# vif: Calculate the Variance Inflation Factor In HH: Statistical Analysis and Data Display: Heiberger and Holland

## 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```vif(xx, ...) ## Default S3 method: vif(xx, y.name, na.action = na.exclude, ...) ## xx is a data.frame ## S3 method for class 'formula' vif(xx, data, na.action = na.exclude, ...) ## xx is a formula ## S3 method for class 'lm' vif(xx, na.action = na.exclude, ...) ## xx is a "lm" object computed with x=TRUE ```

## Arguments

 `xx` `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.

## 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 < .05), a somewhat larger VIF may be tolerable.

## Value

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

## Author(s)

Richard M. Heiberger <[email protected]>

## References

Heiberger, Richard M. and Holland, Burt (2004). 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.

`lm`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```data(usair) if.R(s={usair <- usair}, r={}) 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") ```

### Example output

```Loading required package: lattice

Attaching package: 'TH.data'

The following object is masked from 'package:MASS':

geyser

NULL
temp    lnmfg     wind   precip
1.373342 1.115383 1.253309 1.204027
temp    lnmfg     wind   precip
1.373342 1.115383 1.253309 1.204027
SO2      temp  mfgfirms      popn      wind    precip  raindays     lnSO2
21.649700  6.090131 47.530627 50.924112  2.124705  4.274058  3.806131 20.177457
lnmfg    lnpopn
12.044417 19.708620
SO2      temp  mfgfirms      popn      wind    precip  raindays     lnmfg
3.123775  4.699786 44.006584 50.209386  1.474314  4.195029  3.748426 12.027037
lnpopn
19.522242
```

HH documentation built on May 29, 2017, 7:49 p.m.