proc gmlselect + elastic net without feature selection

[csetzkorn]

is it possible to use:

selection=ELASTICNET ...

in PROC GLMSELECT so that no feature selection is performed (i.e. all featured are 'forced' into model)?

[Rick_SAS]

I don't think so. If you want all variables in the model, use SELECTION=NONE to get the OLS estimates. But I don't think you can get the elastic net estimates for the full model.

[csetzkorn]

OK thanks. Wanted to use elastic net as there are correlations between at least 2 variables ... Do you know if, in this case, OLS estimates could still be used purely for prediction rather than interpretation? Thanks.

[Rick_SAS]

It depends on how correlated the variables are. Strong correlations can result in large standard errors of the OLS estimates due to the X`X matrix being ill-conditioned. You can use the VIF option in PROC REG to examine whether the X`X matrix is ill-conditioned.

If the VIF indicates strong correlations, you might try ridged regression in PROC REG, which is close to the Elastic Net in that it includes the quadratic penalty term. That would probably permit the closest comparison. 

For other options for regression of correlated variables, see a comparison of PLS and PCR (principal component regression).

[csetzkorn]

Thanks. Yes ridge is an option.

[PaigeMiller]

I would say that PLS is superior to PCR in the case of correlated X variables, because PCR may find components that are not good predictors of the Y variable(s), while PLS will find components of X that predict Y well (if such components exist). Studies show that PLS does well with correlated variables, compared to other methods such as stepwise regression, ridge regression and even PCR.

https://amstat.tandfonline.com/doi/abs/10.1080/00401706.1993.10485033