# Reported Coefficients for Glmnet using Caret

I understand GLMnet standardizes the predictor variables by default before fitting the model.

After fitting, the computed regression coefficients are then destandardized to allow reporting in their natural metric:

https://stats.stackexchange.com/a/211390/114271

Is this the same for Caret using GLMnet? So if I get the coefficients for my final model for the best value of lambda by calling:

coef(mymodel$finalModel, mymodel$bestTune$lambda)  Are the coefficients related to standardized predictor variables or unstandarized predictor variables? For example, say I am fitting an model using glmnet in caret for: y = β0 + β1X1 + β2X2  and X1 is on a scale 0-1 but X2 is 1-100. To fit the model X1 and X2 would first be standardised to a mean of zero and a standard deviation of 1. Would the reported coefficients β1 and β2 be for the standardised variables or for the unstandardized variables when using the Caret wrapper for GLMnet? ## 1 Answer Caret will fit the final model using glmnet again, so it reports the coefficients in the same way as glmnet, which is in the scale of the original data: library(mlbench) library(caret) library(glmnet) data(BostonHousing) mymodel = train(medv ~ .,data=BostonHousing, method="glmnet",tuneLength=5,family="gaussian", trControl=trainControl(method="cv",number=3)) coef(mymodel$$finalModel, mymodel$$bestTune$lambda)

1
(Intercept)  35.320709389
crim         -0.103881511
zn            0.043895667
indus         0.003208220
chas1         2.711134571
nox         -16.888148979
rm            3.839322105
age           .
dis          -1.440898136
tax          -0.010852819
ptratio      -0.938477290
b             0.009195566
lstat        -0.521371464

gmodel = glmnet(x=as.matrix(BostonHousing[,-14]),y=BostonHousing[,14],
lambda=mymodel$$bestTune$$lambda)

s0
crim     -0.098276800
zn        0.041402890
indus     .
chas      2.680135523
nox     -16.309105862
rm        3.862803869
age       .
dis      -1.395580453