Like its bestselling predecessor, Multilevel Modeling Using R, Third Edition provides the reader with a helpful guide to conducting multilevel data modeling using the R software environment. After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single level and multilevel data. The third edition of the book includes several new topics that were not present in the second edition. Specifically, a new chapter has been included, focussing on fitting multilevel latent variable modeling in the R environment. With R, it is possible to fit a variety of latent variable models in the multilevel context, including factor analysis, structural models, item response theory, and latent class models. The third edition also includes new sections in chapter 11 describing two useful alternatives to standard multilevel models, fixed effects models and generalized estimating equations. These approaches are particularly useful with small samples and when the researcher is interested in modeling the correlation structure within higher level units (e.g., schools). The third edition also includes a new section on mediation modeling in the multilevel context, in chapter 11. This thoroughly updated revision gives the reader state-of-the-art tools to launch their own investigations in multilevel modeling and gain insight into their research.
This brief book is designed in the model of a practitioner's guide with just enough theory to understand how to call and interpret the R functions. Unfortunately, it partially fails in this; the mathematical background it provides is too thin to explain several key concepts and they are glossed over.
For example, when explaining why to use multilevel models, the book compares them to a strawman of not including the groupings at all; a more meaningful comparison would have been to a linear model which included the grouping variable as a factor. A better explanation is provided for free in one paragraph in section 2.2 of the lmer vignette documentation.
As another example, in describing the lme4 syntax, the book explains how to specify that random slopes are correlated or uncorrelated, but does not explain what that actually means, what it translates to in equations, or how it actually impacts the model fit. The term "shrinkage" is never mentioned.
I would recommend the multilevel modeling book by Gelman and Hill instead, or the unfinished online PDF by Doug Bates.