Ridge regression

Lightweight routine for ridge regression, fitted via a singular value decomposition. The penalty may be automatically determined by leave-one-out cross validation. The intercept term is unpenalized.

Usage

ridge(formula, data, penalty = "auto", ...)

# S3 method for class 'ridge'
fitted(object, ...)

# S3 method for class 'ridge'
coef(object, ...)

# S3 method for class 'ridge'
predict(object, newdata, ...)

Arguments

formula

A model formula; see formula. The intercept term is unpenalized; to fit a penalized intercept, remove the intercept and add your own to the design matrix.

data

An optional data frame or object in which to interpret the variables occurring in formula.

penalty

The ridge penalty. Must be a single numeric or the string "auto", in which case the penalty will be determined via leave-one-out cross validation to minimize the mean squared error.

...

Further arguments, passed on to model.frame() and model.matrix(). These must be provided to predict.ridge() as well, if used.

object

A fitted ridge() model.

newdata

A data frame containing the new data to predict

Value

An object of class ridge with components including:

• coef, a vector of coefficients.

• fitted, a vector of fitted values.

• penalty, the penalty value.

Methods (by generic)

• fitted(ridge): Fitted values

• coef(ridge): Coefficients

• predict(ridge): Predicted values

Examples

m_lm = lm(mpg ~ ., mtcars)
m_ridge = ridge(mpg ~ ., mtcars, penalty=1e3)
plot(fitted(m_lm), fitted(m_ridge), ylim=c(10, 30))
abline(a=0, b=1, col="red")