Cross Validated Asked by L.sicilis on December 13, 2020

I’m currently trying to identify how to evaluate model fit with Bayesian SEM. I’ve been reading that the posterior predictive p-value can be used, with a p-value of approximately 0.5 indicating good model fit (Song and Lee 2012). This source also suggests residual analysis can be used for BSEMs.

I had two questions regarding this:

1.) Are there any additional fit indices or methods used to evaluate BSEMs?

2.) Does anyone know how to perform residual analysis with the blavaan package in R?

Source:

Song, X. and S. Lee. 2012. Basic and Advanced Bayesian Structural Equation Modeling. ISBN 978-0-470-66952-5.

1 - I would start with this article:

Garnier-Villarreal, M., & Jorgensen, T. D. (2019). Adapting fit indices for Bayesian structural equation modeling: Comparison to maximum likelihood. *Psychological Methods*. https://doi.org/10.1037/met0000224

If you need more:

Cain, M. K., & Zhang, Z. (2019). Fit for a Bayesian: An evaluation of PPP and DIC for structural equation modeling. *Structural Equation Modeling: A Multidisciplinary Journal, 26*(1), 39–50. https://doi.org/10.1080/10705511.2018.1490648

Asparouhov, T., & Muthén, B. O. (2019). *Advances in Bayesian model fit evaluation for structural equation models. Statmodel*. http://www.statmodel.com/download/BayesFit.pdf

Hoofs, H., van de Schoot, R., Jansen, N. W. H., & Kant, Ij. (2018). Evaluating model fit in Bayesian confirmatory factor analysis with large samples: Simulation study introducing the BRMSEA. *Educational and Psychological Measurement, 78*(4), 537–568. https://doi.org/10.1177/0013164417709314

2 - You can use `lavaan`

's `lavResiduals`

function, see an example using:

```
library(blavaan)
example(ppmc)
```

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