Longitudinal Dynamics of Substance Use and Psychiatric Symptoms in Count Data with Zero Inflation

We examine the dynamics of substance use and psychiatric symptoms from childhood to adolescence using a longitudinal study of Mexican-origin families (N = 674). We present a longitudinal model capturing the trajectories of substance use and psychiatric symptoms (depression, conduct disorder), as well as the interrelations between these trajectories over time. Such a model is an extension of latent change score models designed to account for the occurrence of psychiatric symptoms while also accommodating a large amount of zeros for nonoccurrence and characterizing the changes over time in the count data. We compare this model with a more traditional approach based on a log transformation of the data. We describe differences between these approaches and highlight the benefits of using the two-part model when the data include a large amount of zeros for nonoccurrence of the behavior.