A Comparison of Estimation Methods for a Multi-unidimensional Graded Response IRT Model

Abstract

This study compared several parameter estimation methods for multi-unidimensional graded response models using their corresponding statistical software programs and packages. Specifically, we compared two marginal maximum likelihood (MML) approaches (Bock-Aitkin expectation-maximum algorithm, adaptive quadrature approach), four fully Bayesian algorithms (Gibbs sampling, Metropolis-Hastings, Hastings-within-Gibbs, blocked Metropolis), and the Metropolis-Hastings Robbins-Monro (MHRM) algorithm via the use of IRTPRO, BMIRT, and MATLAB. Simulation results suggested that, when the intertrait correlation was low, these estimation methods provided similar results. However, if the dimensions were moderately or highly correlated, Hastings-within-Gibbs had an overall better parameter recovery of item discrimination and intertrait correlation parameters. The performances of these estimation methods with different sample sizes and test lengths are also discussed.