Fitting Graded Response Models to Data with Non-Normal Latent Traits

Abstract

Fitting item response theory (IRT) models often relies on the assumption of a normal distribution for the person latent trait(s). Violating the assumption of normality may bias the estimates of IRT item and person parameters, especially when sample sizes are not large. In practice, the actual distribution for person parameters may not always be normal, and hence it is important to understand how IRT models perform under such situations. This study focuses on the performance of the multi-unidimensional graded response model using a Hasting-within-Gibbs procedure. The results of this study provide a general guideline for estimating the multi-unidimensional graded response model under the investigated conditions where the latent traits may not assume a normal distribution.