Modeling Missing Response Data in Item Response Theory: Addressing Missing Not at Random Mechanism with Monotone Missing Characteristics

Item nonresponses frequently occurs in educational and psychological assessments, and if not appropriately handled, it can undermine the reliability of the results. This study introduces a missing data model based on the missing not at random (MNAR) mechanism, incorporating the monotonic missingness assumption to capture individual-level missingness patterns and behavioral dynamics. In specific, the cumulative number of missing indicators allows to consider the tendency of current item's missingness based on the previous missingnesses, which reduces the number of nuisance parameters for modeling missing data mechanisms. Two Bayesian model evaluation criteria were developed to distinguish between missing at random (MAR) and MNAR mechanisms by imposing specific parameter constraints. Additionally, the study introduces a highly efficient Bayesian slice sampling algorithm to estimate the model parameters. Four simulation studies were conducted to show the performance of the proposed model. The PISA 2015 science data was carried out to further illustrate the application of the proposed approach.