In this chapter, we again discuss logistic regression and logit models, but here we use the matrix approach of Chap. 10 . Section 11.1 discusses the equivalence of logit models and log-linear models. This equivalence is used to arrive at results on estimation and testing. Because the data in a typical logistic regression correspond to very sparse data in a contingency table, the asymptotic results of Sect. 10.2 are not appropriate. Section 11.6 presents results from Haberman (Annals of Statistics, 5, 1148–1169 (1977)) that are appropriate for logistic regression models. Section 11.2 discusses model selection criteria for logistic regression. Direct fitting of logit models is considered in Sect. 11.3. The appropriate maximum likelihood equations and Newton-Raphson procedure are given. Section 11.4 indicates how the weighted least squares model-fitting procedure is applied to logit models. Models appropriate for response variables with more than two categories are examined in Sect. 11.5. Finally, Section 11.7 considers the discrimination problem.

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The Matrix Approach to Logit Models

  • Ronald Christensen

摘要

In this chapter, we again discuss logistic regression and logit models, but here we use the matrix approach of Chap. 10 . Section 11.1 discusses the equivalence of logit models and log-linear models. This equivalence is used to arrive at results on estimation and testing. Because the data in a typical logistic regression correspond to very sparse data in a contingency table, the asymptotic results of Sect. 10.2 are not appropriate. Section 11.6 presents results from Haberman (Annals of Statistics, 5, 1148–1169 (1977)) that are appropriate for logistic regression models. Section 11.2 discusses model selection criteria for logistic regression. Direct fitting of logit models is considered in Sect. 11.3. The appropriate maximum likelihood equations and Newton-Raphson procedure are given. Section 11.4 indicates how the weighted least squares model-fitting procedure is applied to logit models. Models appropriate for response variables with more than two categories are examined in Sect. 11.5. Finally, Section 11.7 considers the discrimination problem.