Are marginalized two-part models superior to non-marginalized two-part models for count data with excess zeroes? Estimation of marginal effects, model misspecification, and model selection

The marginalized two-part models, including the marginalized zero-inflated Poisson and negative binomial models, have been proposed in the literature for modelling cross-sectional healthcare utilization count data with excess zeroes and overdispersion. The motivation for these proposals was to directly capture the overall marginal effects and to avoid post-modelling effect calculations that are needed for the non-marginalized conventional two-part models. However, are marginalized two-part models superior to non-marginalized two-part models because of their structural property? Is it true that the marginalized two-part models can provide direct marginal inference? This article aims to answer these questions through a comprehensive investigation. We first summarize the existing non-marginalized and marginalized two-part models and then develop marginalized hurdle Poisson and negative binomial models for cross-sectional count data with abundant zero counts. Our interest in the investigation lies particularly in the (average) marginal effect and (average) incremental effect and the comparison of these effects. The estimators of these effects are presented, and variance estimators are derived by using delta methods and Taylor series approximations. Though the marginalized models attract attention because of the alleged convenience of direct marginal inference, we provide evidence for the impact of model misspecification of the marginalized models over the conventional models, and provide evidence for the importance of goodness-of-fit evaluation and model selection in differentiating between the marginalized and non-marginalized models. An empirical analysis of the German Socioeconomic Panel data is presented.