Multivariate latent growth models for mixed data with covariate effects

The paper presents an extension of a new class of multivariate latent growth models (Bianconcini and Cagnone, 2012) to allow for covariate effects on manifest, latent variables and random effects. The new class of models combines: (i) multivariate latent curves that describe the temporal behavior of the responses, and (ii) a factor model that specifies the relationship between manifest and latent variables. Based on the Generalized Linear and Latent Variable Model framework (Bartholomew and Knott, 1999), the response variables are assumed to follow different distributions of the exponential family, with item-specific linear predictors depending on both latent variables and measurement errors. A full maximum likelihood method is used to estimate all the model parameters simultaneously. Data coming from the Data WareHouse of the University of Bologna are used to illustrate the methodology.