An IRT-based Model for Omitted and Not-reached Items
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Missingness is a common occurrence in educational assessment and psychological measurement. It could not be casually ignored as it may threaten the validity of the test if not handled properly. Considering the difference between omitted and not-reached items, we developed an IRT-based model to handle these missingness. In the proposed method, not-reached responses are captured by the cumulative missingness. Moreover, the nonignorability is attributed to the correlation between ability and person missing trait. We proved that its item parameters estimate under maximum marginal likelihood (MML) estimation is consistent. We further proposed a Bayesian estimation procedure using MCMC methods to estimate all the parameters. The simulation results indicate that the model parameters under the proposed method are better recovered than that under listwise deletion, and the nonignorable model fits the simulated nonignorable nonresponses better than ignorable model in terms of Bayesian model selection. Furthermore, the Program for International Student Assessment (PISA) data set was analyzed to further illustrate the usage of the proposed method.
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