Examining the Performance of the Metropolis-Hastings Robbins-Monro Algorithm in the Estimation of Multilevel Multidimensional IRT Models.

The purpose of this study was to examine the performance of the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm in the estimation of multilevel multidimensional item response theory (ML-MIRT) models. The accuracy and efficiency of MH-RM in recovering item parameters, latent variances and covariances, as well as ability estimates within and between clusters (e.g., schools) were investigated in a simulation study, varying the number of dimensions, the intraclass correlation coefficient, the number of clusters, and cluster size, for a total of 24 conditions. Overall, MH-RM performed well in recovering the item, person, and group-level parameters of the model. Ratios of the empirical to analytical standard errors indicated that the analytical standard errors reported in flexMIRT were somewhat overestimated for the cluster-level ability estimates, a little too large for the person-level ability estimates, and essentially accurate for the other parameters. Limitations of the study, implications for educational measurement practice, and directions for future research are offered.