RMSEA estimation given nonnormal continuous data is usually based on the mean-adjusted ( ) or mean-variance-adjusted ( ) chi-square statistic, but a plain application of these statistics has poor performance. Savalei and colleagues gave a better way (the BSL method) to infer RMSEA using or . However, the BSL method is applicable to continuous data only. For categorical data, currently RMSEA inference is still based on a plain application of or , but such practice is already problematic under continuous data. In this paper, we first show that it is more meaningful to define RMSEA under unweighted least squares (ULS) than under weighted least squares (WLS) or diagonally weighted least squares (DWLS). Then, we propose a correct point estimator and confidence interval for RMSEA given categorical data and ULS. Simulation results show our methods perform well while all the traditional methods break down.

中文翻译：

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给定分类数据的 RMSEA 的正确点估计量和置信区间

给定非正态连续数据的 RMSEA 估计通常基于均值调整 ( ) 或均值方差调整 ( ) 卡方统计量，但这些统计量的简单应用性能较差。Savalei 及其同事提供了一种更好的方法（BSL 方法）来使用 或 来推断 RMSEA。但是，BSL 方法仅适用于连续数据。对于分类数据，目前 RMSEA 推理仍然基于 或 的简单应用，但这种做法在连续数据下已经存在问题。在本文中，我们首先表明在未加权最小二乘法 (ULS) 下定义 RMSEA 比在加权最小二乘法 (WLS) 或对角加权最小二乘法 (DWLS) 下更有意义。然后，我们为 RMSEA 给定分类数据和 ULS 提出了正确的点估计量和置信区间。