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A. ALBERT, J. A. ANDERSON, On the existence of maximum likelihood estimates in logistic regression models, Biometrika, Volume 71, Issue 1, April 1984, Pages 1–10, https://doi.org/10.1093/biomet/71.1.1
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Abstract
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.