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Covariance Model Simulation Using Regular Vines

Author

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  • Steffen Grønneberg

    (BI Norwegian Business School)

  • Njål Foldnes

    (BI Norwegian Business School)

Abstract

We propose a new and flexible simulation method for non-normal data with user-specified marginal distributions, covariance matrix and certain bivariate dependencies. The VITA (VIne To Anything) method is based on regular vines and generalizes the NORTA (NORmal To Anything) method. Fundamental theoretical properties of the VITA method are deduced. Two illustrations demonstrate the flexibility and usefulness of VITA in the context of structural equation models. R code for the implementation is provided.

Suggested Citation

  • Steffen Grønneberg & Njål Foldnes, 2017. "Covariance Model Simulation Using Regular Vines," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1035-1051, December.
  • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-017-9569-6
    DOI: 10.1007/s11336-017-9569-6
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    References listed on IDEAS

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    1. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    4. 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.
    5. Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
    6. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    7. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
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    Cited by:

    1. 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.
    2. Steffen Grønneberg & Jonas Moss & Njål Foldnes, 2020. "Partial Identification of Latent Correlations with Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 1028-1051, December.

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