Performance evaluation of estimators in the presence of outliers or omitted predictors: a study on the Poisson-Exponential regression model

Abstract

The Poisson regression model is vulnerable for overdispersion in the data when estimating model parameters and their standard errors. Overdispersion may occur due to outliers in the data and/or removal of important predictors from the model. This paper employs a regression model that can be used to better cope with outliers and omitted predictor bias in count data compared to the Poisson regression model, namely the Poisson exponential (PE) model which is a reparameterization of the geometric regression model. Along with investigating the distributional properties of the PE distribution, the usual maximum likelihood (ML-I), maximum likelihood with Expectation-maximization algorithm (ML-II), least-square (LS), weighted least-square (WLS), least-absolute deviation (LAD), weighted least-absolute deviation (WLAD), and Cramer-von mises (CVM) estimation methods are utilized in the context of the PE regression model. The performance of these estimation methods with the PE regression model are inspected through two comprehensive simulation studies. The first is conducted on data sets with and without outliers. The second investigates the performance of the estimation methods for the PE regression model with and without omitted predictors. Two real-life applications illustrate the applicability of the PE regression model with the estimation methods for these two situations.