The analysis of longitudinal mixed data via multivariate latent variable models: An analysis on alcohol use disor

lcohol abuse is a dangerous habit in young people. The National Youth Survey is a longitudinal American study in part devoted to the investigationof alcohol disorder over time. The symptoms of alcohol disorder are measured by binary and ordinal items. In the literature it is well recognizedthat alcohol abuse can be measured by a latent construct; therefore generalized latent variable models for mixed data represent the ideal frameworkto analyse these data. However, it might be desirable to cluster individuals according to the different severity of their alcohol use disorder and toinvestigate how the groups vary over time. We present a new methodological framework that includes two levels of latent variables: one continuoushidden variable for dimension reduction and clustering and a discrete random variable accounting for the dynamics of alcohol disorder symptoms.The effect of covariates is also measured and a testing procedure for the temporal assumption is developed. Three important issues are discussed.First, it represents a unified framework for the analysis of longitudinal multivariate mixed data. Secondly, it captures and models the unobservedheterogeneity of the data. Finally, it describes the dynamics of the data through the definition of latent construct