vif.ridge: Variance Inflation Factors for Ridge Regression

In genridge: Generalized Ridge Trace Plots for Ridge Regression

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, returning one row for each value of the \lambda parameter.

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

The plot.vif.ridge method plots variance inflation factors for a "vif.ridge" object in a similar style to what is provided by traceplot. That is, it plots the VIF for each coefficient in the model against either the ridge \lambda tuning constant or it's equivalent effective degrees of freedom.

Usage

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

## S3 method for class 'vif.ridge'
print(x, digits = max(4, getOption("digits") - 5), ...)

## S3 method for class 'vif.ridge'
plot(
  x,
  X = c("lambda", "df"),
  Y = c("vif", "sqrt"),
  col = c("black", "red", "darkgreen", "blue", "darkcyan", "magenta", "brown",
    "darkgray"),
  pch = c(15:18, 7, 9, 12, 13),
  xlab,
  ylab,
  xlim,
  ylim,
  ...
)

Arguments

mod	A "ridge" object computed by ridge
...	Other arguments passed to methods
x	A ridge object, as fit by ridge
digits	Number of digits to display in the print method
X	What to plot as the horizontal coordinate, one of c("lambda", "df")
Y	What to plot as the vertical coordinate, one of c("vif", "sqrt"), where the latter plots \sqrt{VIF}.
col	A numeric or character vector giving the colors used to plot the ridge trace curves. Recycled as necessary.
pch	Vector of plotting characters used to plot the ridge trace curves. Recycled as necessary.
xlab	Label for horizontal axis
ylab	Label for vertical axis
xlim, ylim	x, y limits for the plot. You may need to adjust these to allow for the variable labels.

Value

vif returns a "vif.ridge" object, which is a list of four components

vif	a data frame 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.
lambda	the vector of ridge constants from the original call to ridge
df	the vector of effective degrees of freedom corresponding to lambda
criteria	the optimal values of lambda

Author(s)

Michael Friendly

References

Fox, J. and Monette, G. (1992). Generalized collinearity diagnostics. JASA, 87, 178-183, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1992.10475190")}.

See Also

vif, precision

Examples

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

lambda <- c(0, 0.005, 0.01, 0.02, 0.04, 0.08)
lridge <- ridge(Employed ~ GNP + Unemployed + Armed.Forces + 
                           Population + Year + GNP.deflator, 
		             data=longley, lambda=lambda)

coef(lridge)

# get VIFs for the shrunk estimates
vridge <- vif(lridge)
vridge
names(vridge)



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

plot(vridge, 
     col=clr, pch=pch, cex = 1.2,
     xlim = c(-0.02, 0.08))

plot(vridge, X = "df",
     col=clr, pch=pch, cex = 1.2,
     xlim = c(4, 6.5))

# Better to plot sqrt(VIF). Plot against degrees of freedom
plot(vridge, X = "df", Y="sqrt",
     col=clr, pch=pch, cex = 1.2,
     xlim = c(4, 6.5))

genridge documentation built on April 3, 2025, 11:07 p.m.