RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods
RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods
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DOI：
10.3758/s13428-018-1055-2
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发表时间：
2019-02-01
影响因子：
5.4
通讯作者：
Yang, Yanyun
中科院分区：
文献类型：
--
作者：
Xia, Yan;Yang, Yanyun
在结构方程建模中，近似均方根误差（RMSEA）、比较拟合指数（CFI）和塔克-刘易斯指数（TLI）的应用高度依赖于在连续数据的正态理论最大似然（ML）下开发的常规截止值。对于有序分类数据，基于多元相关矩阵的未加权最小二乘（ULS）和对角加权最小二乘（DWLS）在以前的研究中已经被推荐。虽然没有明确的建议存在关于这些拟合指数的应用时，分析有序的分类变量，从业者仍然倾向于采用传统的截止规则。我们研究的目的是回答这样一个问题：给定一个群体多元相关矩阵和一个假设模型，如果ML导致一个特定的RMSEA值（例如，.08），当应用ULS或DWLS时，RMSEA值是多少？以相同的方式研究CFI和TLI。模拟和经验的多元相关矩阵与不同程度的模型误设，以解决上述问题。结果表明，DWLS和ULS导致较小的RMSEA和较大的CFI和TLI值比ML的所有操作条件下，无论是否缩放的指数。因此，将传统的截止值应用于DWLS和ULS，有一个明显的趋势，即不能发现模型-数据失配。讨论了有序分类数据的RMSEA，CFI和TLI的使用。
In structural equation modeling, application of the root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker-Lewis index (TLI) highly relies on the conventional cutoff values developed under normal-theory maximum likelihood (ML) with continuous data. For ordered categorical data, unweighted least squares (ULS) and diagonally weighted least squares (DWLS) based on polychoric correlation matrices have been recommended in previous studies. Although no clear suggestions exist regarding the application of these fit indices when analyzing ordered categorical variables, practitioners are still tempted to adopt the conventional cutoff rules. The purpose of our research was to answer the question: Given a population polychoric correlation matrix and a hypothesized model, if ML results in a specific RMSEA value (e.g., .08), what is the RMSEA value when ULS or DWLS is applied? CFI and TLI were investigated in the same fashion. Both simulated and empirical polychoric correlation matrices with various degrees of model misspecification were employed to address the above question. The results showed that DWLS and ULS lead to smaller RMSEA and larger CFI and TLI values than does ML for all manipulated conditions, regardless of whether or not the indices are scaled. Applying the conventional cutoffs to DWLS and ULS, therefore, has a pronounced tendency not to discover model-data misfit. Discussions regarding the use of RMSEA, CFI, and TLI for ordered categorical data are given.