# [R] lasso and ridge regression

Gafar Matanmi Oyeyemi gmoyeyemi at gmail.com
Tue Oct 31 07:02:40 CET 2017

```Dear All

The problem is about regularization methods in multiple regression when the
independent variables are collinear. A modified regularization method with
two tuning parameters l1 and l2 and their product l1*l2 (Lambda 1 and
Lambda 2) such that l1 takes care of ridge property and l2 takes care of
LASSO property is proposed

The proposed method is given
<https://i.stack.imgur.com/Ta8FR.jpg>

The extract of the code used is reproduced as follows;

cv.ridge<- glmnet(x, y, family="gaussian", alpha=0,
lambda=lambda1, standardize=TRUE)
cv.lasso<- glmnet(x, y, family="gaussian", alpha=1,
lambda=lambda2, standardize=TRUE)
##weight
a=1/abs(matrix(coef(cv.ridge, s=lambda1)[, 1][2:(ncol(x)+1)]
))^1
b=1/abs(matrix(coef(cv.lasso, s=lambda2)[, 1][2:(ncol(x)+1)]
))^1
c=a*b
w4 <-a+b+c
w4[w4[,1] == Inf] <- 9
# Fit modified procedure
fit<- glmnet(x, y, family="gaussian",
alpha=alpha,lambda=lambda1+lambda2, penalty.factor=w4)

The question is; Does the code address the modified procedure in as shown
in the equation? If not, suggestions are please welcome.

Thanks

--
OYEYEMI, Gafar Matanmi (Ph.D)