Latent Growth Models for Count Outcomes: Specification, Evaluation, and Interpretation

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case is frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the Poisson or negative binomial distribution and their zero-inflated extensions to account for excess zero counts. This article demonstrates how to specify, evaluate, and interpret LGMs for count outcomes using the Mplus program in the structural equation modeling framework. The foundations of LGMs for count outcomes are discussed and illustrated using empirical count data on self-reported criminal offenses of adolescents (N = 1,664; age 15-18). Annotated syntax and output are presented for all model variants. A negative binomial LGM is shown to best fit the crime growth process, outperforming Poisson, zero-inflated, and hurdle LGMs.