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Hierarchical linear models. Applications and data analysis methods. 2nd ed. (English) Zbl 1001.62004

Advanced Quantitative Techniques in the Social Sciences Series. 1. Thousand Oaks, CA: Sage Publications. xxiv, 483 p. (2002).
This is the second revised and enlarged edition of a famous book on hierarchical models written for researchers in the area of social and behavioral sciences. While the first edition from 1992 concerned mostly continuously distributed outcomes at level 1, the present one also covers discrete and categorical outcomes. The book is divided into four parts: I. Logic (Chapters 1-3); II. Basic applications (Chapters 4-9); III. Advanced Applications (Chapters 10-13) and IV. Statistical theory and computations (Chapter 14). The first two sections are closely parallel to the first edition with some additional extensions and clarifications, while the latter ones are new and reflect the developments during the last 10 years.
Chapter 1 is an introduction into the area of hierarchical models including some basic notions and the scope of the book. In Chapter 2, Basic logic of hierarchical models, simpler concepts from regression models and models with random effects are explained, and Chapter 3 summarizes the basic elements of statistical theory (estimation theory and hypothesis testing) used with these models.
Applications of this technique to a number of some particular situations are presented in Chapter 4. Chapters 5-7 illustrate the logic of hierarchical models on a range of applications of two-level models. Chapter 8 introduces three-level models and describes a number of applications. Chapter 9 reviews the basic model assumptions and discusses the problems of how to validate these assumptions and of the sensitivity of inferences to violations of the assumptions.
Chapter 10 covers generalized linear models, namely, applications of hierarchical models in the case of discrete outcomes (binary outcomes, counted data ordered categories, multinomial outcomes). Chapter 11 concerns hierarchical models for latent variables including estimating regressions. It includes estimating regressions from missing data and estimating regressions when predictors are measured with errors. Chapter 12 concerns cross-classified random effects models. Chapter 13 gives a Bayesian perspective on hierarchical models and discusses Markov chain Monte Carlo computations.
Chapter 14 provides statistical theory and computational approaches used throughout the book. It considers univariate linear models with normal level-1 errors, multivariate linear models and hierarchical generalized linear models.
The chapter headings are as follows: 1. Introduction; 2. Logic of hierarchical linear models; 3. Principles of estimation and hypothesis testing for hierarchical models; 4. An illustration; 5. Applications in organizational research; 6. Applications in the study of individual change; 7. Applications of meta-analysis and other cases where level-1 variances are known; 8. Three level models; 9. Assessing the adequacy of hierarchical models; 10. Hierarchical generalized linear models; 11. Hierarchical models for latent variables; 12. Models for cross-classified random effects; 13. Bayesian inference for hierarchical models; 14. Estimation theory.
The book provides quite comprehensive information on hierarchical models for the purposes of social and behavioral scientists. It does not only present a well-structured material of possible models accompanied by many explanations, remarks and illustrative examples, but it also gives hints how to build models for particular situations and points out the importance that the assumptions of the considered models should be fulfilled. The book really provides many varied illustrative examples. At the end of each chapter, the basic notions and information are summarized.
One can read the book on several levels. It can be studied as a cook book only, but one can learn more to understand of the insight of the used models on a more abstract way or, of course, one can choose an intermediate level. Technical details are on a level acceptable for social and behavioral researchers. Basic knowledge of statistics is assumed. The book is very well written and the applied part is well balanced with technical details. I think that it will be useful not only for social and behavioral researchers but also for applied statisticians, practitioners and students analyzing data with hierarchical-type structures.

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62J99 Linear inference, regression
62J12 Generalized linear models (logistic models)
62P25 Applications of statistics to social sciences
62P15 Applications of statistics to psychology

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