Chou C P, Bentler P M, Satorra A
Department of Preventive Medicine, University of Southern California, Alhambra 91803-1358.
Br J Math Stat Psychol. 1991 Nov;44 ( Pt 2):347-57. doi: 10.1111/j.2044-8317.1991.tb00966.x.
Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.
关于协方差结构分析中最大似然（ML）统计量稳健性的研究得出结论，在严重非正态情况下，检验统计量和标准误存在偏差。已提出一种称为渐近无分布（ADF）的估计程序，该程序不做分布假设，以避免这些偏差。也有人提出对正态理论统计量进行修正，以获得更合适的性能。本研究比较了在几种非正态条件下两个模型的缩放检验统计量和稳健标准误的性能，并将其与ML和ADF方法的结果进行比较。ML和ADF检验统计量在一个模型中表现相当好，而在另一个模型中则差得多。总体而言，缩放检验统计量的表现似乎优于ML检验统计量，而ADF统计量表现最差。在大多数非正态条件下的两个模型中，稳健和ADF标准误比通常存在向下偏差的ML标准误能更恰当地估计抽样变异性。当数据具有对称和平峰分布或非对称和零峰度分布时，发现ML检验统计量和标准误对违反正态性假设相当稳健。
