Olvera Astivia Oscar L, Zumbo Bruno D
Department of ECPS, University of British Columbia, Vancouver, British Columbia, Canada.
Br J Math Stat Psychol. 2018 Nov;71(3):437-458. doi: 10.1111/bmsp.12126. Epub 2018 Jan 11.
The Fleishman third-order polynomial algorithm is one of the most-often used non-normal data-generating methods in Monte Carlo simulations. At the crux of the Fleishman method is the solution of a non-linear system of equations needed to obtain the constants to transform data from normality to non-normality. A rarely acknowledged fact in the literature is that the solution to this system is not unique, and it is currently unknown what influence the different types of solutions have on the computer-generated data. To address this issue, analytical and empirical investigations were conducted, aimed at documenting the impact that each solution type has on the design of computer simulations. In the first study, it was found that certain types of solutions generate data with different multivariate properties and wider coverage of the theoretical range spanned by population correlations. In the second study, it was found that previously published recommendations from Monte Carlo simulations could change if different types of solutions were used to generate the data. A mathematical description of the multiple solutions to the Fleishman polynomials is provided, as well as recommendations for users of this method.
弗莱什曼三阶多项式算法是蒙特卡罗模拟中最常用的非正态数据生成方法之一。弗莱什曼方法的关键在于求解一个非线性方程组，以获得将数据从正态转换为非正态所需的常数。文献中一个很少被提及的事实是，该方程组的解不是唯一的，目前尚不清楚不同类型的解对计算机生成的数据有何影响。为了解决这个问题，进行了分析和实证研究，旨在记录每种解类型对计算机模拟设计的影响。在第一项研究中，发现某些类型的解会生成具有不同多变量属性的数据，并且能更广泛地覆盖总体相关性所跨越的理论范围。在第二项研究中，发现如果使用不同类型的解来生成数据，之前发表的蒙特卡罗模拟建议可能会改变。本文提供了弗莱什曼多项式多重解的数学描述，以及对该方法使用者的建议。
