Modeling Not-Reached Items in Cognitive Diagnostic Assessments

In cognitive diagnostic assessments with time limits, not-reached items (i.e., continuous nonresponses at the end of tests) frequently occur because examinees drop out of the test due to insufficient time. Oftentimes, the not-reached items are related to examinees' specific cognitive attributes or knowledge structures. Thus, the underlying missing data mechanism of not-reached items is non-ignorable. In this study, a missing data model for not-reached items in cognitive diagnosis assessments was proposed. A sequential model with linear restrictions on item parameters for missing indicators was adopted; meanwhile, the deterministic inputs, noisy "and" gate model was used to model the responses. The higher-order structure was used to capture the correlation between higher-order ability parameters and dropping-out propensity parameters. A Bayesian Markov chain Monte Carlo method was used to estimate the model parameters. The simulation results showed that the proposed model improved diagnostic feedback results and produced accurate item parameters when the missing data mechanism was non-ignorable. The applicability of our model was demonstrated using a dataset from the Program for International Student Assessment 2018 computer-based mathematics cognitive test.