A Bayesian Approach for Estimating Multilevel Latent Contextual Models |
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| Authors: | Steffen Zitzmann Oliver Lüdtke Alexander Robitzsch Herbert W Marsh |
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| Institution: | 1. Leibniz Institute for Science and Mathematics Education;2. Centre for International Student Assessment;3. Institute for Positive Psychology and Education, Australian Catholic University;4. King Saud University, Saudi Arabia |
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| 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 Mplus. 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. |
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| Keywords: | Bayesian estimation contextual analysis multilevel latent contextual model multilevel modeling structural equation modeling |
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