Abstract: 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.

Key words: structural equation model, fit indices, testing, cutoff value