Bentler P M
Department of Psychology, University of California, Los Angeles 90024-1563.
Psychol Bull. 1990 Mar;107(2):238-46. doi: 10.1037/0033-2909.107.2.238.
Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statistics for evaluating the fit of a structural model. A drawback of existing indexes is that they estimate no known population parameters. A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models. Two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes. CFI avoids the underestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI). FI is a linear function of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extreme underestimation and overestimation often found in NNFI. Asymptotically, CFI, FI, NFI, and a new index developed by Bollen are equivalent measures of comparative fit, whereas NNFI measures relative fit by comparing noncentrality per degree of freedom. All of the indexes are generalized to permit use of Wald and Lagrange multiplier statistics. An example illustrates the behavior of these indexes under conditions of correct specification and misspecification. The new fit indexes perform very well at all sample sizes.
标准化和非标准化拟合指数经常被用作卡方统计量的辅助手段，以评估结构模型的拟合度。现有指数的一个缺点是它们不估计任何已知的总体参数。本文提出了一个新的系数，用于总结两个嵌套模型非中心参数的相对减少量。该系数的两个估计量产生了新的标准化（CFI）和非标准化（FI）拟合指数。CFI避免了在小样本中经常出现的对拟合度的低估，而Bentler和Bonett（1980）的标准化拟合指数（NFI）则经常出现这种情况。FI是Bentler和Bonett的非标准化拟合指数（NNFI）的线性函数，避免了NNFI中经常出现的极端低估和高估。渐近地，CFI、FI、NFI以及Bollen开发的一个新指数是比较拟合的等效度量，而NNFI通过比较每自由度的非中心性来度量相对拟合度。所有这些指数都被推广以允许使用Wald和拉格朗日乘数统计量。一个例子说明了这些指数在正确设定和错误设定条件下的表现。新的拟合指数在所有样本量下都表现得非常好。
