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The asymptotic covariance matrix and its use in simulation studies

Foldnes, Njål; Grønneberg, Steffen
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2471641
Date
2017
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  • Publikasjoner fra CRIStin - BI [1179]
  • Scientific articles [2318]
Original version
Structural Equation Modeling. 2017, 24 (6), 881-896   10.1080/10705511.2017.1341320
Abstract
The asymptotic performance of structural equation modeling tests and standard errors are influenced by two factors: the model and the asymptotic covariance matrix Γ of the sample covariances. Although most simulation studies clearly specify model conditions, specification of Γ is usually limited to values of univariate skewness and kurtosis. We illustrate that marginal skewness and kurtosis are not sufficient to adequately specify a nonnormal simulation condition by showing that asymptotic standard errors and test statistics vary substantially among distributions with skewness and kurtosis that are identical. We argue therefore that Γ should be reported when presenting the design of simulation studies. We show how Γ can be exactly calculated under the widely used Vale–Maurelli transform. We suggest plotting the elements of Γ and reporting the eigenvalues associated with the test statistic. R code is provided.
Description
The accepted and peer reviewed manuscript to the article
Publisher
Taylor and Francis
Journal
Structural Equation Modeling

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