A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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in: Mathematics, Jahrgang 10, Nr. 5, 842, 07.03.2022.
Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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TY - JOUR
T1 - A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs
AU - Zitzmann, Steffen
AU - Lohmann, Julian F.
AU - Krammer, Georg
AU - Helm, Christoph
AU - Aydin, Burak
AU - Hecht, Martin
PY - 2022/3/7
Y1 - 2022/3/7
N2 - 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.
AB - 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.
KW - Bayes
KW - EAP
KW - Micro–macro design
KW - Multilevel modeling
KW - Nonlinear
KW - Educational science
UR - http://www.scopus.com/inward/record.url?scp=85126293249&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/323fba54-f90d-3f1c-adcd-ab51ac5400ea/
U2 - 10.3390/math10050842
DO - 10.3390/math10050842
M3 - Journal articles
AN - SCOPUS:85126293249
VL - 10
JO - Mathematics
JF - Mathematics
SN - 2227-7390
IS - 5
M1 - 842
ER -