Is Bayesian structural equation modelling better than maximum likelihood with smaller sample sizes? Does using the bayesian estimator to complete SEM in Mplus mitigate some concerns with a limited sample size (n=120). I.e is this approach preferred over using the traditional ML estimator with associated p values?
 A: This question is very broad. It first of all really depends on the model you want to test, in which a higher complexity would decrease the validity of an ML-SEM model (but probably also of a BSEM model). I would say, as a starter, try both and experience/see which difference you get. To give you a gross insight in the debate between both you could read the following literature (as a start):


*

*Asparouhov, T., Muthén, B., & Morin, A. J. S. (2015). Bayesian
structural equation modeling with cross-loadings and residual
covariances: Comments on Stromeyer et al. Journal of Management,
41(6), 1561-1577. doi:10.1177/0149206315591075

*Barrett, P. (2007). Structural equation modelling: Adjudging model
fit. Personality and Individual Differences, 42(5), 815–824.
doi:10.1016/j.paid.2006.09.018

*Kaplan, D., & Depaoli, S. (2012). Bayesian structural equation
modeling. In R. Hoyle (Ed.), Handbook of structural equation modeling
(pp. 650–673). New York, NY: Guilford Press.

*Markland, D. (2005). The golden rule is that there are no golden
rules: A commentary on Paul Barrett's recommendations for reporting
model fit in structural equation modeling. Personality and Individual
Differences, 42(5), 851–858. doi:10.1016/j.paid.2006.09.023

*Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation
modeling: A more flexible representation of substantive theory.
Psychological Methods, 17(3), 313–335. doi:10.1037/a0026802

*Stromeyer, W. R., Miller, J. W., Sriramachandramurthy, R., &
DeMartino, R. (2015). The prowess and pitfalls of Bayesian structural
equation modeling: Important considerations for management research.
Journal of Management Research, 41(2), 491–520.

