A Comprehensive IRT Approach for Modeling Binary, Graded, and Continuous Responses With Error in Persons and Items

Dual item response theory (IRT) models in which items and individuals have different amounts of measurement error have been proposed in the literature. Any developments in these models, however, are feasible only for continuous responses. This article discusses a comprehensive dual modeling approach, based on underlying latent response variables, from which specific models for continuous, graded, and binary responses are obtained. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are discussed for all the resulting models. Simulation results suggest that the proposal is quite feasible. A practical illustration is given with an empirical example in the personality domain