一种新的评价结构方程模型拟合效果的校正拟合指数

A New Corrected-Good-of-Fit Index(CGFI) for Model Evaluation in Structural Equation Modeling

目的建立一种新的用于评价结构方程模型(SEM)拟合效果的方法—校正拟合指数(CGFI)。方法在已有拟合指数(GFI)方法的基础上,通过增加1/(N-1)项校正样本量导致的低估效应,通过自由度与变量个数的比值项对模型的复杂程度进行惩罚,构建了CGFI,表达为:CGFI=1-[df_(test)/k(k+1)][1-GFI-1/(N-1)]。基于预设的SEM,采用Monte Carlo技术模拟产生数据,考虑样本量、参数估计方法、模型误设类型及误设程度四种因素,将所提出的CGFI与其他3种拟合指数(GFI,AGFI,PGFI)进行比较。评价标准基于稳健性和对模型误设的敏感性。结果 CGFI较GFI有一定改善效果,受样本量的影响更小,对模型误设更为敏感;GFI和AGFI受样本量的影响较大,在样本量较小时存在一定低估。PGFI对模型误设不敏感,且存在较为严重低估。GLS参数估计方法在模型严重误设时容易得到反常的结果。结论CGFI较GFI有较好的表现,临界值为0.95,可用于模型拟合效果的评价。

Objective To propose a new Corrected-Good-of-Fit Index（CGFI） for model evaluation in structural equa- tion modeling （SEM）. Methods Based on the GFI, we firstly corrected the underestimation effect caused by smaller sample size by adding the 1/（N - 1 ） term, and then punished the complexity of the model by the ratio of the degrees of freedom over the number of variables. The CGFI was expressed as CGFI = 1 - [ dftest/k （k ＋ 1 ） ] × [ 1 - GFI- 1/（ N- 1 ） ]. A Monte Carlo simu- lation study was conducted for comparison between the CGFI and other three fit indexes （GFI, AGFI, PGFI）considering the do- mains of sample size, estimation method, model misspecification types and misspecification degrees based on a pre-set SEM. We assessed the statistical performances by robustness and the sensitivity to model misspecification. Results The CGFI has better statistical performances than the GFI with less affect by sample size and higher sensitivity to model misspecification. The GFI and AGFI are affected by sample size obviously and trend to underestimation when sample size is small. The PGFI has a poor misspecification sensitive and serious underestimation. The GLS estimation method may result the GFI et al. with a high values when the fitted model was seriously misspecified. Conclusion In the model evaluation, we recommend the use of the CGFI pro- nosed hv us which is reasonable and practieable for goodness fit evaluation in SEM, with recommended critical value of 0. 95.