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r.vif - To calculate the stepwise variance inflation factor.


raster, variance inflation factor, VIF


r.vif --help
r.vif [-sf] maps=string[,string,...] [retain=string[,string,...]] [n=number] [maxvif=number] [file=name] [--overwrite] [--help] [--verbose] [--quiet] [--ui]


Only print selected variables to screen
low-memory option (will use full raster layers)
Allow output files to overwrite existing files
Print usage summary
Verbose module output
Quiet module output
Force launching GUI dialog


maps=string[,string,...] [required]
number of sample points (number or percentage)
Default: 100%
Maximum vif
Name of output text file

Table of contents


The r.vif module computes the variance inflation factor (VIF) [1] and the square root of the VIF. The VIF quantifies how much the variance (the square of the estimate's standard deviation) of an estimated regression coefficient is increased because of multi-collinearity. The square root of VIF is a measure of how much larger the standard error is, compared with what it would be if that variable were uncorrelated with the other predictor variables in the model.

By default the VIF is calculated for each variable. If the user sets a VIF threshold value (maxvif) a stepwise variable selection procedure [2] is used whereby after computing the VIF for each explanatory variable, the variable with the highest VIF is removed. Next, the VIF values are computed again for the reduced set of variables. This will be repeated till the VIF is smaller than maxvif. This can thus be used to select a sub-set of variables for e.g., multiple regression analysis.

The user can optionally select one or more variables to be retained in the stepwise selection. For example, let's assume the user selects the variable bio_5 to be retained. If in any step this variable has the highest VIF, the variable with the next highest VIF will be removed instead (see the examples).

The user can set the 's' flag to only print the finally selected variables to the standard output (console). Note that this only works when the stepwise selection procedure is invoked, i.e., when the maxvif is set. This option makes it easier to use the output of r.vif in another function directly (see example ).


To compute the vif all data layers are read in as a numpy array (non-data cells are ignored). When input layers are large or many memory usage may become problematic. In such cases the user may opt to sample raster values for random locations and use that to compute the vif. The quantity of random locations to be generated either can be defined as a positive integer, or as a percentage of the raster map layer's cells (see r.random for details).

Using random sub-set of raster cells as input means that the vif values may vary between runs. If the sub-set is too small it may even lead to differences in variables selected when running the step-wise procedure. Special care should be taken when many of the equations are underdetermined (the value of vif is shown as Inf).

As an alternative, the user can set the f flag to evoke the 'low-memory option'. This will use the r.regression.multi function in the background to compute R2, the most memory demanding part of the computation. With this option, the addon can handle much larger data sets. The disadvantage is that it runs much slower.


The following examples are based on the nc_climate_spm_2000_2012 sample data set which you can download from GRASS GIS sample data download page. This data set contains monthly rainfall and temperature data for the years 2000 - 2012. In the examples below the monthly data of 2000 is used. The analyses are run on a smaller region, set below, to reduce the run time.
g.region n=226000 s=168500 w=229500 e=298500

Example 1

Run VIF, setting the maximum VIF at 10. The function will print the VIF computed at each step to the console. The same will also be written to a text file.
MAPS=`g.list type=raster pattern=*2011*precip sep=,`
r.vif maps=$MAPS file=results1.csv maxvif=10
Below the results are shown (here only the first and last part of the output is shown to save space):
VIF round 1
variable            vif  sqrtvif
2011_01_precip    65.03     8.06
2011_02_precip    29.10     5.39
2011_03_precip    40.20     6.34
2011_04_precip    13.12     3.62
2011_05_precip     6.81     2.61


VIF round 7
variable            vif  sqrtvif
2011_01_precip     4.25     2.06
2011_04_precip     5.22     2.29
2011_05_precip     4.86     2.20
2011_06_precip     7.13     2.67
2011_07_precip     7.58     2.75
2011_08_precip     3.32     1.82

selected variables are:
2011_01_precip, 2011_04_precip, 2011_05_precip, 2011_06_precip, 2011_07_precip, 2011_08_precip

Statistics are written to results.csv
The same results are (optionally) written to a comma delimited file (csv). It contains variables and the corresponding vif and sqrt(vif) for each round in the stepwise variable selection. The column 'removed' gives the variable that was removed in the previous round.

Example 2

Run the same VIF analysis as above, but this time tell the function to retain the variable 2011_02_precip. Only the last few lines of the results are shown below. As you can see, a different set of variables is selected, which includes the variable '2011_02_precip'.
MAPS=`g.list type=raster pattern=*2011*precip sep=,`
r.vif maps=$MAPS maxvif=10 retain=2011_02_precip file=results2.csv
The output is:
VIF round 6
variable            vif  sqrtvif
2011_02_precip     9.29     3.05
2011_03_precip     9.02     3.00
2011_04_precip     6.30     2.51
2011_05_precip     4.99     2.23
2011_06_precip     9.72     3.12
2011_07_precip     8.36     2.89
2011_08_precip     3.30     1.82

selected variables are:
2011_02_precip, 2011_03_precip, 2011_04_precip, 2011_05_precip, 2011_06_precip,
2011_07_precip, 2011_08_precip

Statistics are written to results2.csv

Example 3

Like example 1, but without writing the results to file, and with the 's' flag set, which means only the list with finally selected variables are printed to screen. This output can be directl parsed in a script.
MAPS=`g.list type=raster pattern=*2011*precip sep=,`
r.vif -s maps=$MAPS maxvif=10

The output is:
This output can be captured in a variable 'SELECTION', which is used as input in to create a group.
MAPS=`g.list type=raster pattern=*2011*precip sep=,`
SELECTION=`r.vif -s maps=$MAPS maxvif=10` group=group_example input=$SELECTION

This selects raster layers using the r.vif functions, and adds these raster layers to the group 'group_example':
Adding raster map <2011_01_precip@climate_1970_2012> to group
Adding raster map <2011_04_precip@climate_1970_2012> to group
Adding raster map <2011_05_precip@climate_1970_2012> to group
Adding raster map <2011_06_precip@climate_1970_2012> to group
Adding raster map <2011_07_precip@climate_1970_2012> to group
Adding raster map <2011_08_precip@climate_1970_2012> to group


Suggested citation:

van Breugel, P., Friis, I., Demissew, S., Lillesø, J.-P. B., & Kindt, R. 2015. Current and Future Fire Regimes and Their Influence on Natural Vegetation in Ethiopia. Ecosystems. doi: 10.1007/s10021-015-9938-x.


[1] Graham, M.H. 2003. Confronting multicollinearity in ecological multiple regression. Ecology 84: 2809-2815.

[2] Craney, T.A., & Surles, J.G. 2002. Model-Dependent Variance Inflation Factor Cutoff Values. Quality Engineering 14: 391-403.


Paulo van Breugel, paulo at

Last changed: $Date: 2017-03-31 21:22:26 +0200 (Fri, 31 Mar 2017) $


Available at: r.vif source code (history)

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