanding on discussions in the original edition and adding new in-text examples and end-of-chapter exercises. In particular, the authors have thoroughly covered the new Stata commands xtmelogit and xtmepoisson. The first chapter provides a review of the methods of linear regression. Rabe-Hesketh and Skrondal then begin with the comparatively simple random-intercept linear model without covariates, developing the mixed model from principles and 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 a discussion of the various estimators (between, within, and random-effects). The authors then discuss models with random coefficients, followed by models for growth curves. 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 text continues with a discussion of how to use multilevel methods in discrete-time survival analysis, for example, using complimentary log-log regression to fit the proportional hazards model. 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. As of version 10, Stata contains the xtmixed, xtmelogit, and xtmepoisson commands for fitting multilevel models, in addition to other xt commands for fitting standard random-intercept models. 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, available predictions, and available postestimation statistics. In reference to the first edition, 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-analysis tool. For further details or to order online, please visit the Stata Bookstore.