Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit statistic. While a noncentrality parameter estimate is well suited for quantifying the amount of systematic error, the complex weighting function involved in its calculation makes indices derived from it challenging to interpret. Moreover, noncentrality-parameter-based fit indices yield systematically different values, depending on the indicators’ level of measurement. For instance, RMSEA and CFI yield more favorable fit indices for models with categorical as compared to metric variables under otherwise identical conditions. In the present article, approaches for obtaining an approximation discrepancy estimate that is independent from any specific weighting function are considered. From these unweighted approximation error estimates, fit indices analogous to RMSEA and CFI are calculated and their finite sample properties are investigated using simulation studies. The results illustrate that the new fit indices consistently estimate their true value which, in contrast to other fit indices, is the same value for metric and categorical variables. Advantages with respect to interpretability are discussed and cutoff criteria for the new indices are considered.

拟合指数经常用于评估潜在变量模型的拟合优度。大多数突出的拟合指数，例如均方根近似误差 (RMSEA) 或比较拟合指数 (CFI)，都是基于从模型拟合统计派生的非中心参数估计。虽然非中心参数估计非常适合量化系统误差的数量，但其计算中涉及的复杂加权函数使得从中得出的指标难以解释。此外，基于非中心参数的拟合指数会产生系统性不同的值，具体取决于指标的测量水平。例如，与其他相同条件下的度量变量相比，RMSEA 和 CFI 为具有分类的模型产生更有利的拟合指数。在本文中，考虑了获得独立于任何特定加权函数的近似差异估计的方法。根据这些未加权的近似误差估计，计算类似于 RMSEA 和 CFI 的拟合指数，并使用模拟研究研究它们的有限样本属性。结果表明，新的拟合指数始终如一地估计它们的真实值，与其他拟合指数相比，度量和分类变量的值相同。讨论了可解释性方面的优势，并考虑了新指数的截止标准。计算类似于 RMSEA 和 CFI 的拟合指数，并使用模拟研究研究它们的有限样本属性。结果表明，新的拟合指数始终如一地估计它们的真实值，与其他拟合指数相比，度量和分类变量的值相同。讨论了可解释性方面的优势，并考虑了新指数的截止标准。计算类似于 RMSEA 和 CFI 的拟合指数，并使用模拟研究研究它们的有限样本属性。结果表明，新的拟合指数始终如一地估计它们的真实值，与其他拟合指数相比，度量和分类变量的值相同。讨论了可解释性方面的优势，并考虑了新指数的截止标准。