Bayesian Modeling and Inference for Item Response Model with Nonignorable Missing Data

Not-reached (dropout) and omitted (intermittent missingness) behaviors are often inevitable in timed computerized tests. These missingness behaviors may be related to the subject's latent traits, the difficulty of the item, or even the unobserved item response itself. In order to better understand the underlying test-taking behaviors, a Bayesian hierarchical framework is adopted to jointly model the item response, the item response time, the not-reached, and the omitted behaviors. For missing data, a sequential multinomial model is developed for the not-reached behavior, and a conditional model is proposed for the omitted behavior conditioning on the not-reached behavior. A decomposed logarithm of the pseudo marginal likelihood (LPML) is then developed to assess the fit of the missing data models. It can be further used to quantify the importance of modeling item response and response time jointly versus individually in identifying the missing data mechanism. The empirical performance of the proposed models and the model assessment criterion are examined through extensive simulations. The proposed methodology is further applied to analyze the Program for International Student Assessment (PISA) 2018 Test.