Affiliation: College of Arts and Sciences, Department of Psychology and Neuroscience
Multilevel Confirmatory Factor Analysis (MCFA) models are most commonly estimated with full information maximum likelihood (FIML). FIML is asymptotically efficient and asymptotically unbiased given correct model specification and no excessive multivariate kurtosis. When these assumptions are violated, we have no guarantee about the asymptotic properties of FIML. In single level SEMs, the Model Implied Instrument Variable (MIIV-2SLS) estimator has been shown to be an excellent alternative to maximum likelihood. Following prior work for single level SEMs, this paper develops two MIIV-2SLS estimators for MCFA models. I evaluate both estimators in comparison to FIML with a Monte Carlo simulation study varying number of clusters, cluster size, distribution of data, balance of clusters and correct versus incorrect model specifications. Results suggest that both MIIV estimators are good alternatives to FIML across a variety of conditions. Most importantly, they are more robust to model misspecification and offer local tests of fit with Sargan’s test. The primary limitation found in this simulation study suggests that these estimators may underestimate standard errors given small number of clusters, unbalanced clusters, and skew/kurtosis.