Violations of ignorability in computerized adaptive testing

Using auxiliary information and allowing item review in computerized adaptive testing produces a violation of the ignorability principle for missing data (Rubin, 1976) that may bias parameter estimates in IRT models. However, the violation of ignorability does not automatically lead to bias. In this report, two situations are distinguished. 1. Estimation of the proficiency parameters in computerized adaptive testing using auxiliary information about proficiency and allowing item review, where the item parameters are considered known. Both analytically and through simulation studies, it is shown that the violation of ignorability does not lead to a gross inflation of bias. 2. Calibration of item and population parameters using maximum marginal likelihood estimation. Through simulation studies it is shown that violation of ignorability does result in bias. An analytical explanation of the result is given.