zbMATH — the first resource for mathematics

Categorical data analysis. (English) Zbl 0716.62001
Wiley Series in Probability and Mathematical Statistics. New York etc.: John Wiley & Sons. xv, 558 p. £39.80 (1990).
This book consists of 13 chapters and 3 Appendices. The chapters can be divided into four sets of results, if the first one is excluded which gives a brief introduction to the theme. The first set is related to classical results. The usual methods for analyzing categorical variables appear in chapters 2 and 3. The style of presentation of the results is clear and oriented to the solution of practical problems. Statisticians can go through them very fast or avoid the lecture if they are skilled in the usage of 2-way contingency tables. The other chapters are dedicated to the study of models. The second set of subjects is given in chapters 4-7. Chapter 4 presents models for binary responses. A generalized linear model (GLM) family is described that includes well-known models (logit, log-linear,..). This approach permits to unify the exposition and to study, regression and goodness of fit (gf). Chapter 5 tackles log-linear modelling for contingency tables (CT) of key problems as independence checking and saturation in two and higher dimensions. Modelling and studying the performance of statistical properties of estimators (sufficiency, maximum likelihood (ML)) and testing are discussed in the next chapter. The analysis of iteration procedures in ML estimation is analyzed. Especially the treatment of the role and behavior of ‘iterative proportional fitting’ and Newton-Raphson methods is well managed. Commonly used families of problems are modelled and an overview on log- linear model fitting is given. Model building is the subject of Chapter 7. Different problems belonging to a wide class are thoroughly analyzed and the results serve as a guide for practical modelling.
The following three chapters are devoted to the generalization of the previously given basic models. The treatment of bivariate problems under log-linear and logit models is presented in Chapter 8. The study of multinomial models is the focus of the next chapter. GLM, for log-linear and logit, are developed. The analysis of dependent samples and different inference procedures are presented in Chapter 10. The results of these chapters are of practical importance but the rest of the book has a theoretical objective. There are derived large sample properties which permit to tackle problems appearing in longitudinal surveys, applied Bayesian methods, etc.
The Appendices present a discussion on the performance of the most powerful packages for dealing with the different models. A reference to each chapter is given. The needed tables are printed. Each chapter finishes with notes on the subject, and a set of exercises is proposed. They enable to fix ideas and to train the usage of the models.
This book represents a main contribution to the theme and a necessary complement to the other book of the author, “Analysis of ordinal categorical data” (1984; Zbl 0647.62052).
Reviewer: C.Bouza

62-07 Data analysis (statistics) (MSC2010)
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62H17 Contingency tables
62H20 Measures of association (correlation, canonical correlation, etc.)