Bayesian Inference for IRT Models with Non-Normal Latent Trait Distributions

Normality of latent traits is a common assumption made when estimating parameters for item response theory (IRT) models, but this assumption may be violated. The purpose of this research was to present a new Markov chain Monte Carlo (MCMC) method for ordinal items with flexible latent trait distributions (i.e., skewed and bimodal). Specifically, the Davidian curve (DC) was used to approximate the distribution of latent traits. The performance of the proposed MCMC algorithm with DCs was evaluated via a simulation study and compared with an EM method using DCs that is available in the "mirt" package (Chalmers, 2012). The manipulated factors included the number of response categories, sample size, and the shape of the latent trait distribution. The Hanna-Quinn (HQ) criterion was used to choose the best DC order. Results indicated that when informative priors were used, the MCMC algorithm with DCs could fit a flexible distribution well and the method provided good parameter estimates which, under some circumstances, had lower bias and RMSE than the EM method.