Accounting for non-normal covariates in treatment effects from count regressions

Summary:  View help for Summary The effects of a treatment or an intervention on a count outcome is often of interest in applied research. When controlling for additional covariates, a negative binomial regression model is usually applied to estimate conditional expectations of the count outcome. The difference in conditional expectations under treatment and under control is then defined as the (conditional) treatment effect. While traditionally aggregates of these conditional treatment effects (e.g., average treatment effects) are computed by averaging over the empirical distribution, a recently proposed moment-based approach allows for computing aggregate effects as a function of distribution parameters. The moment-based approach makes it possible to control for (latent) multivariate normally distributed covariates and provides more reliable inferences under certain conditions.

In this paper, we propose three different ways to account for non-normally distributed continuous covariates in this approach: (a) an alternative, known non-normal distribution, (b) a plausible factorization of the joint distribution, and (c) an approximation using finite Gaussian mixtures. A saturated model is used for categorical covariates, making a distributional assumption obsolete.