pedometrics (version 0.3-0)

stepVIF: Variable selection using the variance-inflation factor

Description

This function takes a linear model and selects the subset of predictor variables that meet a user-specific collinearity threshold measured by the variance-inflation factor (VIF).

Usage

stepVIF(model, threshold = 10, verbose = FALSE)

Arguments

model

Linear model (object of class 'lm') containing collinear predictor variables.

threshold

Positive number defining the maximum allowed VIF. Defaults to threshold = 10.

verbose

Logical for indicating if iteration results should be printed. Defaults to verbose = FALSE.

Value

• A linear model (object of class 'lm') with low collinearity.

TODO

1. Include other criteria (RMSE, AIC, etc) as option to drop collinear predictor variables.

Details

stepVIF() starts computing the VIF of all predictor variables in the linear model. Because some predictor variables can have more than one degree of freedom, such as categorical variables, generalized variance-inflation factors (Fox and Monette, 1992) are calculated instead using vif. Generalized variance-inflation factors (GVIF) consist of VIF corrected to the number of degrees of freedom (df) of the predictor variable:

$GVIF = VIF^{1/(2\times df)}$

GVIF are interpretable as the inflation in size of the confidence ellipse or ellipsoid for the coefficients of the predictor variable in comparison with what would be obtained for orthogonal data (Fox and Weisberg, 2011).

The next step is to evaluate if any of the predictor variables has a VIF larger than the specified threshold. Because stepVIF() estimates GVIF and the threshold corresponds to a VIF value, the last is transformed to the scale of GVIF by taking its square root. If there is only one predictor variable that does not meet the VIF threshold, it is authomatically removed from the model and no further processing occurs. When there are two or more predictor variables that do not meet the VIF threshold, stepVIF() fits a linear model between each of them and the dependent variable. The predictor variable with the lowest adjusted coefficient of determination is dropped from the model and new coefficients are calculated, resulting in a new linear model.

This process lasts until all predictor variables included in the new model meet the VIF threshold.

Nothing is done if all predictor variables have a VIF value inferior to the threshold, and stepVIF() returns the original linear model.

References

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

Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage.

Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition. Thousand Oaks: Sage.

Hair, J. F., Black, B., Babin, B. and Anderson, R. E. (2010) Multivariate data analysis. New Jersey: Pearson Prentice Hall. Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

vif, stepAIC.

Examples

require(car)
fit <- lm(prestige ~ income + education + type, data = Duncan)
fit <- stepVIF(fit, threshold = 10, verbose = TRUE)