Department of Psychology, Karl Franzens University of Graz, Graz A-8010, Austria.
Psychol Methods. 2011 Sep;16(3):319-36. doi: 10.1037/a0024917.
Fit indices are widely used in order to test the model fit for structural equation models. In a highly influential study, Hu and Bentler (1999) showed that certain cutoff values for these indices could be derived, which, over time, has led to the reification of these suggested thresholds as "golden rules" for establishing the fit or other aspects of structural equation models. The current study shows how differences in unique variances influence the value of the global chi-square model test and the most commonly used fit indices: Root-mean-square error of approximation, standardized root-mean-square residual, and the comparative fit index. Using data simulation, the authors illustrate how the value of the chi-square test, the root-mean-square error of approximation, and the standardized root-mean-square residual are decreased when unique variances are increased although model misspecification is present. For a broader understanding of the phenomenon, the authors used different sample sizes, number of observed variables per factor, and types of misspecification. A theoretical explanation is provided, and implications for the application of structural equation modeling are discussed.
拟合指数被广泛用于检验结构方程模型的模型拟合情况。在一项极具影响力的研究中，Hu 和 Bentler（1999）表明，可以得出这些指数的某些临界值，随着时间的推移，这些建议的阈值已经被具体化，成为了建立结构方程模型拟合或其他方面的“黄金法则”。本研究展示了独特方差差异如何影响全局卡方模型检验和最常用的拟合指数的数值：近似均方根误差、标准化均方根残差和比较拟合指数。作者通过数据模拟说明了当存在模型误定时，独特方差的增加如何降低卡方检验、近似均方根误差和标准化均方根残差的值。为了更全面地了解这一现象，作者使用了不同的样本大小、每个因子的观测变量数量和不同的误定类型。提供了理论解释，并讨论了对结构方程建模应用的影响。
