When using RFE in linear regression and logistic regression, do we one-hot encode the features (K levels and K dummy features) or dummy-encode the features (K levels and K-1 dummy features leaving one out).
As per a comment by @Matthew Drury in an answer (URL below), one hot encoding is applied for a regularized linear model and for unregularized linear model dummy encoding. My doubt is what type of encoding when using RFE without any L1/L2 penalties.
My understanding is since in RFE some features gets eliminated so if for a categorical variable with say 4 levels we do dummy encoding and have 3 features/levels in model & RFE eliminated 1, we will only have 2 features/levels left and the interpretation of its coefficient would not make sense in absence of the one level which was left out as reference.
Whereas if we have done one-hot encoding and RFE considers 2 features as important and eliminates other 2 then we can very well judge/interpret the coefficients or importance of 2 features RFE keeps.
So question which type of encoding is needed to be done when using RFE with linear and logistic regression?