Modified Distribution-Free Goodness-of-Fit Test Statistic
Modified Distribution-Free Goodness-of-Fit Test Statistic
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DOI：
10.1007/s11336-017-9574-9
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发表时间：
2018-03-01
期刊：
影响因子：
3
通讯作者：
Shapiro, Alexander
中科院分区：
文献类型：
--
作者：
Chun, So Yeon;Browne, Michael W.;Shapiro, Alexander
协方差结构分析及其结构方程建模扩展已成为心理学、教育学和经济学等社会科学中最广泛使用的方法之一。这种分析中的一个重要问题是评估分析模型的拟合优度。在协方差结构分析中使用的最流行的检验统计量之一是由Browne（Br J Math Stat Psychol 37：62-83，1984）引入的无渐近分布（ADF）检验统计量。ADF统计量可用于测试模型，而无需任何特定的分布假设（例如，多变量正态分布）。尽管它的优势，它已被证明在各种实证研究，除非样本量非常大，这种ADF统计量可以在实践中表现得非常差。在本文中，我们提供了一个理论解释这种现象，并进一步提出了一个修改后的测试统计量，提高了在现实规模的样本的性能。所提出的统计量处理所涉及的大规模协方差矩阵的可能的病态。
Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62-83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.