Effect of covariate misspecifications in the marginalized zero-inflated Poisson model

Abstract

Count outcomes are often modelled using the Poisson regression. However, this model imposes a strict mean-variance relationship that is unappealing in many contexts. Several studies in the life sciences result in count outcomes with excessive amounts of zeros. The presence of the excess zeros introduces extra dispersion in the data which cannot be accounted for by the traditional Poisson regression. The zero-inflated Poisson (ZIP) and zero-inflated negative binomial models are popular alternative. The zero-inflated models comprise two key components; a logistic part which models the zeros, and a Poisson component to handle the positive counts. Both components allow the inclusion of covariates. Civettini and Hines [3] investigated misspecification effects in the zero-inflated negative binomial regression models. Long,Preisser, Herring and Golin [10] proposed a so-called marginalized zero-inflated Poisson (MZIP) model that allows direct marginal interpretation for fixed effect estimates to overcome the often sub-population specific interpretation of the traditional zero-inflated models. In this research, the effects of misspecification of components of the MZIP regression model are investigated through a comprehensive simulation study. Two different incorrect specifications of the components of an MZIP model were considered, namely ‘Omission’ and ‘Misspecification’. Bias, standard error (precision) of estimates and mean square error (MSE) are computed while varying the sample size. Type I error rates are also evaluated for the misspecified models. Results of a Monte Carlo simulation are reported. It was observed that omissions in both parts of the models lead to biases in the estimated parameters. The intercept parameters were the most severely affected. Furthermore, in all the types of omissions, parameters in the zero-inflated part of the models were much affected compared to the Poisson part in terms of both bias and MSE. Generally, bias and MSE decrease as sample sizes increase for all parameters. It was also found that misspecification can either increase, preserve or decrease the type I error rates depending on the sample size.