Modeling Omitted and Not-Reached Items in IRT Models

Item nonresponse is a common problem in educational and psychological assessments. The probability of unplanned missing responses due to omitted and not-reached items may stochastically depend on unobserved variables such as missing responses or latent variables. In such cases, missingness cannot be ignored and needs to be considered in the model. Specifically, multidimensional IRT models, latent regression models, and multiple-group IRT models have been suggested for handling nonignorable missing responses in latent trait models. However, the suitability of the particular models with respect to omitted and not-reached items has rarely been addressed. Missingness is formalized by response indicators that are modeled jointly with the researcher's target model. We will demonstrate that response indicators have different statistical properties depending on whether the items were omitted or not reached. The implications of these differences are used to derive a joint model for nonignorable missing responses with ability to appropriately account for both omitted and not-reached items. The performance of the model is demonstrated by means of a small simulation study.