Interaction terms and non-linear additive effects in projpred

The intuition behind projpred is amazing and the tutorials walkin through the steps are extremely informative. Thank you very much @avehtari @jpiironen

I had a question on including interaction terms and non - linear effects for continous predictors.
Interactions - If I have a priori reason to believe that two effects interact, should I include this in the calculation of tau? If these are categorical predictors, this would amount to the total number of parameters to estimate this interaction?

Non - linear - Non linearity of continous predictors is quite common esp in medical data and binning/dichotmizing often looses a lot of information. Instead, I’d like to model these as restricted cubic splines. I can’t say how many knots but typically suggested are 4 - 5. Would that mean, for each continous covariate I model as a restricted cubic spline, I would need to incorporate 4 for the calculation of tau? (assuming I have prior reason to believe that all the covariates I’m modeling as splines are related to the outcome).

Thank you and looking forward to hearing your insights on this!

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Thanks for compliments.

Prior and projection are separate issues.

For prior for interactions and splines, see

For projpred we have support for interactions and splines hopefully after the summer. The method doesn’t change, we just need to add support for automatically grouping the design matrix columns based on the formula (and to check that the projection is identifiable).

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Thank you very much for the response and the reference!