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

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 appro...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 5; p. 842
Main Authors Zitzmann, Steffen, Lohmann, Julian F., Krammer, Georg, Helm, Christoph, Aydin, Burak, Hecht, Martin
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2022
Subjects
Bayes
Bayesian analysis
EAP
Employees
Estimates
Estimation
Leadership
Mathematics
micro–macro design
multilevel modeling
nonlinear
Perceptions
Productivity
Regression analysis
Resampling
Software
Teams
Variables
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10050842