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On the existence of maximum likelihood estimates for weighted logistic regression

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  • Guoping Zeng

Abstract

The problems of existence and uniqueness of maximum likelihood estimates for logistic regression were completely solved by Silvapulle in 1981 and Albert and Anderson in 1984. In this paper, we extend the well-known results by Silvapulle and by Albert and Anderson to weighted logistic regression. We analytically prove the equivalence between the overlap condition used by Albert and Anderson and that used by Silvapulle. We show that the maximum likelihood estimate of weighted logistic regression does not exist if there is a complete separation or a quasicomplete separation of the data points, and exists and is unique if there is an overlap of data points. Our proofs and results for weighted logistic apply to unweighted logistic regression.

Suggested Citation

  • Guoping Zeng, 2017. "On the existence of maximum likelihood estimates for weighted logistic regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(22), pages 11194-11203, November.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:22:p:11194-11203
    DOI: 10.1080/03610926.2016.1260742
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