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

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 adopted for data analysis. An empirical example demonstrates practical implications and applications of the proposed models to the Verbal Aggression data. The empirical findings show that the proposed models with random item errors perform better than the existing models without random item errors in terms of the goodness-of-fit and reconstructing the step difficulties and also demonstrate methodological and practical differences of the proposed models in interpreting the item property effects in each of the item location explanatory Many-Facet Rasch Model and the step difficulty explanatory Linear Partial Credit Model approaches.