On Latent Trait Estimation in Multidimensional Compensatory Item Response Models

Making inferences from IRT-based test scores requires accurate and reliable methods of person parameter estimation. Given an already calibrated set of item parameters, the latent trait could be estimated either via maximum likelihood estimation (MLE) or using Bayesian methods such as maximum a posteriori (MAP) estimation or expected a posteriori (EAP) estimation. In addition, Warm's (Psychometrika 54:427-450, 1989) weighted likelihood estimation method was proposed to reduce the bias of the latent trait estimate in unidimensional models. In this paper, we extend the weighted MLE method to multidimensional models. This new method, denoted as multivariate weighted MLE (MWLE), is proposed to reduce the bias of the MLE even for short tests. MWLE is compared to alternative estimators (i.e., MLE, MAP and EAP) and shown, both analytically and through simulations studies, to be more accurate in terms of bias than MLE while maintaining a similar variance. In contrast, Bayesian estimators (i.e., MAP and EAP) result in biased estimates with smaller variability.