Modeling change trajectories with count and zero-inflated outcomes: Challenges and recommendations

The goal of this article is to describe models to examine change over time with an outcome that represents a count, such as the number of alcoholic drinks per day. Common challenges encountered with this type of data are: (1) the outcome is discrete, may have a large number of zeroes, and may be overdispersed, (2) the data are clustered (multiple observations within each individual), (3) the researchers needs to carefully consider and choose an appropriate time metric, and (4) the researcher needs to identify both a proper individual (potentially nonlinear) change model and an appropriate distributional form that captures the properties of the data. In this article, we provide an overview of generalized linear models, generalized estimating equation models, and generalized latent variable (mixed-effects) models for longitudinal count outcomes focusing on the Poisson, negative binomial, zero-inflated, and hurdle distributions. We review common challenges and provide recommendations for identifying an appropriate change trajectory while determining an appropriate distributional form for the outcome (e.g., determining zero-inflation and overdispersion). We demonstrate the process of fitting and choosing a model with empirical longitudinal data on alcohol intake across adolescence collected as part of the National Longitudinal Survey of Youth 1997.