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

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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. / Zitzmann, Steffen; Lohmann, Julian F.; Krammer, Georg et al.
in: Mathematics, Jahrgang 10, Nr. 5, 842, 07.03.2022.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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Zitzmann S, Lohmann JF, Krammer G, Helm C, Aydin B, Hecht M. A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs. Mathematics. 2022 Mär 7;10(5):842. doi: 10.3390/math10050842

Bibtex

@article{01d9f78015fd41858cd71e4162562768,
title = "A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven{\textquoteright}s Model for Analyzing Data from Micro–Macro Multilevel Designs",
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 = "Bayes, EAP, Micro–macro design, Multilevel modeling, Nonlinear, Educational science",
author = "Steffen Zitzmann and Lohmann, {Julian F.} and Georg Krammer and Christoph Helm and Burak Aydin and Martin Hecht",
year = "2022",
month = mar,
day = "7",
doi = "10.3390/math10050842",
language = "English",
volume = "10",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "5",

}

RIS

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 -

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