Person parameter estimation for irt models of forced-choice data: Merits and perils of pseudo-likelihood approaches

Abstract

The Thurstonian IRT model for forced-choice data (Brown A, Maydeu-Olivares A, Educ Psychol Measur 71:460–502, 2011) capitalizes on including structural local dependencies in the structural equation model. However, local dependencies of pairwise comparisons within forced-choice blocks are only considered for item parameter estimation by this approach but are explicitly ignored by the respective methods of person parameter estimation. The present paper introduces methods of person parameter estimation (MLE, MAP, and WLE) that rely on the exact likelihood of the response pattern that adequately considers local stochastic dependencies by multivariate integration. Moreover, it is argued that the common practice of ignoring local stochastic dependencies for person parameter estimation can be understood as a pseudo-likelihood approach (based on the independence likelihood) that will lead to similar estimates in most applications. However, standard errors and Bayesian estimation techniques are affected by falsely precise inference based on the independence likelihood. Fortunately, these distortions can be amended almost completely by a correction factor to the (independence) pseudo-likelihood for MLE and MAP estimation. Moreover, unbiased weighted (pseudo-)likelihood estimation becomes feasible without facing the prohibitive computational burden of weighted likelihood estimation with the proper likelihood based on multivariate integration.