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How General is the Vale–Maurelli Simulation Approach?

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  • Njål Foldnes
  • Steffen Grønneberg

Abstract

The Vale–Maurelli (VM) approach to generating non-normal multivariate data involves the use of Fleishman polynomials applied to an underlying Gaussian random vector. This method has been extensively used in Monte Carlo studies during the last three decades to investigate the finite-sample performance of estimators under non-Gaussian conditions. The validity of conclusions drawn from these studies clearly depends on the range of distributions obtainable with the VM method. We deduce the distribution and the copula for a vector generated by a generalized VM transformation, and show that it is fundamentally linked to the underlying Gaussian distribution and copula. In the process we derive the distribution of the Fleishman polynomial in full generality. While data generated with the VM approach appears to be highly non-normal, its truly multivariate properties are close to the Gaussian case. A Monte Carlo study illustrates that generating data with a different copula than that implied by the VM approach severely weakens the performance of normal-theory based ML estimates. Copyright The Psychometric Society 2015

Suggested Citation

  • Njål Foldnes & Steffen Grønneberg, 2015. "How General is the Vale–Maurelli Simulation Approach?," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1066-1083, December.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:1066-1083
    DOI: 10.1007/s11336-014-9414-0
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    References listed on IDEAS

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    1. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    2. Pandu Tadikamalla, 1980. "On simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 273-279, June.
    3. Todd C. Headrick & Mohan D. Pant, 2012. "Simulating non-normal distributions with specified L-moments and L-correlations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 422-441, November.
    4. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    5. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
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    Cited by:

    1. Steffen Grønneberg & Njål Foldnes, 2017. "Covariance Model Simulation Using Regular Vines," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1035-1051, December.
    2. Njål Foldnes & Steffen Grønneberg, 2019. "On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1000-1017, December.
    3. Steffen Grønneberg & Njål Foldnes, 2019. "A Problem with Discretizing Vale–Maurelli in Simulation Studies," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 554-561, June.

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