Detecting and Correcting for Separation in Strategic Choice Models

Abstract

Separation or perfect prediction is a common problem in discrete choice models that, in practice, leads to inflated point estimates and standard errors. Standard statistical packages do not provide clear advice on how to correct these problems. Furthermore, separation can go completely undiagnosed in fitting advanced models that optimize a user-supplied log-likelihood rather than relying on pre-programmed estimation procedures. In this paper, we both describe the problems that separation can cause and address the issue of detecting it in empirical models of strategic interaction. We then consider several solutions based on penalized maximum likelihood estimation. Using Monte Carlo experiments and a replication study, we demonstrate that when separation is detected in the data, the penalized methods we consider are superior to ordinary maximum likelihood estimators.