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

Author

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  • Steffen Zitzmann

    (Hector Research Institute of Education Sciences and Psychology, University of Tübingen, 72072 Tübingen, Germany
    Faculty of Humanities and Social Sciences, Helmut Schmidt University, 22043 Hamburg, 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)

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.

Suggested Citation

  • Steffen Zitzmann & Julian F. Lohmann & Georg Krammer & Christoph Helm & Burak Aydin & Martin Hecht, 2022. "A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs," Mathematics, MDPI, vol. 10(5), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:842-:d:765715
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    References listed on IDEAS

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    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. Roderick McDonald, 2011. "Measuring Latent Quantities," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 511-536, October.
    3. Andreas Klein & Helfried Moosbrugger, 2000. "Maximum likelihood estimation of latent interaction effects with the LMS method," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 457-474, December.
    4. Tenenhaus, Michel & Vinzi, Vincenzo Esposito & Chatelin, Yves-Marie & Lauro, Carlo, 2005. "PLS path modeling," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 159-205, January.
    5. Robert Mislevy, 1991. "Randomization-based inference about latent variables from complex samples," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 177-196, June.
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    Cited by:

    1. Alexander Robitzsch, 2022. "Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches," Stats, MDPI, vol. 5(3), pages 1-42, July.

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