Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.