Normal theory full-information maximum likelihood (FIML) is a common estimation technique for incomplete data in structural equation modeling (SEM). However, it is not commonly known that approximate fit indices (AFIs) can be distorted, relative to their complete data counterparts, when FIML is used to handle missing data. In this article, we show that two most popular AFIs, the root-mean-square error of approximation (RMSEA) and the comparative fit index (CFI) often approach different population values under FIML estimation when missing data are present. By deriving the FIML fit function for incomplete data and showing that it is different from the usual maximum likelihood (ML) fit function for complete data, we provide a mathematical explanation for this phenomenon. We also present several analytic examples as well as the results of two large sample simulation studies to illustrate how AFIs change with missing data.

中文翻译：

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在正态理论全信息最大似然下检查缺失数据对 RMSEA 和 CFI 的影响

正态理论全信息最大似然 (FIML) 是结构方程建模 (SEM) 中不完整数据的常用估计技术。然而，当使用 FIML 处理缺失数据时，近似拟合指数 (AFI) 相对于其完整数据对应物可能会失真，这一点并不为人所知。在本文中，我们展示了两个最流行的 AFI，即近似均方根误差 (RMSEA) 和比较拟合指数 (CFI)，当存在缺失数据时，通常会在 FIML 估计下接近不同的总体值。通过推导出不完整数据的 FIML 拟合函数并表明它与完整数据的通常最大似然 (ML) 拟合函数不同，我们为这种现象提供了数学解释。