genridge (version 0.7.0)

vif.ridge: Variance Inflation Factors for Ridge Regression

Description

The function vif.ridge calculates variance inflation factors for the predictors in a set of ridge regression models indexed by the tuning/shrinkage factor.

Usage

# S3 method for ridge
vif(mod, ...)

Value

Returns a matrix of variance inflation factors of the same size and shape as coef{mod}. The columns correspond to the predictors in the model and the rows correspond to the values of lambda in ridge estimation.

Arguments

mod

A ridge object

...

Other arguments (unused)

Author

Michael Friendly

Details

Variance inflation factors are calculated using the simplified formulation in Fox & Monette (1992).

References

Fox, J. and Monette, G. (1992). Generalized collinearity diagnostics. JASA, 87, 178-183

See Also

vif, precision

Examples

data(longley)
lmod <- lm(Employed ~ GNP + Unemployed + Armed.Forces + Population + 
                      Year + GNP.deflator, data=longley)
vif(lmod)

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)
coef(lridge)


vridge <- vif(lridge)
vridge

# plot VIFs
pch <- c(15:18, 7, 9)
clr <- c("black", rainbow(5, start=.6, end=.1))

matplot(rownames(vridge), vridge, type='b', 
	xlab='Ridge constant (k)', ylab="Variance Inflation", 
	xlim=c(0, 0.08), 
	col=clr, pch=pch, cex=1.2)
text(0.0, vridge[1,], colnames(vridge), pos=4)

matplot(lridge$df, vridge, type='b', 
	xlab='Degrees of freedom', ylab="Variance Inflation", 
	col=clr, pch=pch, cex=1.2)
text(6, vridge[1,], colnames(vridge), pos=2)

# more useful to plot VIF on the sqrt scale

matplot(rownames(vridge), sqrt(vridge), type='b', 
	xlab='Ridge constant (k)', ylab=expression(sqrt(VIF)), 
	xlim=c(-0.01, 0.08), 
	col=clr, pch=pch, cex=1.2, cex.lab=1.25)
text(-0.01, sqrt(vridge[1,]), colnames(vridge), pos=4, cex=1.2)

matplot(lridge$df, sqrt(vridge), type='b', 
	xlab='Degrees of freedom', ylab=expression(sqrt(VIF)), 
	col=clr, pch=pch, cex=1.2, cex.lab=1.25)
text(6, sqrt(vridge[1,]), colnames(vridge), pos=2, cex=1.2)