title: Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model.
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.
authors.affiliation: Department of Psychology, School of Social Sciences, University of Mannheim, Mannheim, Germany. auerswald@uni-kassel.de.|Institute of Psychology, University of Kassel, Holländische Straße 36-38, 34127 , Kassel, Germany. auerswald@uni-kassel.de.
authors.forename: Max
authors.initials: M
authors.lastname: Auerswald
authors.affiliation: Institute of Psychology, University of Kassel, Holländische Straße 36-38, 34127 , Kassel, Germany.
authors.forename: Morten
authors.initials: M
authors.lastname: Moshagen
mesh_terms: D000465:Algorithms; D015233:Models, Statistical; D015999:Multivariate Analysis; D017711:Nonlinear Dynamics; D011594:Psychometrics / Q000706:statistics & numerical data
keywords: Non-normal multivariate data; Simulation; Structural equation modeling