Bayes factor favours full model while the credible intervals of the predictor of interest include 0

Modeling
1

Hello,
I have compared two models with the same priors using the Bayes factor in brms.

# Settings for BRMS
niter=20000
nchains=4
adaptdeltas=0.9

h4<- brm(formula= GC_InabilStop ~ b_PrevSearch  + Compulsivity+Apathy+DeprAnx+SocialAnx+Age+Gender+mo(EducationLevel),
           data=df.h4,save_all_pars = TRUE, family='gaussian',iter=niter,chains=nchains,cores=nchains,control=list(adapt_delta=adaptdeltas))

while the other model is reduced removing b_PrevSearch which is the predictor of interest for the experiment.

# Settings for BRMS
niter=20000
nchains=4
adaptdeltas=0.9

h4.null<- brm(formula= GC_InabilStop ~  Compulsivity+Apathy+DeprAnx+SocialAnx+Age+Gender+mo(EducationLevel),
           data=df.h4,save_all_pars = TRUE, family='gaussian',iter=niter,chains=nchains,cores=nchains,control=list(adapt_delta=adaptdeltas))

The BF is 78 in favour of the model that includes the predictor of interest. However, credible intervals of the predictor of interest include zero.
How do i interpret the results?

1 Like
2

In your brm calls I don’t see prior definitions, so it seems you are possible using some improper flat priors and veru wide priors, so I given the information shown, I would not trust the BF estimate at all.

If the predictors are correlated, the (usual length) posterior credible intervals can overlap zero. See e.g. case studies Bayesian version of Does model averaging make sense? and Bayesian Logistic Regression with rstanarm

2 Likes
3

Thank you very much for your answer!

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