Multilevel Statistical Models

complex structure is required for the error covariance matrix. In Chapter 8, the growth-curve model is extended to latent growth-curve models by expressing the multilevel model as a structural equation model. This latter chapter, the most difficult material in the book, requires further reading to implement such an analysis. The second part of the book (Chaps. 9–15) starts with a discussion of the basic and necessary concepts required for studying when events occur. There are some redundancies with respect to the first part of the book, especially in terms of concepts related to the nature of longitudinal data and the treatment of time in the models. This part is further divided into two major sections: data and models for discrete time (Chaps. 10–12) and data and models for continuous time (Chaps. 13–15). In each subpart, the authors begin with exploratory data analyses, then explore building a model for the data. The models for continuous time are presented as generalizations of the models for discrete time; however, the former involves some additional complications. As I read this half of the book, I kept thinking to myself “Isn’t this just ,” where the blank could be filled in with terms or models from standard categorical data analysis methods. For example, the basic model for discrete time is a logistic regression model, and the basic model for continuous time (Cox’s regression model) is essentially a Poisson regression model. I have always been somewhat skeptical of introductory books on complex statistical models that emphasize concepts and keep math to a minimum. However, Applied Longitudinal Data Analysis provides readers with a solid, thorough, and relatively accurate understanding of concepts and procedures. There are places where verbal descriptions of precise statistical material are a bit loose (for a statistician), but in many of these instances, more precise statements and detailed discussions are given later in the text. There are some typographical errors that may momentarily puzzle a careful reader. A novice to longitudinal data analysis could be left with the impression that multilevel models and survival analysis are the only two methods for analyzing longitudinal data. The book is not a comprehensive treatment of all methods for longitudinal data (e.g., transition models and time series analysis are not mentioned). With respect to the two general methods covered in the book, extensions of growth-curve models not covered include models for three or more levels (e.g., individuals grouped into higher-level units, such as schools or neighborhoods), and, with the exception of a model in Chapter 6, multilevel models for discrete data (i.e., multilevel generalized or nonlinear models). Extensions of survival analysis not covered in this text include situations where the outcome (response variable) has more than two levels. These omissions are reasonable given that this is an introduction to multilevel models and survival analysis, and what the authors do present covers a wide range of applications. Methods for longitudinal data analysis, particularly multilevel modeling, have developed at a rapid pace. The methodology for growth-curve analysis (of numerical variables) and survival analysis have reached a level of maturity such that these methods should be used more often than they are. In my experience, substantive researchers may have been introduced to multilevel models or methods for categorical data analysis (and used them in nonlongitudinal settings), but they have difficulty seeing how these methods can be applied to longitudinal data. The authors make this connection, and also comprehensively introduce the methods to those completely unfamiliar with either multilevel models or survival analysis.