A Reconsideration of the Assumptions about Latent Trait Values in Item Response Theory Models

This paper reconsiders item response theory (IRT) models from the perspective of multilevel modeling. We formulate the one-parameter logistic IRT model within a multilevel modeling framework. Based on the cross-classified structure inherent in item responses, we introduce four types of models while clearly distinguishing whether latent traits and item parameters are treated as fixed or random effects. Several extended models related to multilevel modeling are also introduced. We then clarify the correspondence between each model and likelihood-based estimation methods. In addition, we examine the modeling assumptions involved in Bayesian estimation for these models. Finally, we discuss the choice among these models and their corresponding estimation methods, taking into account the specific research questions and data-collection designs.