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

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  • Max Auerswald
  • Morten Moshagen

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. Copyright The Psychometric Society 2015

Suggested Citation

  • Max Auerswald & Morten Moshagen, 2015. "Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 920-937, December.
  • Handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:920-937
    DOI: 10.1007/s11336-015-9468-7
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    References listed on IDEAS

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    1. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Pandu Tadikamalla, 1980. "On simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 273-279, June.
    4. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 251-251, June.
    5. Todd Headrick & Shlomo Sawilowsky, 1999. "Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 25-35, March.
    6. Headrick, Todd C. & Mugdadi, Abdel, 2006. "On simulating multivariate non-normal distributions from the generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3343-3353, July.
    7. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.
    8. Headrick, Todd C., 2002. "Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 685-711, October.
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