David L. Weakliem and Bradley R. Entner Wright Robustness of Group-Based Models for Longitudinal Count Data Sociological Methods & Research 2009 38: 147-170.
In recent years, there have been efforts to develop latent class models for trajectories. The semiparametric mixed Poisson regression (SMPR) model has been used in many empirical studies, but there have been few attempts to evaluate the robustness of the estimates from this model. The authors use simulated data to evaluate the performance of the SMPR model under a variety of assumptions. They find that estimates are sensitive to the conditional distribution of counts and misspecification of the shape of the trajectory. When there is only one underlying trajectory and overdispersion is present, the SMPR model frequently finds multiple groups, which often appear to differ in shape as well as level. The tendency can be substantially reduced by use of the zero-inflated Poisson distribution in conjunction with top-coding of large counts. The article concludes with a discussion of other extensions and alternatives to the standard SMPR model that might provide more robust estimates.
Key Words: semiparametric mixed Poisson regression • overdispersion • robustness • latent class models