Latent Variable Selection in Multidimensional Item Response Theory Models With Nonignorable Missingness

Abstract

Nonignorable item nonresponses commonly occur in educational and psychological measurement and pose challenges for statistical inference in item response theory (IRT) models. In multidimensional IRT (MIRT), a key issue is identifying the relationships between multiple latent abilities and test items, known as latent variable selection. However, the latent variable selection in MIRT models with nonresponses remains largely unexplored. A common strategy for modeling omissions introduces a latent propensity variable to capture individuals’ tendency to omit items, leading to a joint MIRT model that combines a Rasch model for missingness and a multidimensional two-parameter logistic model for responses. Existing latent variable selection methods are developed mainly for fully observed response data and are not directly applicable when omissions are incorporated through this joint MIRT model. In this article, we develop an efficient expectation model selection (EMS) algorithm for MIRT models with omitted items, termed EMS-OI. Simulation studies show that EMS-OI performs competitively in both latent variable selection and parameter estimation, compared with existing EMS- and expectation maximization-based alternatives. An application to the PISA 2012 dataset further illustrates the proposed EMS-OI algorithm.