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The good news where I am is that researchers are doing less stepwise covariate selection now that I've introduced penalized regression. The bad news is that researchers want to use elastic-net regression for variable selection, then use that covariate choice to build an unpenalized model.

Can someone suggest a reference summarizing why this is a bad idea? I can make arguments as to why I wouldn't want to do this ---

  • these are the maximum-likelihood covariates for regression with a certain penalty term, but are not in any sense optimal for a model without a penalty term;

  • the new model fixes some of the coefficient values chosen by the penalized model -- the ones equal to zero -- and then allows the others to vary;

  • you lose the regularization that the penalized model gives you, so the unpenalized model can still bias coefficients high, and tend to overfit;

  • and, of course, the p values and CIs are off, as there was a whole model-selection process before the final regression model.

But I'd like to be better educated on this, and be better able to help my colleagues.

Or, is this process in fact a reasonable thing to do?

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