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Bayesian Joint Item Response Model of Multidimensional Response Data with Application to Computerized Testing (309615)

Keywords: DIC decomposition, LPML decomposition, Computerized Tests, Pencil-and-paper Tests, Item Response Theory Models, Response Time Models.

The computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time measures. A key question in the modeling is how to assess the response time data, for example, in aid of ability estimation in the item response theory (IRT) models. To answer it, we have proposed two new model comparison criteria based on the decomposition of deviance information criterion (DIC) and the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement on the fit of item responses due to incorporating the response time (and standard scores from pencil-and-paper tests) in conjointly modeling with item response data. Simulation studies are conducted to examine the empirical performance of the proposed model selection criteria, and these approaches are illustrated on a real dataset coming from a computerized educational assessment program called AppRISE. In the real analysis, we also put forward some novel ideas to rank the item difficulty with uncertainty and examine the residuals of the proposed joint model for model adequacy.