| The purpose of this study was to review the challenges that exist in the estimation of complex (multidimensional) models applied to complex (multilevel) data and to examine the performance of the recently developed Metropolis-Hastings Robbins-Monro (MH-RM) algorithm (Cai, 2010a, 2010b), designed to overcome these challenges and implemented in both commercial and open-source software programs. Unlike other methods, which either rely on high-dimensional numerical integration or approximation of the entire multidimensional response surface, MH-RM makes use of Fisher's Identity to employ stochastic imputation (i.e., data augmentation) via the Metropolis-Hastings sampler and then apply the stochastic approximation method of Robbins and Monro to approximate the observed data likelihood, which decreases estimation time tremendously. Thus, the algorithm shows great promise in the estimation of complex models applied to complex data.;To put this promise to the test, the accuracy and efficiency of MH-RM in recovering item parameters, latent variances and covariances, as well as ability estimates within and between groups (e.g., schools) was examined 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. More replications are needed to better determine the accuracy of analytical standard errors for some of the parameters. Limitations of the study, implications for educational measurement practice, and directions for future research are offered. |
