On the use of discrete choice models for causal inference

Methodology for causal inference based on propensity scores has been developed and popularized in the last two decades. However, the majority of the methodology has concentrated on binary treatments. Only recently have these methods been extended to settings with multi-valued treatments. We propose a number of discrete choice models for estimating the propensity scores. The models differ in terms of flexibility with respect to potential correlation between treatments, and, in turn, the accuracy of the estimated propensity scores. We present the effects of discrete choice models used on performance of the causal estimators through a Monte Carlo study. We also illustrate the use of discrete choice models to estimate the effect of antipsychotic drug use on the risk of diabetes in a cohort of adults with schizophrenia.