Variance Inflation Factor

Description

Calculates variance inflation factor (VIF) for a set of variables and exclude the highly correlated variables from the set through a stepwise procedure.

Usage

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vif(x, ...)
vifcor(x,th=0.9, ...)
vifstep(x,th=10, ...)

Arguments

x

explanatory variables (predictors), defined as a raster object (RasterStack or RasterBrick), or as a matrix, or as a data.frame.

th

a number specifying the correlation threshold for vifcor and VIF threshold for vifstep (see details).

...

additional arguments. see details.

Details

VIF can be used to detect collinearity (Strong correlation between two or more predictor variables). Collinearity causes instability in parameter estimation in regression-type models. The VIF is based on the square of the multiple correlation coefficient resulting from regressing a predictor variable against all other predictor variables. If a variable has a strong linear relationship with at least one other variables, the correlation coefficient would be close to 1, and VIF for that variable would be large. A VIF greater than 10 is a signal that the model has a collinearity problem. vif function calculates this statistic for all variables in x. vifcor and vifstep uses two different strategy to exclude highly collinear variable through a stepwise procedure. vifcor, first find a pair of variables which has the maximum linear correlation (greater than th), and exclude one of them which has greater VIF. The procedure is repeated untill no variable with a high corrrelation coefficient (grater than threshold) with other variables remains. vifstep calculate VIF for all variables, exclude one with highest VIF (greater than threshold), repeat the procedure untill no variables with VIF greater than th remains.

addtional arguments:

maxobservations a number (default=5000) specifying the maximum number of observations should be contributed in calculation of VIF. When the number of observations (cells in raster or rows in data.frame/matrix) is greater than maxobservations, then a random sample with a size of maxobservations is drawn to keep the calculation effecient.

Value

an object of class VIF

Author(s)

Babak Naimi naimi.b@gmail.com

http://r-gis.net

References

Chatterjee, S. and Hadi, A. S. 2006. Regression analysis by example. John Wiley and Sons.;

Dormann, C. F. et al. 2012. Collinearity: A review of methods to Deal with it and a simulation study evaluating their performance. Ecography 35: 001-020.;

Naimi, B., Hamm, N.A.S., Groen, T.A., Skidmore, A.K., and Toxopeus, A.G. 2012. Where is positional uncertainty a problem for species distribution modelling, Ecography. Submitted.

See Also

exclude

Examples

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file <- system.file("external/spain.grd", package="usdm")

r <- brick(file) # reading a RasterBrick object including 10 raster layers in Spain

r 

vif(r) # calculates vif for the variables in r

v1 <- vifcor(r, th=0.9) # identify collinear variables that should be excluded

v1

v2 <- vifstep(r, th=10) # identify collinear variables that should be excluded

v2