The purpose of this study was to evaluate the sensitivity of selected fit index statistics in determining model fit in structural equation modeling (SEM). The results indicated a large dependency on correlation magnitude of the input correlation matrix, with mixed results when the correlation magnitudes were low and a primary indication of good model fit. This was due to the default SEM method of Maximum Likelihood that assumes unstandardized correlation values. However, this warning is not well-known, and is only obscurely mentioned in some textbooks. Many SEM computer software programs do not give appropriate error indications that the results are unsubstantiated when standardized correlation values are provided.
Rose, S. A., Markman, B., & Sawilowsky, S. (2017). Limitations in the systematic analysis of structural equation model fit indices. Journal of Modern Applied Statistical Methods, 16(1), 69-85. doi: 10.22237/jmasm/1493597040