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On the existence of maximum likelihood estimates in logistic regression models. (English) Zbl 0543.62020

For multinomial logistic regression models, the authors study the existence of maximum likelihood estimates of the model parameters by considering the three possible patterns of data points: complete separation, quasicomplete separation, and overlap defined in an appropriate sense.
Two of the results are: (i) If there is a complete separation of data points, then the maximum likelihood estimate does not exist; and (ii) if there is overlap of the data points, then the maximum likelihood estimate exists and is unique. These results suggest useful rules for identifying infinite parameter estimates in log linear models for frequency tables.
Reviewer: W.J.Padgett

MSC:

62F10 Point estimation
62J99 Linear inference, regression
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