# Sensitivity of BF Model Comparison for (Multi-) Collinearity

Hi all,

how sensitive is a model comparison using BF for (multi-) collinearity? Is there any mechanism within bayesian model comparison that is sensitive to collinearity? If so, is it OK to choose models with high BF and high collinearity?

Best wishes,

Ulrich Dettweiler & Christoph Becker

## Comments

Hi,

Perhaps you can explain what you mean with being 'sensitive to collinearity'?

As far as I'm aware, there is no difference between how Bayesian and classical statistics deal with correlated predictors. If model X has a high Bf relative to model Y, then the data is more likely under X than Y—collinearity or no.

But the trouble with collinearity is that you may end up with multiple models under which the data is about equally likely. For example, if A and B are two highly correlated factors, then a model with only A may do well relative to the null, as may the model with only B. But the model with both A and B will not do better than the models with only A or B, and so you cannot say which predictor is better, A or B.

Does that make sense? Or is that not what you mean?

Cheers,

Sebastiaan

There's much bigger issues in the world, I know. But I first have to take care of the world I know.

cogsci.nl/smathot

Hi Sebastian,

thanks for your reply. For our current analyses, this is a sufficient answer.

Best, Ulrich