Handbook of Multilevel Analysis

Multilevel analysis is the statistical modelling of hierarchical and non-hierarchical clustered data. These data structures are common in social and medical sciences. This handbook is an edited volume, organized into 12 chapters on selected topics within multilevel analysis, each written by distinguished authors. The first five chapters deal with the design of multilevel studies and the estimation of and inference from the linear two-level model. Chapter 1 provides a detailed overview of multilevel analysis, although this is more a refresher than an introduction for the uninitiated. Chapter 2 provides an accessible overview of Bayesian methods for fitting multilevel models and particular attention is given to Markov chain Monte Carlo diagnostics in the WinBUGS and MLwiN software packages. Chapter 3 refers to multilevel diagnostic checks, but it also has an interesting discussion of spline functions to examine non-linear fixed effects of explanatory variables. Chapter 4 focuses on optimal design of multilevel experiments and includes discussion of the number of units at each level and the level at which randomization occurs. Chapter 5 focuses on issues that arise when there are many small groups, e.g. individuals within families. The next four chapters are especially useful to the applied researcher and include some excellent detailed examples. Chapters 6 and 9 depart from the rest of the handbook by considering generalized linear models. Chapter 6 covers extensions to ordered and unordered multinomial responses whereas Chapter 9 focuses mainly on multilevel survival models. The latter details a simulation study and gives practical advice for using different estimation methods (e.g. quadrature, marginal and penalized quasi-likelihood and Markov chain Monte Carlo methods) that applies to all types of discrete response multilevel models. Chapter 7 discusses multilevel models for longitudinal data and touches on a wide range of issues, including the discussion of discrete mixture distributions for random coefficients, lagged responses as explanatory variables and conditional versus marginal modelling approaches. Chapter 8 describes non-hierarchical cross-classified and multiple membership data structures and how these can be modelled simultaneously. There is an excellent guide to notational and graphical approaches to communicating these models. The final three chapters are more technical. Chapter 10 discusses use of the EM algorithm with a multiple-imputation approach to account for missing data in multilevel models. However, there is little discussion of the use of, for example, multilevel pattern–mixture and selection models for when the patterns of missingness are non-random. Chapter 11 focuses on bootstrap and jackknife methods for multilevel models. Chapter 12 is on multilevel structural equation modelling, but its treatment of the topic is ill suited to a handbook as, rather than provide an overview of the topic, the authors concentrate on a new approach that they propose to fitting such models. This chapter, with its comprehensive derivations, will be of most use to researchers who would like to write their own multilevel structural equation modelling routines. My overall impression of this handbook is that it is a series of stand alone chapters rather than a tightly edited volume. The technical difficulty of the topics that are covered in the handbook varies from chapter to chapter and some authors give a more theoretical treatment of their material than others. Thus, the treatment of a topic, rather than the topic itself, may unfortunately determine its usefulness to the reader. It is also difficult to locate particular topics in the handbook as the contents page provides only the titles of the chapters and entries in the subject index often refer to an overly long list of pages. Inevitably only a selection of topics can be covered in any detail. Topics with relatively little coverage include multilevel models for count data, spatial data and multivariate responses. However, for the topics that are covered, the extensive and up-to-date reference lists at the end of each chapter are a valuable resource and will allow the interested reader to pursue them in more detail. A final point is that there are no electronic materials to accompany the handbook. The data sets that are used in the examples are not provided and, with the exception of Chapter 12, nor is the syntax to fit the models. This limits the usefulness of the book to applied researchers. This omission is a particular shame as a valuable aspect of the handbook is that its examples use a range of multilevel statistical packages. Such a resource would encourage researchers to move between packages and not simply to stick to the one that they know best. I would strongly encourage the electronic materials for each chapter to be placed on the publisher’s Web site. Overall the handbook is aimed at statistical methodologists but will also be of interest to applied researchers with a firm grounding in multilevel analysis. Researchers who are new to multilevel modelling would be advised first to consider one of the many excellent multilevel textbooks that have been written by the contributing authors (e.g. Goldstein (2003), Raudenbush and Bryk (2002) and Snijders and Bosker (1999)).