On the asymmetry, complexity and predicted data patterns of nontraditional item response theory models

Traditional item response theory (IRT) models involve symmetric response probability functions, but a developing area of research has focused on asymmetric alternatives. To date, these studies have focused primarily on introducing new asymmetric models, detailing their mathematical formulations, explaining how to interpret their item parameters and demonstrating their distinctive psychometric properties through simulations and empirical data analysis. We add to this burgeoning research area by exploring model evaluation in the context of asymmetric IRT. We begin by introducing a new asymmetric IRT model based on the Aranda-Ordaz (Biometrika, 68, 1981, 357) link function and comparing it to two established models that parameterize asymmetry in distinct ways. Our comparison of these models then allows us to demonstrate three uncommon methods of IRT model evaluation: (1) characterizing asymmetry in the response probability and pseudo-information functions, (2) quantifying configural complexity through fitting propensity analysis and (3) exploring the pattern signatures of each model. Through this in-depth evaluation, we find that all three models possess subtly unique psychometric properties that will benefit applied research. More generally, the model evaluation methods that we consider in this work can offer unique insights into any IRT model.