Abstract
It is known that the maximum likelihood estimate of a logistic regression model may not exist. Specifically, the maximum likelihood estimate only exists if the dataset is non separable. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset, a type of regularization. This is equivalent to treating logistic regression as a mixed-membership (grade-of-membership) model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 766-776 |
| Number of pages | 11 |
| Journal | Communications in Statistics - Theory and Methods |
| Volume | 55 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2026 |
| Externally published | Yes |
Keywords
- Regularization
- existence
- grade-of-membership
- logistic regression
- maximum likelihood estimate
- mixed-membership
ASJC Scopus subject areas
- Statistics and Probability
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