SCALED TEST STATISTICS AND ROBUST STANDARD ERRORS FOR NONNORMAL DATA IN COVARIANCE STRUCTURE-ANALYSIS - A MONTE-CARLO STUDY
SCALED TEST STATISTICS AND ROBUST STANDARD ERRORS FOR NONNORMAL DATA IN COVARIANCE STRUCTURE-ANALYSIS - A MONTE-CARLO STUDY
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DOI：
10.1111/j.2044-8317.1991.tb00966.x
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发表时间：
1991-11-01
影响因子：
2.6
通讯作者：
SATORRA, A
中科院分区：
文献类型：
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作者：
CHOU, CP;BENTLER, PM;SATORRA, A
对协方差结构分析中最大似然统计量鲁棒性的研究表明，在严重的非正态性下，检验统计量和标准误差存在偏倚。为了避免这些偏差，提出了一种不做任何分布假设的估计方法，称为无渐近分布（ADF）。还提出了对正常理论统计量的修正，以获得更充分的性能。本研究比较了两种模型在几种非正态条件下的比例检验统计量和鲁棒标准误差的性能，并将其与ML和ADF方法的结果进行了比较。ML和ADF测试统计数据在一个模型中表现相当好，而在另一个模型中表现相当差。一般来说，缩放测试统计量似乎比ML测试统计量表现得更好，而ADF统计量表现得最差。在大多数非正态条件下，两种模型的鲁棒性和ADF标准误差比ML标准误差产生了更合适的抽样可变性估计，ML标准误差通常是向下偏置的。发现ML检验统计量和标准误差对于违反正态性假设是相当稳健的，当数据具有对称和平峰度分布或非对称和零峰度分布时。
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.