© 1984 by Biometrika Trust
On the existence of maximum likelihood estimates in logistic regression models
Laboratoire de Chimie médicale, Université de Liége Belgium
*Professor J. A. Anderson died in February 1983. The final version of the paper was prepard by Dr A. Albert.
The problems of existence, uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature (Haberman, 1974, Chapter 2; Wedderburn, 1976; Silvapulle, 1981). For multinomial logistic regression models, we prove existence theorems by considering the possible patterns of data points, which fall into three mutually exclusive and exhaustive categories: complete separation, quasicomplete separation and overlap. Our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables.
Key Words: Complete separation • Cox model • Generalized linear model • Log linear model • Logistic discrimination • Logistic regression • Maximum likelihood estimator • Overlap • Quasicomplete separation
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