Regularized Mislevy-Wu Model for Handling Nonignorable Missing Item Responses

Missing item responses are frequently found in educational large-scale assessment studies. In this article, the Mislevy-Wu item response model is applied for handling nonignorable missing item responses. This model allows that the missingness of an item depends on the item itself and a further latent variable. However, with low to moderate amounts of missing item responses, model parameters for the missingness mechanism are difficult to estimate. Hence, regularized estimation using a fused ridge penalty is applied to the Mislevy-Wu model to stabilize estimation. The fused ridge penalty function is separately defined for multiple-choice and constructed response items because previous research indicated that the missingness mechanisms strongly differed for the two item types. In a simulation study, it turned out that regularized estimation improves the stability of item parameter estimation. The method is also illustrated using international data from the progress in international reading literacy study (PIRLS) 2011 data.