Bayesian SEM

Frequentist estimation of parameters in structural equation models requires large numbers of participants due to the large number parameters in even relatively simple SEMs. To cajole models toward convergence, modelers often constrain certain parameters to 0, or to equal other parameters – sometimes based on a priori theory, and sometimes based on criteria that could capitalize on chance.

Bayesian estimation of the parameters of complex interdependencies modeled in SEMs can yield valuable information even with small samples that might not converge by FIML, and posterior parameter densities can illuminate the structure of relations that may not be apparent from parameter and SE frequentist estimates.

I’ve collected below some literature both theoretical and practical regarding Bayesian Structural Equation Models.

  • An early (2005) chapter by David B. Dunson, Jesus Palomo, and Ken Bollen, Bayesian Structural Equation Modeling, gives a detailed explication of the math behind the matrix behind the SEM, pointing out all the parameters you might want to estimate. It’s dense, but there’s a fun example at the end.
  • For some theoretical background on BSEM that is geared toward practicality, check out the Mplus BSEM resource.
  • While you can use R and Jags to do your BSEM, if you’re already familiar with Mplus, just check out the user guide for a practical guide.

One comment

  1. Chuan-Peng Hu

    It seems that there is another paper also relevant:

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

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