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A Problem with Discretizing Vale–Maurelli in Simulation Studies

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  • Steffen Grønneberg

    (BI Norwegian Business School)

  • Njål Foldnes

    (BI Norwegian Business School)

Abstract

Previous influential simulation studies investigate the effect of underlying non-normality in ordinal data using the Vale–Maurelli (VM) simulation method. We show that discretized data stemming from the VM method with a prescribed target covariance matrix are usually numerically equal to data stemming from discretizing a multivariate normal vector. This normal vector has, however, a different covariance matrix than the target. It follows that these simulation studies have in fact studied data stemming from normal data with a possibly misspecified covariance structure. This observation affects the interpretation of previous simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:2:d:10.1007_s11336-019-09663-8
    DOI: 10.1007/s11336-019-09663-8
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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. Albert Maydeu-Olivares, 2006. "Limited information estimation and testing of discretized multivariate normal structural models," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 57-77, March.
    3. 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.
    4. Ulf Olsson, 1979. "Maximum likelihood estimation of the polychoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 443-460, December.
    5. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
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