lm.ridge {MASS}R Documentation

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.
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?
x should the design matrix be returned?
y should the response be returned?
contrasts a list of contrasts to be used for some or all of
... additional arguments to lm.fit.

Value

A list with components

coef matrix of coefficients, one row for each value of lambda.
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.

References

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

See Also

lm

Examples

data(longley)
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)))
# modified HKB estimator is 0.0042754
# modified L-W estimator is 0.032295
# smallest value of GCV  at 0.0028
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