I am using AMOS-21 for the estimation of the model fit for a questionnaire. I have found the following values. Are these values enough and appropriate? Which of the following are important to present while reporting?
CMIN/df= 2.426
RMR= .05
GFI=.921
AGFI= .890
NFI= .951
TLI=.964
CFI=.970
RMSEA=.064
Your model fit indices look very good and quite acceptable. The most commonly reported important indices are CFI, RMSEA, SRMR and CMIN/df, where the last one is not a decision criteria in SEM. However, the specific results to be reported mostly depends on specific journal or other platform where you will reporting your results. You need to calculate the SRMR using the Plugin function in AMOS.
All the best.
Hello Shamas,
1) Forget GFI and AGFI, they are outdated
2) Forget the ratio of chisquare and df. It makes to sense and never has
3) With regard to the rest, there is quite a debate whether using fit indices are useful at all. I am on the side of the argument that you use the statistical chi-square test and omit the fit indices (although I tend to report the CFI and RMSEA as reviewers want to see them.
The problem with the fit indices is that they measure the degree of deviations between the empirical covariances and the covariances implied by the model. The "degree" of similarity however, does not reflect the degree of correctness. Hence you can have very close matches albeit the model being complete nonsense. The chisquare test, has a clear statistical theory underlying it. If the test is significant, it means that there are deviations greater than those expected by pure chance. This MAY mean that the model is slightly wrong, vastly wrong or that something with the underlying data assumptions is wrong. At any rate, it provides the basis to understand/learn how the model can be improved.
I don't know your test but would bet (as in most cases, also mine) that it is significant. No reason for despair, just learn what's wrong.
For more info see the following thread
https://www.researchgate.net/post/Dear_scholars_how_to_design_a_Structural_Equation_Modeling_surveys
and papers
Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21, 1086-1120. doi:10.1016/j.leaqua.2010.10.010
McIntosh, C. (2007). Rethinking fit assessment in structural equation modeling: A commentary and elaboration on barrett (2007). Personality and Individual Differences, 42(5), 859-867.
Thoemmes, F., Rosseel, Y., & Textor, J. (2018). Local fit evaluation of structural equation models using graphical criteria. Psychological Methods, 23(1), 27-41. doi:10.1037/met0000147
Hayduk, L. A. (2014). Shame for disrespecting evidence: The personal consequences of insufficient respect for structural equation model testing. BMC Medical Research Methodology, 14(1), 124-124. doi:10.1186/1471-2288-14-124
Best,
--Holger
As the colleagues already described, your model seems good.
I would like to complete the suggestions already done. Here is a "checklist" for best practices. It is applied to leadership but could be useful.
Crawford, J. A., & Kelder, J. A. (2019). Do we measure leadership effectively? Articulating and evaluating scale development psychometrics for best practice. Leadership Quarterly, 30(1), 133–144. https://doi.org/10.1016/j.leaqua.2018.07.001
Best,
Amalia
Thank you Holger, Khan and Amalia for detailed and logical explanation and suggesting me some documents to read.
Dear Amalia Raquel Pérez Nebra ,
just for the record. I doubt that the model is "good" and recommended the chi square test as a guideline. I Shamas Suleman Arshad is interested, we can run through his data and model and try to improve it. A problematic model is no eternal bad fate and one can do something about it. Unfortunately, like so many, he uses AMOS which represents the gate to eternal bad fate :)
The paper you recommend is interesting, given that it is published in Leadership Quarterly--whose editor, John Antonakis, has strong oppositions against fit indices (see his paper that I cited). Crawford & Kelder repeat the same nonsense that is repeated for decades (e.g., the test is sensitive for sample size). Yes, it is a test and this should be sensitive (which is called statistical power). Second the true statement that "high N + trivial misspecification = significant misfit" is turned around in "high N + sign. misfit = trivial misspecification". This is called conversion fallacy and it is a logical error.
Yes, often a significant chi square will mean nothing, however, likewise often it may mean a fundamental misspecification of the model. The problem: you don't know which is the case in a current situation.
The problem with the fit indices, finally, run much deeper and reflect the equation of a causal model with a descriptive model. From this perspective, it is deemed enough to have a model which is "good" (to use your term) to describe the data. This is wrong. The goal behind causal modeling is to get the structure right because otherwise you will have biased parameter estimates up to completely nonsensical estimates which mean nothing. For instance, the model y --> x describes the data (i.e., cov(X,Y) ) very good. But if the true model is x-->y what is this fit worth? Model fit is a tool not a goal.
Yes, modeling is hard work and often we don't get it right (perhaps never?). But this no excuse to not at least try it. I also have nothing against publishing failing models. The problem is to denote a model as "good" when it is not. This leads to a conservation bias of our scientific knowledge.
My 2 c
All the best,
-- Holger
The fit indices look promising. The model has a good fit based on these indices. Just add P- Value for RMSEA and also quote ECVI.
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