Approximations to the Distributions of Fit Indexes for Misspecified Structural Equation Models
Approximations to the Distributions of Fit Indexes for Misspecified Structural Equation Models
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错误指定结构方程模型拟合指数分布的近似
DOI：
10.1207/s15328007sem0804_03
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
H. Ogasawara
中科院分区：
文献类型：
--
作者：
H. Ogasawara
在多元正态性假设和模型的轻微误设定下，导出了结构方程模型拟合优度指数分布的近似表达式。本文所考虑的拟合指数有：Joreskog和Sorbom的拟合优度指数（GFI）和调整GFI，McDonald的绝对GFI，Steiger和Lind的近似均方根误差，Steiger的Γ1和Γ2，Bentler和Bonett的赋范拟合指数，Bollen的增量拟合指数和ρ1，Tucker和刘易斯的指数ρ2，Bentler的拟合指数（McDonald和Marsh的相对非中心性指数）。拟合指数的渐近协方差矩阵的近似值是通过使用delta方法导出的。此外，拟合指数的密度的近似得到的渐近非中心卡方分布变量的转换。进行了模拟，以确认近似的准确性。
Approximations to the distributions of goodness-of-fit indexes in structural equation modeling are derived with the assumption of multivariate normality and slight misspecification of models. The fit indexes considered in this article are Joreskog and Sorbom's goodness-of-fit index (GFI) and the adjusted GFI, McDonald's absolute GFI, Steiger and Lind's root mean squared error of approximation, Steiger's Γ1 and Γ2, Bentler and Bonett's normed fit index, Bollen's incremental fit index and ρ1, Tucker and Lewis's index ρ2, and Bentler's fit index (McDonald and Marsh's relative noncentrality index). An approximation to the asymptotic covariance matrix for the fit indexes is derived by using the delta method. Furthermore, approximations to the densities of the fit indexes are obtained from the transformations of the asymptotically noncentral chi-square distributed variable. A simulation is carried out to confirm the accuracy of the approximations.