title: A Bayesian Approach to More Stable Estimates of Group-Level Effects in Contextual Studies.
abstract: Multilevel analyses are often used to estimate the effects of group-level constructs. However, when using aggregated individual data (e.g., student ratings) to assess a group-level construct (e.g., classroom climate), the observed group mean might not provide a reliable measure of the unobserved latent group mean. In the present article, we propose a Bayesian approach that can be used to estimate a multilevel latent covariate model, which corrects for the unreliable assessment of the latent group mean when estimating the group-level effect. A simulation study was conducted to evaluate the choice of different priors for the group-level variance of the predictor variable and to compare the Bayesian approach with the maximum likelihood approach implemented in the software Mplus. Results showed that, under problematic conditions (i.e., small number of groups, predictor variable with a small ICC), the Bayesian approach produced more accurate estimates of the group-level effect than the maximum likelihood approach did.
authors.affiliation: a Leibniz Institute for Science and Mathematics Education.
authors.forename: Steffen
authors.initials: S
authors.lastname: Zitzmann
authors.affiliation: c Centre for International Student Assessment, Leibniz Institute for Science and Mathematics Education.
authors.forename: Oliver
authors.initials: O
authors.lastname: Lüdtke
authors.affiliation: b Federal Institute for Education Research, Innovation, and Development of the Austrian School System.
authors.forename: Alexander
authors.initials: A
authors.lastname: Robitzsch
mesh_terms: D001499:Bayes Theorem; D035841:Behavioral Research / Q000379:methods*; D003198:Computer Simulation; D006801:Humans; D055361:Multilevel Analysis / Q000379:methods*; D011594:Psychometrics / Q000379:methods*; D015203:Reproducibility of Results
keywords: Bayesian estimation; contextual analysis; latent covariate model; multilevel modeling; structural equation modeling