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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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2 Answers 2

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The short answer to your question is that yes, when sample sizes are small, Bayesian SEM (BSEM) is preferable to traditional SEM, though only when reasonable priors are used. Recently, it has been pointed out in many places (e.g., McNeish, 2016) that Bayesian methods generally are particularly sensitive to the specification of the prior distribution. I would certainly say that a sample size of $n = 120$ is small by SEM standards, so if you are to use BSEM, make sure you are able to justify your priors, and definitely avoid using the Mplus software defaults (e.g., see Smid & Winter, 2020 for more details). Also, I would suggest conducting a sensitivity analysis to assess the extent to which priors impact your results.

References

McNeish, Daniel. "On using Bayesian methods to address small sample problems." Structural Equation Modeling: A Multidisciplinary Journal 23.5 (2016): 750-773.

Smid, S. C., & Winter, S. D. (2020). Dangers of the defaults: A tutorial on the impact of default priors when using Bayesian SEM with small samples. Frontiers in Psychology, 11, 611963.

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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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