# Selected variables varies depending on whether or not standardization is in lasso regression (glmnet)

The paper often suggests both standardized and unstandardized coefficients in the lasso model (glmnet in R).

However, when I run glmnet, the selected variable is different depending on standardized = True and False.

If I get standardized cofficients from six variables in lasso model, how do I get unstandardized coffiencients from those six variables?

Simply selecting standardized = FALSE in glmnet showed different variables.

(I got 6 variables from standardize = TRUE, but I got 2 variables from standardize = FALSE)

• If standardize=T then glmnet will standardize the values during optimization, but it will return the results on the original scale. Post some data with an example. – user2974951 Sep 6 '19 at 7:42
• Main point is that for whatever data set, glmnet estimates a single hyperparameter $\lambda$ value. Therefore, usually standartization is expected and is enabled by default, since we want that one value of $\lambda$ to give an appropriate penalty for all variables simultaneously. On the other hand, Adaptive LASSO solves this problem differently -- here re-weighting the $\hat\lambda_j := \hat w_j \lambda_j, \forall j$ allows for standardized = F since the weights now also account for the scale, among other important qualities. – Nutle Sep 9 '19 at 15:29