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Missingness is a common occurrence in educational assessment andpsychological measurement. It could not be casually ignored as it may threatenthe validity of the test if not handled properly. Considering the differencebetween omitted and not-reached items, we developed an IRT-based model tohandle these missingness. In the proposed method, not-reached responses arecaptured by the cumulative missingness. Moreover, the nonignorability isattributed to the correlation between ability and person missing trait. Weproved that its item parameters estimate under maximum marginal likelihood(MML) estimation is consistent. We further proposed a Bayesian estimationprocedure using MCMC methods to estimate all the parameters. The simulationresults indicate that the model parameters under the proposed method are betterrecovered than that under listwise deletion, and the nonignorable model fitsthe simulated nonignorable nonresponses better than ignorable model in terms ofBayesian model selection. Furthermore, the Program for International StudentAssessment (PISA) data set was analyzed to further illustrate the usage of theproposed method.

An IRT-based Model for Omitted and Not-reached Items