The Asymptotic Covariance Matrix and its Use in Simulation Studies |
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| Authors: | Njål Foldnes Steffen Grønneberg |
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| Institution: | BI Norwegian Business School |
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| 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. |
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| Keywords: | asymptotic covariance matrix kurtosis Monte Carlo nonnormality structural equation modeling Vale-Maurelli |
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