Multivariate Latent Variable Transition Models of Longitudinal Mixed Data: an Analysis on Alcohol Use Disorder

Alcohol abuse is a dangerous habit in young people. The National Youth Survey is a longitudinal American study in part devoted to the investigation of alcohol disorder during time. The symptoms of alcohol disorder are measured by binary and ordinal items. In the literature it is well recognized that the alcohol abuse can be measured by a latent construct; therefore generalized latent variable models for mixed data represents the ideal framework to analyze these data. However, it might be desirable to cluster individuals according to the different severity of the alcohol use disorder and to investigate how the groups vary during time. We present a new methodological framework that includes two levels of latent variables: one continuous hidden variable for dimension reduction and clustering and a discrete random variable accounting for the dynamics of the alcohol disorder symptoms. The effect of covariates is also measured and a testing procedure for the temporal assumption is developed. This work addresses three important issues. First, it represents a unified framework for the analysis of longitudinal multivariate mixed data. Secondly, it captures and models the unobserved heterogeneity of the data. Finally it describes the dynamics of the data through the definition of latent constructs.