Currently, the best confidence interval (CI) for RMSEA in covariance structure analysis given nonnormal data is proposed by Brosseau-Liard, Savalei, and Li (BSL). A key assumption for the BSL CI often overlooked is that all the nonzero eigenvalues are equal in a matrix related to the model and data nonnormality. This assumption rarely holds in practice, especially for mean and covariance structure analysis, and violating this assumption can entail serious mistakes when the model’s degrees of freedom are small. One important application of moment structure analysis with small degrees of freedom is growth models. In this paper, we propose a new CI method for RMSEA in growth models given nonnormal data, without assuming equal eigenvalues. Although we focus on growth models, our method applies to any other models in moment structure analysis. Simulation results verify the new method is trustworthy and better than all the current methods.

中文翻译：

---

给定非正态数据的增长模型中 RMSEA 的更好置信区间

目前，在给定非正态数据的协方差结构分析中，RMSEA 的最佳置信区间 (CI) 是由 Brosseau-Liard、Savalei 和 Li (BSL) 提出的。BSL CI 的一个关键假设经常被忽视，即所有非零特征值在与模型和数据非正态性相关的矩阵中都是相等的。这个假设在实践中很少成立，特别是对于均值和协方差结构分析，当模型的自由度很小时，违反这个假设可能会导致严重的错误。小自由度力矩结构分析的一项重要应用是增长模型。在本文中，我们在给定非正态数据的增长模型中为 RMSEA 提出了一种新的 CI 方法，不假设特征值相等。尽管我们专注于增长模型，但我们的方法适用于矩结构分析中的任何其他模型。