I need to compare two SEM models, one for high performing firms and other for low performing firms, on the basis of its overall r-square value. Please advise how can I calculate the r-square value of the overall SEM model.
Please also suggest any other other method!
If you're looking at a SEM model, there should be a few things that you'll need to assess: First, you'll want to look at the Chi Square statistic that is provided. That is the overall examination of the SEM model. Unfortunately, this statistic is heavily reliant on sample size, so you'll likely reject the null hypothesis here (you actually want to fail to reject it). The other metrics that you'll want to examine are the CFI and the SRMSR. They should be above .95 and below .05 respectively. Alternatively, you can use two models and try to check for measurement invariance. The following readings should help with this:
Bentler, P.M. (1990). Comparative fit indices in structural equation models. Psychological
Bulletin, 107, 238-246.
Browne, M.W., MacCallum, R.C., Kim, C.T., Andersen, B.L., & Glaser, R. (2002).
When fit indices and residuals are incompatible. Psychological Methods, 7,
403-421.
If you're running this on MPlus, the Byrnes are very responsive to questions pertaining to SEM. You can find their lab page here:
http://byrneslab.net/teaching/sem/
I hope this helped!
Because you're explicitly comparing 2 different samples/groups (high/low performers), it is nonsensical to attempt any meaningful comparison of R2 across SEM models. That said, a fair alternative would be to conduct 2 separate, multigroup analyses: 1) Firstly, with "equality constraints" imposed across groups for the structural relations, then 2) Secondly, without "equality constraints" imposed (free estimation). Then, the difference (Δ) in R^2's (R^2 groupA11 -minus- R^2 group A.2) for your focal group of interest (non-referent group, e.g., "high performers") can be obtained between the two versions of the model (constrained vs. unconstrained), allowing you to make a statement about the 'decrement in %variance explained from imposing equality constraints between high/low performing compaies.
Far as readings go, I could recommend following two:
1) Bentler, P. M. (2006). EQS 6 structural equations program manual, AND
2) Ryu, E., & Cheong, J. (2017). Comparing Indirect Effects in Different Groups in Single-Group and Multi-Group Structural Equation Models. Frontiers in psychology, 8, 747.
I hope this may be of some help to you, and best of luck!
With kind regards and cordially yours,
Matthew J. Kerry
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