Olvera Astivia Oscar L, Zumbo Bruno D
University of British Columbia, Vancouver, British Columbia, Canada.
Educ Psychol Meas. 2015 Aug;75(4):541-567. doi: 10.1177/0013164414548894. Epub 2014 Sep 12.
To further understand the properties of data-generation algorithms for multivariate, nonnormal data, two Monte Carlo simulation studies comparing the Vale and Maurelli method and the Headrick fifth-order polynomial method were implemented. Combinations of skewness and kurtosis found in four published articles were run and attention was specifically paid to the quality of the sample estimates of univariate skewness and kurtosis. In the first study, it was found that the Vale and Maurelli algorithm yielded downward-biased estimates of skewness and kurtosis (particularly at small samples) that were also highly variable. This method was also prone to generate extreme sample kurtosis values if the population kurtosis was high. The estimates obtained from Headrick's algorithm were also biased downward, but much less so than the estimates obtained through Vale and Maurelli and much less variable. The second study reproduced the first simulation in the Curran, West, and Finch article using both the Vale and Maurelli method and the Heardick method. It was found that the chi-square values and empirical rejection rates changed depending on which data-generation method was used, sometimes sufficiently so that some of the original conclusions of the authors would no longer hold. In closing, recommendations are presented regarding the relative merits of each algorithm.
为了进一步了解多变量非正态数据生成算法的特性，我们进行了两项蒙特卡罗模拟研究，比较了瓦尔和莫雷利方法以及黑德里克五次多项式方法。我们运行了在四篇已发表文章中发现的偏度和峰度的组合，并特别关注单变量偏度和峰度的样本估计质量。在第一项研究中，我们发现瓦尔和莫雷利算法产生的偏度和峰度估计值存在向下偏差（特别是在小样本情况下），而且变化很大。如果总体峰度较高，这种方法还容易产生极端的样本峰度值。从黑德里克算法获得的估计值也有向下偏差，但比通过瓦尔和莫雷利方法获得的估计值偏差小得多，且变化也小得多。第二项研究使用瓦尔和莫雷利方法以及黑德里克方法重现了柯伦、韦斯特和芬奇文章中的第一次模拟。结果发现，卡方值和经验拒绝率会根据所使用的数据生成方法而变化，有时变化程度足以使作者的一些原始结论不再成立。最后，我们针对每种算法的相对优点提出了建议。
