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Résumé :
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This book discusses models that provide a framework for descriptive and inferential analyses of categorical response variables. These models closely resemble regression models for continuous response variables, but they assume binomial, multinomial, or Poisson response distributions, rather than normal. We present two types of models in detail, logit and loglinear models. Logit models are used with binomial or multinomial responses, whereas loglinear models are used with Poisson responses. Many equivalences exist between these two types of models. The book has four main units. The first, consisting of chapters 2 and 3, gives descriptive and inferential methods for bivariate categorical data. These chapters introduce basic measures of association as well as classic chi-squared tests. This first unit summarizes the non-model-based methods developed prior to about 1960. The second unit, chapters 4-7, develops the basics model building. Chapter 4 describes a class of generalized linear models that has loglinear and logit models as special cases. That chapter focuses on models for binary response variables, with primary emphasis on logit models. Chapter 5 introduces concepts used in analyzing multivariate categorical data, and shows how to represent association patterns by loglinear models. Chpater 6 gives the mechanics for fitting loglinear and logit models to categorical data, using the maximum likelihood approach. Chapter 7 discusses topics related to model-building, such as strategies for models selection, model diagnostics, and sample size and power considerations. The third unit, Chapter 8-11, discusses applications generalizations of these mdels. Chapter 8 shows how loglinear and logit models can efficiently utilize ordinal information. Chapter 9 discusses alternative models for responses variables having more than two response categories. Generalized forms of logits receive special attention. Chapter 10 presents models for dependent samples, which occur when we measure a categorical response for matched pairs or for the same subjects at two separate occasions. Chapter 11 gives models applicable to more general forms of repeated categorical data, such as longitudinal data from several occasions. The fourth and final unit is more theoretical. Chapter 12 develops asymptotic theory for categorical data models. This theory is the basis for gauging large-sample behavior of model parameter estimators and goodness-of-fit statistics. Chapter 13 discusses methods of estimation for categorical data analysis. Maximum likehood estimation receives primary attention.
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