In a structural equation model with relative variables (for example, percentage change from the previous week), does it make sense to use the chi-square/df value as a measurement for the goodness of fit (requested threshold for example 2-3)? Or does this not make sense, because the expected values deviate too much from the observed values due to relative data, which makes the chi-square value too large?
You should definitely post this question on the SEMNET listserv--you would get some very interesting responses 😂. (Just kidding, don't do it unless you're ready for some substantial drama--different SEM experts tend to have very different opinions on this topic and there have been decades-long discussions about this issue on SEMNET. In case you're interested, search the SEMNET archives.)
My personal opinion is that it is good to strive for a low and "non-significant" chi-square, but in the end all cut-off values are rather arbitrary, whether it be alpha levels or chi-square/df ratios.
Hello Philipp,
For awhile, making up new fit indices was seemingly a thriving cottage industry in the SEM world, which is part of the admonition in Christian Geiser's answer that not everyone will agree with you (or each other), no matter what you select.
However, do have a look at this very readable overview of a lot of the common fit indices; it may help you to understand better the reasons for selecting a specific index: http://davidakenny.net/cm/fit.htm
Good luck with your work.
Three groups of goodness of fit (GIF) measures are available: absolute fit indices, incremental fit indices, and parsimony fit indices. However, it is not expected that all of these would be used or reported. This rather depends on the purpose for which the work is intended. For example, different journals may have different requirements regarding what indices to be reported.
Absolute Fit Indices assess how well a researcher’s theoretical model fits the observed data they have collected. The only statistically based measure of fit is that of the Likelihood Ratio Test, better known as the “Chi-square” (CMIN) statistic and its associated “probability” or p-value - which should not be statistically significant if there is a good model fit. However, the x² statistic is very sensitive to sample size and is no longer relied upon as a basis for acceptance or rejection (Schlermelleh-Engel et al. 2003, Vandenberg 2006).
As a result, the use of multiple fit indexes has developed to provide a more holistic view of GOF, taking account not only of sample size but also of model complexity and other relevant issues of the study.
- Schermelleh-Engel, K., Moosbrugger, H., and Müller, H. (2003), “Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodnessof-Fit Measures”, Methods of Psychological Research Online, Vol. 8, No. 2, pp.23-74.
- Vandenberg, R. J. (2006), “Statistical and Methodological Myths and Urban Legends”, Organizational Research Methods, Vol. 9, No. 2, pp. 194-201.
All the best,
Khan
Thank you very much for the helpful answers! I will rather not post the question on SEMNET :D
And the answers correspond to my assumption that it depends. Since in my research project the CFI, TLI, RMSEA, and SRMR completely fulfill the requirements and I work with real purchase data (over 8000 data rows), I am a bit reassured about the Chi² value. Thanks!
Best
Philipp
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Techniques
- Structural Equation Modeling