ridge: Ridge Regression Estimates

In genridge: Generalized Ridge Trace Plots for Ridge Regression

Ridge Regression Estimates

Description

The function ridge fits linear models by ridge regression, returning an object of class ridge designed to be used with the plotting methods in this package.

Ridge regression shrinkage can be parameterized in several ways. If a vector of lambda values is supplied, these are used directly in the ridge regression computations. Otherwise, if a vector df is supplied the equivalent values of lambda. In either case, both lambda and df are returned in the ridge object, but the rownames of the coefficients are given in terms of lambda.

Usage

ridge(y, ...)

## S3 method for class 'formula'
ridge(formula, data, lambda = 0, df, svd = TRUE, ...)

## Default S3 method:
ridge(y, X, lambda = 0, df, svd = TRUE, ...)

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

## S3 method for class 'ridge'
print(x, digits = max(5, getOption("digits") - 5), ...)

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

Arguments

y	A numeric vector containing the response variable. NAs not allowed.
...	Other arguments, passed down to methods
formula	For the formula method, a two-sided formula.
data	For the formula method, data frame within which to evaluate the formula.
lambda	A scalar or vector of ridge constants. A value of 0 corresponds to ordinary least squares.
df	A scalar or vector of effective degrees of freedom corresponding to lambda
svd	If TRUE the SVD of the centered and scaled X matrix is returned in the ridge object.
X	A matrix of predictor variables. NA's not allowed. Should not include a column of 1's for the intercept.
x, object	An object of class ridge
digits	For the print method, the number of digits to print.

Value

A list with the following components:

lambda	The vector of ridge constants
df	The vector of effective degrees of freedom corresponding to lambda
coef	The matrix of estimated ridge regression coefficients
scales	scalings used on the X matrix
kHKB	HKB estimate of the ridge constant
kLW	L-W estimate of the ridge constant
GCV	vector of GCV values
kGCV	value of lambda with the minimum GCV

If svd==TRUE, the following are also included:

svd.D	Singular values of the svd of the scaled X matrix
svd.U	Left singular vectors of the svd of the scaled X matrix. Rows correspond to observations and columns to dimensions.
svd.V	Right singular vectors of the svd of the scaled X matrix. Rows correspond to variables and columns to dimensions.

Author(s)

Michael Friendly

References

Hoerl, A. E., Kennard, R. W., and Baldwin, K. F. (1975), "Ridge Regression: Some Simulations," Communications in Statistics, 4, 105-123.

Lawless, J.F., and Wang, P. (1976), "A Simulation Study of Ridge and Other Regression Estimators," Communications in Statistics, 5, 307-323.

See Also

lm.ridge for other implementations of ridge regression

traceplot, plot.ridge, pairs.ridge, plot3d.ridge, for 1D, 2D, 3D plotting methods

pca.ridge, biplot.ridge, biplot.pcaridge for views in PCA/SVD space

precision.ridge for measures of shrinkage and precision

Examples

#\donttest{
# Longley data, using number Employed as response
longley.y <- longley[, "Employed"]
longley.X <- data.matrix(longley[, c(2:6,1)])

lambda <- c(0, 0.005, 0.01, 0.02, 0.04, 0.08)
lridge <- ridge(longley.y, longley.X, lambda=lambda)

# same, using formula interface
lridge <- ridge(Employed ~ GNP + Unemployed + Armed.Forces + Population + Year + GNP.deflator, 
		data=longley, lambda=lambda)


coef(lridge)

# standard trace plot
traceplot(lridge)
# plot vs. equivalent df
traceplot(lridge, X="df")
pairs(lridge, radius=0.5)
#}


data(prostate)
py <- prostate[, "lpsa"]
pX <- data.matrix(prostate[, 1:8])
pridge <- ridge(py, pX, df=8:1)
pridge

plot(pridge)
pairs(pridge)
traceplot(pridge)
traceplot(pridge, X="df")


# Hospital manpower data from Table 3.8 of Myers (1990) 
data(Manpower)
str(Manpower)

mmod <- lm(Hours ~ ., data=Manpower)
vif(mmod)
# ridge regression models, specified in terms of equivalent df
mridge <- ridge(Hours ~ ., data=Manpower, df=seq(5, 3.75, -.25))
vif(mridge)

# univariate ridge trace plots
traceplot(mridge)
traceplot(mridge, X="df")


# bivariate ridge trace plots
plot(mridge, radius=0.25, labels=mridge$df)
pairs(mridge, radius=0.25)

# 3D views
# ellipsoids for Load, Xray & BedDays are nearly 2D
plot3d(mridge, radius=0.2, labels=mridge$df)
# variables in model selected by AIC & BIC
plot3d(mridge, variables=c(2,3,5), radius=0.2, labels=mridge$df)

# plots in PCA/SVD space
mpridge <- pca(mridge)
traceplot(mpridge, X="df")
biplot(mpridge, radius=0.25)

genridge documentation built on Aug. 8, 2023, 5:08 p.m.