Modeling nonignorable missing data processes in item calibration

In this report, it is shown that the problem of nonignorable missing data in the calibration phase for computerized adaptive testing can be handled by introducing an item response theory (IRT) model for the missing data indicator. In the first simulation study, it is shown that treating data with nonignorable missing data as if ignorability held, does indeed lead to a significant increase in the estimation errors, and introducing an IRT model for the missing data process solves the problem to a large extent. In the second simulation study, it is shown that the correction obtained using the IRT model is almost as good as the correction that can be obtained if the covariates determining the missing data were actually observed.