Both regularization methods, ridge regression and LASSO, are implemented in the glmnet R package. The workhorse of the glmnet package is the eponymous glmnet() function. Type ?glmnet to review the help page on that function. The glmnet() function basically fits a generalized linear model via penalized maximum likelihood. The alpha argument is the so-called mixing parameter, with \(0 \le \alpha \le 1\). If \(\alpha = 1\) the penalty term corresponds to the LASSO regularized regression and if \(\alpha = 0\) the penalty term corresponds to the ridge regularized regression. Values of \(\alpha\) between \(0\) and \(1\) are related to the elastic net regularization, which is discussed elsewhere.

It is important to realize that the degree of regularization depends on the regularization parameter \(\lambda\). Thus, it is useful to evaluate the regression function for a sequence of \(\lambda\). By default the glmnet() evaluates a sequence of 100 \(\lambda\) values (note that in cases where no change occurs the function stops earlier). The number of \(\lambda\) may be set by the nlambda argument and the sequence of \(\lambda\) may be specified by the lambda argument to glmnet() function call.

The glmnet() function does not work with the formula notation, but uses matrices instead. At the begin of the section we assigned the response vector and the model matrix of the training set and the test set to the variables y.train, y.test, X.train, and y.train, respectively.

# load processed data set from previous section
# load helper functions from previous section
# load list object from previous section

Ridge regression in R

We start with the ridge regression (alpha = 0) and plot the results.

m.ridge <- glmnet(X.train, y.train, alpha=0)
# plot model coefficients vs. shrinkage parameter lambda
plot(m.ridge, xvar = "lambda", label = TRUE)