Commonalities and differences in IRT-based methods for nonignorable item nonresponses

Missing responses resulting from omitted or not-reached items are beyond researchers’ control and potentially threaten the validity of test results. Empirical evidence concerning the relationship between missingness and test takers’ performance on the test have suggested that the missing data mechanism is nonignorable and needs to be taken into account. Various IRT-based models for nonignorable item nonresponses have been proposed (Glas & Pimentel, 2008; Holman & Glas, 2005; Korobko, Glas, Bosker, & Luyten, 2008; Moustaki & Knott, 2000; O’Muircheartaigh & Moustaki, 1999; Rose, 2013; Rose, von Davier, & Xu, 2010). In this article, we adopted Rubin’s (1976) definitions of missing data mechanisms for educational and psychological measurement and consider the implications for maximum likelihood (ML) estimation in IRT models for incomplete data. Next, we derived multidimensional IRT models for nonignorable item nonresponses. Further, we investigated latent regression models and multiple group IRT models for nonignorable missing responses and compared to multidimensional IRT models. Although these models have a great deal in common, there are important distinctions in the underlying assumptions and restrictions; these have critical implications with respect to their use in real applications. Then, we provided additional insight on how models for nonignorable item nonresponses adjust for missing responses. Finally, we offered a list of guiding questions, which support the choice of appropriate models in concrete applications.