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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?

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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.
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