Multivariate zero-inflated modeling with latent predictors: Modeling feedback behavior

In educational studies, the use of computer-based assessments leads to the collection of multiple outcomes to assess student performance. The student-specific outcomes are correlated and often measured in different scales, such as continuous and count outcomes. A multivariate zero-inflated model with random effects is proposed and adapted for the challenging situation where the multiple outcomes are zero-inflated and possibly right truncated. The joint model consists of a Bernoulli component to deal with the problem of extra zeros, and a multivariate truncated component to model correlated mixed response outcomes from the same subject. In a Bayesian modeling approach, MCMC methods are used for parameter estimation. Using a simulation study, it is shown that the within-individual correlation between counts can be accurately estimated together with the other model parameters. The multivariate zero-inflated model is applied to a computer-based feedback study about computer literacy, where first-year bachelor students were given the opportunity to receive additional feedback. The total number of feedback pages visited and the total feedback processing time are modeled using a Poisson and a Gamma distribution, respectively. The joint modeling framework is extended to incorporate explanatory latent variables (student performance and speed of working), to explore individual heterogeneity in feedback behavior in a computer-based assessment.