Hypothesis Tests under Separation

Abstract

Separation commonly occurs in political science, usually when a binary explanatory variable perfectly predicts a binary outcome. In these situations, methodologists often recommend penalized maximum likelihood or Bayesian estimation. But researchers might struggle to identify an appropriate penalty or prior distribution. Fortunately, I show that researchers can easily test hypotheses about the model coefficients with standard frequentist tools. While the popular Wald test produces misleading (even nonsensical) p-values under separation, I show that likelihood ratio tests and score tests behave in the usual manner. Therefore, researchers can produce meaningful p-values with standard frequentist tools under separation without the use of penalties or prior information.