MASS (version 7.3-36)

lm.ridge: Ridge Regression

Description

Fit a linear model by ridge regression.

Usage

lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
         x = FALSE, y = FALSE, contrasts = NULL, ...)

Arguments

formula

a formula expression as for regression models, of the form response ~ predictors. See the documentation of formula for other details. offset terms are allowed.

data

an optional data frame in which to interpret the variables occurring in formula.

subset

expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.

na.action

a function to filter missing data.

lambda

A scalar or vector of ridge constants.

model

should the model frame be returned? Not implemented.

x

should the design matrix be returned? Not implemented.

y

should the response be returned? Not implemented.

contrasts

a list of contrasts to be used for some or all of factor terms in the formula. See the contrasts.arg of model.matrix.default.

...

additional arguments to lm.fit.

Value

• A list with components
• coef
  matrix of coefficients, one row for each value of lambda. Note that these are not on the original scale and are for use by the coef method.
• scales
  scalings used on the X matrix.
• Inter
  was intercept included?
• lambda
  vector of lambda values
• ym
  mean of y
• xm
  column means of x matrix
• GCV
  vector of GCV values
• kHKB
  HKB estimate of the ridge constant.
• kLW
  L-W estimate of the ridge constant.

Details

If an intercept is present in the model, its coefficient is not penalized. (If you want to penalize an intercept, put in your own constant term and remove the intercept.)

References

Brown, P. J. (1994) Measurement, Regression and Calibration Oxford.

See Also

lm

Examples

longley # not the same as the S-PLUS dataset
names(longley)[1] <- "y"
lm.ridge(y ~ ., longley)
plot(lm.ridge(y ~ ., longley,
              lambda = seq(0,0.1,0.001)))
select(lm.ridge(y ~ ., longley,
               lambda = seq(0,0.1,0.0001)))