HH (version 2.1-15)

vif: Calculate the Variance Inflation Factor

Description

The VIF for predictor $i$ is $1/(1-R_i^2)$, where $R_i^2$ is the $R^2$ from a regression of predictor $i$ against the remaining predictors.

Usage

vif(x, ...)

## S3 method for class 'default':
vif(x, y.name, na.action = na.exclude, ...) ## x is a data.frame

## S3 method for class 'formula':
vif(x, data, na.action = na.exclude, ...)   ## x is a formula

## S3 method for class 'lm':
vif(x, na.action = na.exclude, ...)  ## x is a "lm" object computed with x=TRUE

Arguments

x

data.frame, or formula, or lm object computed with x=TRUE.

na.action

See na.action.

...

additional arguments.

y.name

Name of Y-variable to be excluded from the computations.

data

A data frame in which the variables specified in the formula will be found. If missing, the variables are searched for in the standard way.

Value

• Vector of VIF values, one for each X-variable.

Details

A simple diagnostic of collinearity is the variance inflation factor, VIF one for each regression coefficient (other than the intercept). Since the condition of collinearity involves the predictors but not the response, this measure is a function of the $X$'s but not of $Y$. The VIF for predictor $i$ is $1/(1-R_i^2)$, where $R_i^2$ is the $R^2$ from a regression of predictor $i$ against the remaining predictors. If $R_i^2$ is close to 1, this means that predictor $i$ is well explained by a linear function of the remaining predictors, and, therefore, the presence of predictor $i$ in the model is redundant. Values of VIF exceeding 5 are considered evidence of collinearity: The information carried by a predictor having such a VIF is contained in a subset of the remaining predictors. If, however, all of a model's regression coefficients differ significantly from 0 ($p$-value $

References

Heiberger, Richard~M. and Holland, Burt (2004b). Statistical Analysis and Data Display: An Intermediate Course with Examples in S-Plus, R, and SAS. Springer Texts in Statistics. Springer. ISBN 0-387-40270-5.

See Also

lm in R or lm in S-Plus.

Examples

usair <- read.table(hh("datasets/usair.dat"),                    
                    col.names=c("SO2","temp","mfgfirms","popn",
                                "wind","precip","raindays"))
usair$lnSO2 <- log(usair$SO2)
usair$lnmfg <- log(usair$mfgfirms)
usair$lnpopn <- log(usair$popn)

usair.lm <- lm(lnSO2 ~ temp + lnmfg + wind + precip, data=usair, x=TRUE)

vif(usair.lm)  ## the lm object must be computed with x=TRUE

vif(lnSO2 ~ temp + lnmfg + wind + precip, data=usair)

vif(usair)

vif(usair, y.name="lnSO2")