Randomization Does Not Justify Logistic Regression

TL;DR

This paper challenges the common assumption that randomization justifies logistic regression, proposing a consistent estimator and highlighting limitations of traditional methods in experimental analysis.

Contribution

It introduces a new consistent estimator for logistic regression in randomized experiments, addressing the inconsistency of usual estimators under Neyman's non-parametric framework.

Findings

Traditional logistic regression estimators can be inconsistent under randomization.

The proposed estimator is consistent within Neyman's potential outcomes framework.

Simulation results demonstrate the estimator's improved performance.

Abstract

The logit model is often used to analyze experimental data. However, randomization does not justify the model, so the usual estimators can be inconsistent. A consistent estimator is proposed. Neyman's non-parametric setup is used as a benchmark. In this setup, each subject has two potential responses, one if treated and the other if untreated; only one of the two responses can be observed. Beside the mathematics, there are simulation results, a brief review of the literature, and some recommendations for practice.