A Bayesian Model For The Estimation Of Latent Interaction And Quadratic Effects When Latent Variables Are Non-Normally Distributed

Multivariate Behavioral Research
Augustin Kelava, Benjamin Nagengast

Abstract

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent predictor variables are nonnormally distributed. The nonnormal predictor distribution is approximated by a finite mixture distribution. We conduct a simulation study that demonstrates the advantages of the proposed Bayesian model over contemporary approaches (Latent Moderated Structural Equations [LMS], Quasi-Maximum-Likelihood [QML], and the extended unconstrained approach) when the latent predictor variables follow a nonnormal distribution. The conventional approaches show biased estimates of the nonlinear effects; the proposed Bayesian model provides unbiased estimates. We present an empirical example from work and stress research and provide syntax for substantive researchers. Advantages and limitations of the new model are discussed.

References

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Citations

Dec 31, 2015·Multivariate Behavioral Research·Karina Rdz-Navarro, Jesús M Alvarado
Nov 27, 2015·Multivariate Behavioral Research·Holger Brandt, Andreas G Klein
Aug 8, 2014·Frontiers in Psychology·Augustin Kelava, Holger Brandt
Sep 28, 2016·Ultrasonography·Keerthi S Valluru, Juergen K Willmann
Apr 25, 2020·Multivariate Behavioral Research·Christoph Kiefer, Axel Mayer
Jul 10, 2021·Structural Equation Modeling : a Multidisciplinary Journal·Yu-Yu HsiaoMark H C Lai
Aug 12, 2021·Multivariate Behavioral Research·Zachary J Roman, Holger Brandt

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Software Mentioned

R
Mplus
EQS
SEM
ExUC
QML
R2WinBUGS package
WinBugs
LISREL

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