Traditional methods of assessing construct stability are reviewed and longitudinal mean and covariance structures (LMACS) analysis, a modern approach, is didactically illustrated using psychological entitlement data. Measurement invariance and latent variable stability results are interpreted, emphasizing substantive implications for educators and the utility of LMACS analysis in longitudinal research.

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.

No abstract

No abstract