Collinearity and Bayesian modeling

#1

Hi!
I have a very simple question regarding collinearity and Bayesian modeling:

In frequentist modeling, when I’m testing for a moderator effect assessing the coefficients of the regression Y ~ X * M, the coefficient of the product term (X:M) may present an inflated p-value, due to its correlation with X and M. For a particular example, I would like to compare the equivalent frequentist and Bayesian models, using brms package.

So, I would like to know if the 95%CI of the Bayesian model can also be affected by collinearity issues. In the affirmative case, I would like to know whether the CI commonly get inflated or deflated (or none of these situations), and if there are recommended Bayesian procedures to obtain more trustable CI.

In particular, I would like to know if the Bayesian model indicates the significance of that coefficient with a 95% CI that does not include 0, should I worry about further Bayesian procedures to obtain more trustable CI?

Kind regards,
csm

#2

The collinearity causes the same problem when examining marginals in frequentist and Bayesian framework. See first this case study https://avehtari.github.io/modelselection/collinear.html. You can find more examples at https://avehtari.github.io/modelselection/. You need to look at the joint distribution or predictions. The above mentioned examples illustrate one way to find a smallest set of predictors which give similar predictive accuracy as all the predictors.

3 Likes