# Bayesian regression coefficients

Hi folks

In a scenario that I run a Bayes linear regression analysis adding say 8 predictors. The analysis may come up with the best regression model incorporating 4 predictors. However, regression coefficients are given for all 8 variables. Should I use these for the regression equation or would it be prudent to re-run the regression just including the best models 4 predictors and then use those regression coefficients?

Cheers

Mark

## Comments

Hi Mark,

When you tick "Posterior Summary", you can select "Best model" -- this should then present the posterior summaries only for the model with 4 predictors.

Cheers,

E.J.

Thanks EJ

missed that one

Mark

Hi EJ. Can I ask about Bayesian linear regression. I am running this for models with 8-10 predictors. When I use the beta-binomial (1,1) prior, my results have the highest BF for the best predictive model (ie. highest R2) but the highest probability is for a different model. (When I run it when a uniform prior this is not the case). The r scale is 0.5. I have read your most recent preprint about how the b-b(1,1). My question is regarding reporting this in results - do I report both the best predictive model and the highest probability model, or have I done this analysis wrong and my priors are biasing the results?

Dear BrittJane,

The model with the highest R2 is *not* the model that predicts best: it is the model with the best fit. This is always the model with all predictors included. So for model selection, R2 is not very informative. Predictive ability is given by the BFs. The model order is based on posterior probability, so if you are not using the uniform assignment you might find that, because of differences in prior model probability, the best predicting model (the one with the best BF against any other model) is not the one in which you should have most posterior belief. You might want to report your results both under the uniform prior and the beta prior -- if the outcome is very different this suggest you'll have to interpret the result with caution.

Cheers,

E.J.