ABSTRACT

Holding model misspecification constant, the behavior of fit indices depends on factors such as the number of variables being modeled (model size), and the average observed correlation (magnitude of factor loadings or measurement quality). We examine by simulation the interplay of these factors with sample size in CFA models. When a biased estimator of the fit index is used (CFI, TLI, or GFI), the behavior of the sample indices depends on sample size, rendering establishing cutoff values impossible. When an unbiased estimator is used (SRMR, or RMSEA) the behavior of the indices matches that of the population parameter and depends on the average R² of the observed variables (communality); and for the RMSEA, also on model size. The use of the unbiased SRMR with a cutoff value adjusted by R² is recommended as it enables assessing the degree of a model misspecification across model size, sample size, and measurement quality.

摘要

保持模型错误指定不变，拟合指数的行为取决于诸如被建模变量的数量（模型大小）和平均观察到的相关性（因子负载的大小或测量质量）等因素。我们通过模拟检查这些因素与 CFA 模型中样本量的相互作用。当使用拟合指数的有偏估计量（CFI、TLI 或 GFI）时，样本指数的行为取决于样本大小，从而无法确定截止值。当使用无偏估计量（SRMR 或 RMSEA）时，指数的行为与总体参数的行为相匹配，并取决于观察到的变量（社区）的平均R ²；对于 RMSEA，还有模型尺寸。使用截止值调整的无偏 SRMR推荐使用R ²，因为它可以跨模型大小、样本大小和测量质量评估模型错误指定的程度。