Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives
Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives
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DOI：
10.1080/10705519909540118
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发表时间：
1999-01-01
影响因子：
6
通讯作者：
Bentler, Peter M.
中科院分区：
文献类型：
--
作者：
Hu, Li-tze;Bentler, Peter M.
本文探讨了充分的“经验法则”的传统截断标准和几个新的替代各种拟合指数用于评估模型拟合在实践中。使用2指数呈现策略，包括使用基于最大似然（ML）的标准化均方根残差（SRMR），并补充Tucker刘易斯指数（TLI）、Bollen（1989）拟合指数（BL 89）、相对非中心性指数（RNI）、比较拟合指数（CFI）、Gamma Hat、McDonald's中心性指数（Mc）或近似均方根误差（RMSEA），基于ML的SRMR和给定的补充拟合指数的选定范围的临界值的各种组合用于计算各种类型的真实群体和错误指定模型的拒绝率;即具有错误指定因子协方差的模型和具有错误指定因子加载的模型。结果表明，对于ML方法，TLI、BL 89、CFI、RNI和Gamma Hat的截止值接近0.95; Mc的截止值接近0.90; SRMR的截止值接近0.08; RMSEA的截止值接近0.06，然后我们才能得出假设模型与观测数据之间存在相对较好拟合的结论。此外，2指数呈现策略需要拒绝合理比例的各种类型的真实群体和错误指定的模型。最后，使用建议的截止标准，基于ML的TLI，Mc和RMSEA往往会在小样本量时过度拒绝真实总体模型，因此在样本量小时不太可取。
This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and Gamma Hat; a cutoff value close to .90 for Mc; a cutoff value close to .08 for SRMR; and a cutoff value close to .06 for RMSEA are needed before we can conclude that there is a relatively good fit between the hypothesized model and the observed data. Furthermore, the 2‐index presentation strategy is required to reject reasonable proportions of various types of true‐population and misspecified models. Finally, using the proposed cutoff criteria, the ML‐based TLI, Mc, and RMSEA tend to overreject true‐population models at small sample size and thus are less preferable when sample size is small.