Logistic Regression without Intercept

Abstract

Logistic regression is a popular statistic modelling algorithm in predicting a binary outcome. Although logistic regression almost always has an intercept, logistic regression without intercept is sometimes appropriate or even necessary. However, logistic regression without intercept has rarely been discussed other than being used explicitly or implicitly. In this paper, we aim at filling this gap by systematically studying logistic regression without intercept. Specifically, we study the 4 most important aspects of logistic regression: (1) Maximum Likelihood Estimate, (2) data configuration (complete separation, quasi-complete separation and overlap) to categorize the existence and uniqueness of maximum likelihood estimate, (3) multicollinearity, and (4) monotonic transformations of independent variables. We adopt an extensional method in that we first present results for logistic regression with intercept and then extend the results to the case of without intercept. Our numerical examples further compare logistic regression with intercept and without intercept.