A Cautionary Note on the Use of the Vale and Maurelli Method to Generate Multivariate, Nonnormal Data for Simulation Purposes

Astivia, Oscar L. Olvera; Zumbo, Bruno D.

doi:10.1177/0013164414548894

Cited by 29 publications

(17 citation statements)

References 28 publications

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“…This method yields skewness and kurtosis values with more precision and less bias than do earlier, third-order power polynomial methods (Olvera Astivia & Zumbo, 2015). Further details of this data-generating method can be found in Supplementary Materials C. Simulations were conducted in the language R (R Development Core Team, 2014).…”

Section: Simulationmentioning

confidence: 99%

Confidence intervals for correlations when data are not normal

2016

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With nonnormal data, the typical confidence interval of the correlation (Fisher z') may be inaccurate. The literature has been unclear as to which of several alternative methods should be used instead, and how extreme a violation of normality is needed to justify an alternative. Through Monte Carlo simulation, 11 confidence interval methods were compared, including Fisher z', two Spearman rank-order methods, the Box-Cox transformation, rank-based inverse normal (RIN) transformation, and various bootstrap methods. Nonnormality often distorted the Fisher z' confidence interval-for example, leading to a 95 % confidence interval that had actual coverage as low as 68 %. Increasing the sample size sometimes worsened this problem. Inaccurate Fisher z' intervals could be predicted by a sample kurtosis of at least 2, an absolute sample skewness of at least 1, or significant violations of normality hypothesis tests. Only the Spearman rankorder and RIN transformation methods were universally robust to nonnormality. Among the bootstrap methods, an observed imposed bootstrap came closest to accurate coverage, though it often resulted in an overly long interval. The results suggest that sample nonnormality can justify avoidance of the Fisher z' interval in favor of a more robust alternative. R code for the relevant methods is provided in supplementary materials.

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Section: Simulationmentioning

confidence: 99%

Confidence intervals for correlations when data are not normal

2016

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“…In summary, the solution proposed by Vale and Maurelli (1983) calculates an intermediate correlation matrix. Its data are the same as the population correlation matrix and, given that one applies the Fleishman method to each marginal distribution, the correlation matrix is transformed to the desired one that is used to generate the data (Olvera Astivia & Zumbo, 2015).…”

Section: Vale-maurelli Methodsmentioning

confidence: 99%

“…Among the various methods developed to generate nonnormal data (Fleishman, 1978;Headrick, 2002Headrick, , 2004L'Ecuyer, 1990;Marsaglia, 2003;Ramberg, Tadikamalla, Dudewicz, & Mykytka, 1979;Tadikamalla, 1980;Vale & Maurelli, 1983, among others), the method of Vale and Maurelli (1983) is one of the most widely used by simulation studies in the social sciences. According to Olvera Astivia and Zumbo (2015), this method has more than 130 citation counts on the ISI Web of Knowledge, and over 230 on Google Scholar. The procedures used to generate data can alter the sphericity of the fixed covariance matrix, since the process of data simulation involves two steps: the generation of a population covariance matrix from sphericity values, and the generation of normal or nonnormal data using this covariance matrix.…”

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confidence: 99%

Sphericity estimation bias for repeated measures designs in simulation studies

et al. 2015

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In this study, we explored the accuracy of sphericity estimation and analyzed how the sphericity of covariance matrices may be affected when the latter are derived from simulated data. We analyzed the consequences that normal and nonnormal data generated from an unstructured population covariance matrix-with low (ε = .57) and high (ε = .75) sphericity-can have on the sphericity of the matrix that is fitted to these data. To this end, data were generated for four types of distributions (normal, slightly skewed, moderately skewed, and severely skewed or log-normal), four sample sizes (very small, small, medium, and large), and four values of the within-subjects factor (K = 4, 6, 8, and 10). Normal data were generated using the Cholesky decomposition of the correlation matrix, whereas the Vale-Maurelli method was used to generate nonnormal data. The results indicate the extent to which sphericity is altered by recalculating the covariance matrix on the basis of simulated data. We concluded that bias is greater with spherical covariance matrices, nonnormal distributions, and small sample sizes, and that it increases in line with the value of K. An interaction was also observed between sample size and K: With very small samples, the observed bias was greater as the value of K increased.

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“…This generating method was chosen because it is more precise than the third-order polynomial in terms of generating intended values of skewness and kurtosis (Olvera Astivia & Zumbo, 2015). Additionally, generating from a slightly different family than the third-order polynomial provides a modest stress test for the adjustment via approximate distribution method used here.…”

Section: Simulationmentioning

confidence: 99%

Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis

Bishara

Nash

2017

Brit J Math & Statis

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When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z 0 under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z 0 interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non-parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods (PM1 and HC4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta-analysis. Supporting information includes R code.

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A Cautionary Note on the Use of the Vale and Maurelli Method to Generate Multivariate, Nonnormal Data for Simulation Purposes

Cited by 29 publications

References 28 publications

Confidence intervals for correlations when data are not normal

Confidence intervals for correlations when data are not normal

Sphericity estimation bias for repeated measures designs in simulation studies

Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis

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