# LASSO - normalization of response variable needed?

I wonder whether the response variable needs to be normalized before LASSO estimation (I am using the lars package in R to perform LASSO estimation). My guess is that only right-hand side variables need to be normalized, is this correct?

For the sake of interpretation, I would prefer to only normalize right-hand side variables and leave out the response variable. If this is fine, I guess I need to normalize the data myself as the argument 'normalize' in the lars package performs normalization on all variables including the response variable - at least I believe so.

Thanks for help!

It doesn't seem that lars normalizes the response variable, anyway. Examine the code by loading the package and typing "lars" (without quotes or parentheses) at the R prompt. As I read the code, if "normalize=TRUE" then only the x (predictor/"right-hand") variables are normalized. The y (response) variable is untouched. I suspect that the statement in the documentation that "each variable is standardized to have unit L2 norm" was only meant to apply to the x values.
• As an FYI, glment does standardize $y$ when doing linear regression (elastic net). – Matthew Drury Jun 8 '15 at 17:14