A Bayesian framework for the logistic positive exponent and its reflection IRT models

Abstract

The logistic positive exponent (LPE) and its reflection (RLPE) models accommodate asymmetric item characteristic curves in item response theory, offering greater flexibility than traditional symmetric specifications. While several asymmetric IRT models exist, the LPE and RLPE framework provides a compelling balance of theoretical foundation, interpretability, and computational tractability. Despite their appeal, key aspects of Bayesian estimation for these models remain understudied, including systematic comparison of prior specifications for the asymmetry parameter, model selection performance relative to symmetric alternatives, and application of modern convergence diagnostics. This study provides a comprehensive methodological investigation of Bayesian estimation for both LPE and RLPE models. We make four primary contributions: First, we conduct extensive simulation studies examining parameter recovery, computational efficiency, and sensitivity to alternative prior specifications for the asymmetry parameter. Second, we present the first systematic evaluation of model selection performance for discriminating between asymmetric and symmetric IRT models. Third, we provide theoretical comparisons with alternative asymmetric IRT approaches, clarifying when LPE/RLPE models offer advantages and when alternatives may be preferable. Fourth, an empirical application to mathematics assessment data demonstrates the practical utility of the framework, with the RLPE model clearly outperforming symmetric alternatives and revealing meaningful asymmetry patterns across items.