检验的临界值：真伪差距多大才能辨别？——评《不同条件下拟合指数的表现及临界值的选择》

Cutoff Values for Testing: How Great the Difference between the True and False Makes Them Distinguishable?

Hu 和Bentler（1998，1999）通过模拟研究推荐结构方程模型拟合指数临界值后，受到不少批评和质疑。此后有关拟合指数的研究重点不再是推出新的临界值标准。郭庆科等人的文章《不同条件下拟合指数的表现及临界值的选择》，仿照Hu和Bentler的做法，通过模拟研究推荐新的拟合指数临界值标准。本文旨在揭示这种做法的错误所在。用简单的Z检验，说明检验的临界值是不能通过模拟研究确定的。通过将一个特定真模型的众多错误模型分类，说明结构方程分析中真模型与错误模型差距的多样性，无法通过模拟一对真伪模型来代表。讨论了统计检验的本质和确定临界值的逻辑，还谈到应当从哪些角度检验和评价结构方程模型。

Subsequent to Hu and Bentler’s (1998， 1999) simulation studies and proposed cutoff criteria for goodness of fit indices in structural equation analyses， several critiques have been published challenging their research design and results. No more new cutoff criteria for fit indices have been proposed since then. However， the recent paper in this journal titled “Performance of fit indices in different conditions and the selection of cut-off values” (in Chinese) imitated Hu and Bentler’s procedures in search for new cut-off values for goodness of fit indices. The purpose of this paper is to explain why this kind of research design is wrong. By using the simple Z-test analogy， we showed that the cutoff values for testing should never be determined through simulation studies. Classifications were proposed for the various misspecified models against a certain true model in structural equation analyses to demonstrate the variety of differences between the true model and the misspecified models. It is obvious that the cutoff values obtained through simulation studies depend on the magnitude of the difference between the true and the misspecified models being chosen， ignoring the variety of the differences involved. The rationales of statistical testing and cutoff value setting were discussed. Guidelines on testing and evaluating a fitted model or alternative models were deliberated.