Bayesian Variable Selection in Dynamic Item Response Theory Models

The recent surge in computerized testing brings challenges in the analysis of testing data with classic item response theory (IRT) models. To handle individually varying and irregularly spaced longitudinal dichotomous responses, we adopt a dynamic IRT model framework and then extend the model to link with individual characteristics at a hierarchical level. Further, we have developed an algorithm to select important characteristics of individuals that can capture the growth changes of one’s ability under this multi-level dynamic IRT model, where we can compute the Bayes factor of the proposed model including different covariates using a single Markov chain Monte Carlo output from the full model. In addition, we have shown the model selection consistency under the modified Zellner–Siow prior, and we have conducted simulations to illustrate the properties of the model selection consistency in finite samples. Finally, we have applied our proposed model and computational algorithms to a real data application, called EdSphere dataset, in educational testing.