Generating Nonnormal Multivariate Data Using Copulas: Applications to SEM

Multivariate Behavioral Research
Patrick MairPeter M Bentler

Abstract

This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo evaluation of structural equation models within the context of nonnormal data. The new procedure for nonnormal data simulation is theoretically described and also implemented in the widely used R environment. The quality of the method is assessed by Monte Carlo simulations. A 1-sample test on the observed covariance matrix based on the copula methodology is proposed. This new test for evaluating the quality of a simulation is defined through a particular structural model specification and is robust against normality violations.

References

Sep 1, 1992·Psychological Bulletin·L T HuY Kano
May 1, 1984·The British Journal of Mathematical and Statistical Psychology·M W Browne
Jul 1, 2008·Multivariate Behavioral Research·John Ruscio, Walter Kaczetow
Oct 1, 1997·Multivariate Behavioral Research·S Mattson

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Citations

Mar 26, 2016·Multivariate Behavioral Research·Njål Foldnes, Ulf Henning Olsson
Jun 11, 2015·Psychometrika·Max Auerswald, Morten Moshagen
Aug 7, 2014·Psychometrika·Njål Foldnes, Steffen Grønneberg
Nov 27, 2015·Multivariate Behavioral Research·Jennifer KoranTzu Chun Kuo
May 27, 2015·IEEE Transactions on Neural Networks and Learning Systems·Marko Robnik-Sikonja
Jan 13, 2018·The British Journal of Mathematical and Statistical Psychology·Oscar L Olvera Astivia, Bruno D Zumbo
Jan 24, 2018·Psychometrika·Yen Lee, David Kaplan
Apr 26, 2017·Psychometrika·Steffen Grønneberg, Njål Foldnes
Nov 1, 2013·Multivariate Behavioral Research·Johan BraekenFrancis Tuerlinckx
Aug 1, 2015·Educational and Psychological Measurement·Oscar L Olvera Astivia, Bruno D Zumbo
Jul 27, 2021·Multivariate Behavioral Research·Ji Yeh Choi, Juwon Seo

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Software Mentioned

R
REQS
EQS
SEM
copula
R package
R Development Core Team

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