When fit indices and residuals are incompatible
When fit indices and residuals are incompatible
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DOI：
10.1037//1082-989x.7.4.403
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发表时间：
2002-12-01
影响因子：
7
通讯作者：
Glaser, R
中科院分区：
文献类型：
--
作者：
Browne, MW;MacCallum, RC;Glaser, R
用于因子分析和相关模型的标准卡方拟合指数有一个鲜为人知的属性：当唯一方差较小时，它们对失配的敏感性高于当它们较大时。因此，当唯一方差很小时，非常小的相关残差指示极好的拟合可能伴随着拟合指数的不良拟合指示。残差和拟合指数之间的这种不相容性的一个经验的例子。为了说明的目的，提供了一个人工示例，其产生与经验示例完全相同的相关残差，但具有更大的唯一方差。对于该示例，拟合指数指示极好的拟合。利用拟合相关矩阵的特征值和唯一方差之间的关系，对这一现象进行了理论解释。
Standard chi-square-based fit indices for factor analysis and related models have a little known property: They are more sensitive to misfit when unique variances are small than when they are large. Consequently, very small correlation residuals indicating excellent fit can be accompanied by indications of bad fit by the fit indices when unique variances are small. An empirical example of this incompatibility between residuals and fit indices is provided. For illustrative purposes, an artificial example is provided that yields exactly the same correlation residuals as the empirical example but has larger unique variances. For this example, the fit indices indicate excellent fit. A theoretical explanation for this phenomenon is provided using relationships between unique variances and eigenvalues of the fitted correlation matrix.