Multilevel Measurement: Factor Models and Explanatory Item Response Models

In this chapterindividual and shared constructs and composition models; aggregation indices ICC(1), ICC(2), and rmathrmwg(J); two-level factor models with invariance across levels, cluster bias, and level-specific reliability; the Rasch and 2PL models as mixed models with crossed person and item effects; the accuracy of the Laplace approximation; explanatory item response models with person, item, and person-by-item covariates; multilevel item response models and differential item functioning across clusters; reporting.