Accounting for Latent Covariates in Average Effects from Count Regressions

Abstract

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.

Keywords:

• Average treatment effect
• latent covariates
• negative binomial regression

Article information

Conflict of Interest Disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was not supported.

Acknowledgments: The authors would like to thank the Associate Editor Stephen G. West and anonymous reviewers for their valuable suggestions and comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institution is not intended and should not be inferred.

Notes

1 In the supplementary material, we provide a Shiny app, that allows readers to examine the effects of measurement error on regression coefficients in a Poisson regression with two (fallible) covariates. The computations are based on Kukush et al. (2004).

2 Analogous to the standard maximum likelihood estimation described in Appendix, the full information maximum likelihood approach used in this example (i.e., its implementation in Mplus) treats the count outcome as conditionally negative binomial distributed.