A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs

Steffen Zitzmann, Julian F. Lohmann, Georg Krammer, Christoph Helm, Burak Aydin and Martin Hecht
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Steffen Zitzmann: Hector Research Institute of Education Sciences and Psychology, University of Tübingen, 72072 Tübingen, Germany
Julian F. Lohmann: Institute for Psychology of Learning and Instruction, Kiel University, 24118 Kiel, Germany
Georg Krammer: Institute for Education Practice and Practitioner Research, University College of Teacher Education Styria, 8010 Graz, Austria
Christoph Helm: Linz School of Education, Johannes Kepler University Linz, 4040 Linz, Austria
Burak Aydin: Institute of Educational Sciences, Leuphana University, 21335 Lüneburg, Germany
Martin Hecht: Hector Research Institute of Education Sciences and Psychology, University of Tübingen, 72072 Tübingen, Germany

Mathematics, 2022, vol. 10, issue 5, 1-15

Abstract: Croon and van Veldhoven discussed a model for analyzing micro–macro multilevel designs in which a variable measured at the upper level is predicted by an explanatory variable that is measured at the lower level. Additionally, the authors proposed an approach for estimating this model. In their approach, estimation is carried out by running a regression analysis on Bayesian Expected a Posterior (EAP) estimates. In this article, we present an extension of this approach to interaction and quadratic effects of explanatory variables. Specifically, we define the Bayesian EAPs, discuss a way for estimating them, and we show how their estimates can be used to obtain the interaction and the quadratic effects. We present the results of a “proof of concept” via Monte Carlo simulation, which we conducted to validate our approach and to compare two resampling procedures for obtaining standard errors. Finally, we discuss limitations of our proposed extended Bayesian EAP-based approach.

Keywords: multilevel modeling; micro–macro design; nonlinear; Bayes; EAP (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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