Hi all! I'm getting into BSEM approach and I am specially concerned about when it is recommended or not to use this model. I have tested a BSEM with a small sample obtaining excellent results, but the fit of the SEM with the same data gets briefly worse. I know that the Bayesian estimator is specially recommended when sample sizes are relatively small (just like mine), but does anyone know more about that? Any paper or reference on when to use BSEM/SEM? I am really concerned about whether I can trust my results, their implications, and also whether I can properly justify the use of this model. Any help would be more than welcomed. Thank you very much in advance!
Dear Zuleica Ruiz Alfonso
Since your sample size is relatively small thus I am concerned that once you use the covariance-based structrual equation modeling (CB-SEM) approach which is mainly based on maxium likelihood estimator (ML). Although this estimator is often referred to as a robust but in the background runs the analysis based on an assumption that the data follow the normal distribution, which I am in doubt if it is achieved or not. I suspect that it is not since the results diverge as you apply the (CB-SEM).
My suggestion is to apply the partial least square structural equation modeling (PLS-SEM) which does not require the data to fit any prior particular distribution.
The (PLS-SEM) can be applied within the R environment via the following packages:
1. semPLS
2. plspm
Here is a book that was written by the designer of the package to illustrate how to use it
https://www.gastonsanchez.com/PLS_Path_Modeling_with_R.pdf
Also, you can use the SmartPLS software, which is a very powerful software that is mainly dedicated to run the partial least square analysis.
Hi,
The Mplus BSEM dedicated website has both theoretical and applied papers. See below:
https://www.statmodel.com/BSEM.shtml
I guess you have already checked the website's documentation to fit your model. In that case, it's always good to read about Bayesian and classical stats. This is one of the best books out there on Bayesian inference: http://www.stat.columbia.edu/~gelman/book/
It is always a good idea to run a simulation (similar to your data) to assess both BSEM and SEM approaches. For small samples, models with strong priors (BSEM) will almost always outperform ML (SEM). I'm not sure how simple/complex your is your model. I guess it has weak priors. In this case it could be mainly due to the use of MCMC relative to Maximum Likelihood, as it is more efficient for complex problems (i.e. numerical integration fails whereas MCMC in theory in the long run converges). In standard conditions a BSEM with weak priors should lead to similar results that with SEM. But really a simulation is the better way to know all these things. Mplus runs simulations quite easily.
I personally almost always would fit a BSEM. Unless your sample is informative.
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