Bayesian predictive projection for variable selection

arthur_albuquerque:

In the same post, Aki suggested:

You can use it with multiple imputation by repeating the projection and variable selection for each imputed data set and combine the results in the end (this is the usual multiple imputation approach)

I wonder how one would “combine the results in the end”.

If the selected variables are all the same with different imputed datasets, then that’s it. If the selected variables are different with different imputed datasets, I would use majority voting and report the variation due to missing data uncertainty.

arthur_albuquerque:

There is an opened issue about this in GitHub, but no progress whatsoever.

Changing projpred to support output of brm_multiple() is a big task, and unfortunately we have limited resources. I’d be happy to learn more about cases where the simpler approach would not be sufficient and then we could first experiment how much difference there would be if the search in the projpred would support brm_multiple() output.

For the priors, recently we have been using R2D2 type priors more often than horsehoe especially with normal data models, see, e.g. https://users.aalto.fi/\~ave/casestudies/VariableSelection/student.html