Accounting for Latent Covariates in Average Effects from Count Regressions

The effectiveness of a treatment on a count outcome can be assessed using a negative binomial regression, where treatment effects are defined as the difference between the expected outcome under treatment and under control. These treatment effects can to date only be estimated if all covariates are manifest (observed) variables. However, some covariates are latent variables that are measured by multiple fallible indicators. In such cases, it is important to control for measurement error of covariates in order to avoid attenuation bias and to get unbiased treatment effect estimates. In this paper, we propose a new approach to compute average and conditional treatment effects in regression models with a logarithmic link function involving multiple latent and manifest covariates. We extend the previously presented moment-based approach in several aspects: Building on a multigroup SEM framework for count variables instead of the generalized linear model, we allow for latent covariates and multiple covariates. We provide an illustrative example to explain the application and estimation in structural equation modeling software.