A Bayesian Approach for Estimating Multilevel Latent Contextual Models. Issue 5 (2nd September 2016) - Zitzmann, Steffen; Lüdtke, Oliver; Robitzsch, Alexander; Marsh, Herbert W.
Abstract : In many applications of multilevel modeling, group-level (L2) variables for assessing group-level effects are generated by aggregating variables from a lower level (L1). However, the observed group mean might not be a reliable measure of the unobserved true group mean. In this article, we propose a Bayesian approach for estimating a multilevel latent contextual model that corrects for measurement error and sampling error (i.e., sampling only a small number of L1 units from a L2 unit) when estimating group-level effects of aggregated L1 variables. Two simulation studies were conducted to compare the Bayesian approach with the maximum likelihood approach implemented in M plus . The Bayesian approach showed fewer estimation problems (e.g., inadmissible solutions) and more accurate estimates of the group-level effect than the maximum likelihood approach under problematic conditions (i.e., small number of groups, predictor variable with a small intraclass correlation). An application from educational psychology is used to illustrate the different estimation approaches.