Multilevel Statistical Models, 3rd edn

Published under the classic ‘Kendall's library of statistics’, this third edition emphasizes the book's success. Its topic is the statistical modelling and analysis of hierarchically structured data. The established techniques, experience, software packages and the author's work in this area are described in detail. These methods are widely applicable in diverse fields including education, epidemiology, geography, child growth and household surveys. The present edition aims to integrate existing methodological developments within a consistent ter-minology and notation, to provide examples and to explain some new developments, especially in the areas of discrete response data, multiple-membership structures, factor analysis, random cross-classifications, errors of measurement and missing data. Since the publication of the second edition, many expository volumes have appeared, and this new edition aims at integrating all the available information in the area. The style of writing avoids undue statistical complexity and methodological derivations are given in appendices to chapters. The book has 15 chapters. The first introduces multilevel models through the example of schooling systems with pupils clustered within schools, which themselves may be clustered within education authorities or boards. Chapter 2 uses a data set from the ‘Junior school project’ in inner London to illustrate the development of the basic two-level model. The appendices to this chapter contain the general structure and maximum likelihood estimation for a multilevel model, multi-level residuals estimation, the EM algorithm and Markov chain Monte Carlo sampling. Chapter 3 includes bootstrapping in the context of a multi-level model and also meta-analysis. Chapters 4–10 cover a variety of topics on multilevel models, including methods for discrete data, repeated measures, multivariate data with several responses, multilevel factor analysis, non-linear models, applications in sample surveys and event history models. Cross-classified data structures are discussed in Chapter 11; multiple-membership models such as friendship patterns arise in Chapter 12 with an example on salmonella infection. The last three chapters cover measurement errors, missing data and the software that is available for multilevel modelling. Many chapters have useful appendices. The book ends with a list of references and author and subject indexes. Further information can be found by consulting www.multilevel.ioe.ac.uk, the Web site of the Centre for Multilevel Modelling. The book is well written but there are a few typographical and citation errors. It is intended for use in graduate level courses and as a general reference. Because of the lucid style of writing interspersed with illustrative analysis of data sets, it will be a very valuable asset to anyone who is interested in the analysis of multilevel highly structured data. As the author warns, models for multilevel analysis cannot be a universal panacea and must be used with care and understanding. The examples that are used and the up-to-date developments that are discussed in the book will give valuable insight to readers analysing complex multilevel structured data.