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Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model

Published online by Cambridge University Press:  01 January 2025

Max Auerswald  and
Morten Moshagen
Max Auerswald*
Affiliation:
University of Mannheim University of Kassel
Morten Moshagen
Affiliation:
University of Kassel
*
Correspondence should be made to Max Auerswald, Institute of Psychology, University of Kassel, Holländische Straße 36-38, 34127 Kassel, Germany. Email: auerswald@uni-kassel.de
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Abstract

An approach to generate non-normality in multivariate data based on a structural model with normally distributed latent variables is presented. The key idea is to create non-normality in the manifest variables by applying non-linear linking functions to the latent part, the error part, or both. The algorithm corrects the covariance matrix for the applied function by approximating the deviance using an approximated normal variable. We show that the root mean square error (RMSE) for the covariance matrix converges to zero as sample size increases and closely approximates the RMSE as obtained when generating normally distributed variables. Our algorithm creates non-normality affecting every moment, is computationally undemanding, easy to apply, and particularly useful for simulation studies in structural equation modeling.

Keywords

Non-normal multivariate dataStructural equation modelingSimulation
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 4 , December 2015 , pp. 920 - 937
Copyright
Copyright © 2015 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-015-9468-7) contains supplementary material, which is available to authorized users.

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