Logistic regression geometry

TL;DR

This paper investigates how boundary effects influence inference in logistic regression, revealing non-uniform asymptotic behavior near boundaries and proposing a diagnostic tool to assess their impact.

Contribution

It demonstrates the non-uniformity of asymptotic results near boundaries and introduces an interpretable diagnostic for boundary effects in logistic regression.

Findings

Asymptotic normality may fail near boundaries due to skewness and collinearity

Boundary effects can significantly distort inference in logistic regression

A diagnostic tool helps identify when boundary effects are problematic

Abstract

This paper looks at effects, due to the boundary, on inference in logistic regression. It shows that first -- and, indeed, higher -- order asymptotic results are not uniform across the model. Near the boundary, effects such as high skewness, discreteness and collinearity dominate, any of which could render inference based on asymptotic normality suspect. A highly interpretable diagnostic tool is proposed allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques.