Lai Keke, Green Samuel B
a Department of Psychological Sciences , University of California , Merced.
b Denny Sanford School of Social and Family Dynamics, Arizona State University.
Multivariate Behav Res. 2016 Mar-Jun;51(2-3):220-39. doi: 10.1080/00273171.2015.1134306. Epub 2016 Mar 25.
The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of "good" fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.
近似均方根误差（RMSEA）和比较拟合指数（CFI）是评估结构方程模型拟合度的两个广泛应用的指标。由于这两个指标受到研究人员的积极看待，有人可能会认为它们的值会对任何数据集的模型拟合产生可比的定性评估。当RMSEA和CFI对模型拟合给出不同评价时，我们认为研究人员可能会感到困惑，并可能得出错误的研究结论。我们推导了这些指标不一致解释的必要条件和充分条件。我们还研究了样本层面RMSEA和CFI结果的不一致性。这两个指标出现分歧并非表明模型以特定方式设定错误或数据存在任何缺陷，而是因为：（a）它们在设计上从不同角度评估模型拟合函数值的大小；（b）这些指标的临界值是任意的；（c）“良好”拟合的含义及其与拟合指标的关系并未得到很好的理解。在使用RMSEA和CFI对拟合做出不一致判断的背景下，我们讨论了在实践中使用临界值评估模型拟合以及设计结构方程模型研究的意义。
