Polytomous item explanatory IRT models with random item effects: Concepts and an application

Abstract

This paper proposes three polytomous item explanatory models with random item errors in Item Response Theory (IRT), by extending the Linear Logistic Test Model with item error (LLTM + ε) approach to polytomous data. The proposed models, also regarded as polytomous random item effects models, can take the uncertainty in explanation and/or the random nature of item parameters into account for polytomous items. To develop the models, the concepts and types of polytomous random item effects are investigated and then added into the existing polytomous item explanatory models. For estimation of the proposed models with crossed random effects for polytomous data, a Bayesian inference method is adop..