Multilevel Item Response Model with Heterogeneous Within-Cluster Variances

Within-cluster variance homogeneity is one of the key assumptions of multilevel models; however, assuming a constant (i.e. equal) within-cluster variance may not be realistic. Moreover, existent within-cluster variance heterogeneity should be regarded as a source of additional information rather than a violation of a model assumption. This study extends the three-level Rasch item response model to estimate cluster-specific variances as random effects adopting the Bayesian approach. Data analysis results provided empirical evidence for the possible violations of the within-cluster variance heterogeneity, as well as the utility of the proposed heterogeneous model. A small-scale simulation study conducted to provide information about the estimation efficiency of the model parameters with varying degrees of within-cluster variance heterogeneity.