## Log-linear models and logistic regression. 2nd ed.(English)Zbl 0880.62073

Springer Texts in Statistics. New York, NY: Springer. xv, 483 p. (1997).
[For the review of the first edition from 1990 see Zbl 0711.62050).]
As the new title indicates, this second edition of “Log-Linear Models” is concerned with the analysis of categorical data using log-linear models and with logistic regression. The logistic discrimination is also examined as a special case of log-linear models. As the author indicates in the Preface to this second edition, the book may be used as textbook at different levels by selecting different combinations from the total of 13 chapters. The fundamental material is contained in Chapters 1-4. Intermediate topics are presented in Chapters 5 through 8. For Master degree students in statistics, all the material from Chapter 1 through 9 should be adopted. For an applied Ph. D. course or for advanced Master students, the material in Chapters 10 and 11 can be incorporated.
The second edition consists of 13 chapters. The first chapter “introduction” reviews basic information on conditional independence, random variables, expected values, variances, standard deviations, covariance and correlations. Some distributions most commonly used in the analysis of contingency tables such as the binomial, the multinomial, product multinomial and the Poisson are also reviewed.
Chapter 2, “Two-dimensional tables and simple logistic regression”, provides a more elementary discussion of these topics. Chapter 3, “Three-dimensional tables”, discusses independence and odds ratio models for three-dimensional tables under multinomial sampling, and iterative proportional fitting algorithm for finding estimates of expected cell counts. Log-linear models for three-, four- and more dimensional tables and model selection criteria are introduced.
Chapter 4, “Logistic regression, Logit models, and logistic discrimination”, discusses regression models for two category responses and measuring the fit of models, logistic regression diagnostics and variable selection. Analysis of variance type models for responses with two and more than two categories and the analysis of retrospective studies via logistic discrimination are also examined. The distinction between retrospective and prospective studies is discussed. Chapter 5, “Independence relationships and graphical models”, examines interpretations of models for four and higher-dimensional tables, graphical models, and conditions that allow tables to collapse.
Chapter 6, “Model selection methods and model evaluation”, examines methods of selecting models for high-dimensional tables. The model selection methods considered are the stepwise methods. In addition, the use of the model selection criteria presented in Section 3.6 is discussed. Chapter 7, “Models for factors with quantitative levels”, discusses models that incorporate the quantitative nature of factor levels. When factor levels are not truly quantitative, the appropriateness of such models will be directly related to the appropriateness of the scores being used. The log-linear models of the expected cell counts are adopted. Chapter 8, “Fixed and random zeros”, discusses the case of contingency tables in which a number of the cell counts are zeros.
Chapter 9, “Generalized linear models”, devotes to some fundamental problems in these models, such as the family of distributions, model fitting and estimation of dispersion. Chapter 10, “The matrix approach to log-linear models”, presents a summary of some basic results in maximum likelihood theory for log-linear models in matrix form. Chapter 11, “The matrix approach to logistic models”, discusses logistic regression and logit models by using the matrix approach of Chapter 10. The equivalence of logit models and log-linear models is examined. Model selection criteria for logistic regression and maximum likelihood equations and Newton-Raphson procedure are given.
Chapter 12, “Maximum likelihood theory for log-linear models”, presents the basic theoretical results of fitting log-linear models by maximum likelihood which include the finite sample and asymptotic properties of maximum likelihood estimators and examines how the theory applies to weighted least squares, obtaining variance estimates, and logit and multinomial response models. Chapter 13 is the largest addition to this second edition. The title of the chapter is “Bayesian binomial regression”. The emphasis is on inferences for the probability of “success”.
To understand the vast majority of the book, courses in regression, analysis of variance, and basic statistical theory are necessary. To fully appreciate the book, it would be helpful to already know linear model theory. This is a well written book and I recommend it as a very nice textbook and reference for analysis of categorical data by using log-linear models.

### MSC:

 62J12 Generalized linear models (logistic models) 62-02 Research exposition (monographs, survey articles) pertaining to statistics 62H17 Contingency tables 62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics

Zbl 0711.62050