Question about Bayesian ANCOVA - fixed factor vs covariate?
Hi all,
I was wondering whether someone could help me with Bayesian ANCOVA.
If I want to test a group difference on a certain outcome, I can add Group as a fixed factor to my ANCOVA, and add some covariates of interest under covariates.
As far as I know, in a 'regular ANCOVA' in SPSS, one can also dummy-code the Group variable and add this as a covariate instead. However, p-values should remain the same, regardless of how one adds the variables (and the results should be the same as multiple linear regression analysis).
However, when I do Bayesian ANCOVA in JASP, my BF10 seems to differ depending on whether I add Group as covariate or as fixed factor. Adding Group as covariate gives the same results as Bayesian linear regression, whereas adding it as fixed factor gives different results. Even when I specify the same values for the priors, and only when there are multiple covariates in the model.
Could someone perhaps explain me where this difference arises from? And/or point me towards some literature on this? I am particularly wondering whether you would recommend me to test group differences with Bayesian ANCOVA with Group added as fixed factor, or with Bayesian linear regression (with Group added as dummy variable).
(Hope this makes sense. Apologies if this question has been asked previously.)
Thanks!
Rik
Comments
Hi Rik,
In the current Bayesian implementation it is problematic to add Group as a covariate; it is a factor, not a covariate. You can feed it as a covariate to the Bayesian linear regression setup, but only because JASP does not realize that Group is really a nominal variable. One reason for the complication is that the prior setup for predictors in linear regression uses a scaling to achieve invariance (e.g., whether the predictor is in grams or kilograms) and this scaling is arbitrary for factors.
Cheers,
E.J.