Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and sample sizes. Sample size and test length explained the largest amount of variance in item and person parameter estimates, respectively. There was little difference in item parameter recovery between MML and MCMC in samples with 300 or more respondents. MCMC recovered some item threshold parameters better in samples with 75 or 150 respondents. Bias in threshold parameter estimates depended on the generating value and the type of threshold. Person parameters were comparable between MCMC and MML/expected a posteriori for all test lengths.