multicol: Analyse multicollinearity in a dataset, including VIF

In fuzzySim: Fuzzy Similarity in Species Distributions

Analyse multicollinearity in a dataset, including VIF

Description

This function analyses multicollinearity in a set of variables or in a model, including the R-squared, tolerance and variance inflation factor (VIF). It also allows selecting variables under a given VIF.

Usage

multicol(vars = NULL, model = NULL, reorder = TRUE,
vif.thresh = Inf, verbosity = 2, plot = FALSE, ...)

Arguments

vars	A matrix, an object inheriting class data.frame, or a multi-layer SpatRaster containing the numeric variables for which to calculate multicollinearity. Note that only the 'independent' (predictor, explanatory, right hand side) variables should be entered, as the result obtained for each variable depends on all the other variables present in the analysed data set.
model	Alternatively to 'vars', a model object of class "glm" to calculate 'multicol' among the included variables.
reorder	logical, whether variables should be output in decreasing order or VIF value rather than in their input order. The default is TRUE.
vif.thresh	numeric value specifying the maximum VIF allowed in the output. The default is Inf, for no limit. Variables above the threshold are excluded in a stepwise manner, starting from the highest one and recomputing the VIFs every time, until no variable exceeds the 'vif.thresh' value.
verbosity	integer specifying the amount of messages to display along the process. The default is 2, for the maximum amount of messages available.
plot	logical value (default TRUE) indicating whether to plot the output VIF values.
...	(if plot=TRUE) additional arguments to pass to modEvA::lollipop.

Details

Testing (multi)collinearity among covariates is a recommended step of data exploration before applying a statistical model (Zuur et al. 2010). You can also assess the multicollinearity among the variables already included in a model.

The multicol function calculates the degree of multicollinearity in a set of numeric variables, using three closely related measures:

• R squared: the coefficient of determination of a linear regression of each predictor variable on all other predictor variables, i.e., the amount of variation in each variable that is accounted for by other variables in the dataset;

• Tolerance = 1 - R squared, i.e., the amount of variation in each variable that is not included in the remaining variables;

• Variance Inflation Factor: VIF = 1 / (1 - R squared), which, in a linear model with these variables as predictors, reflects the degree to which the variance of an estimated regression coefficient is increased due only to the correlations among covariates (Marquardt 1970; Mansfield & Helms 1982).

The function optionally performs a stepwise backward removal of variables whose VIF exceeds a specified threshold. Note, however, that a high VIF does not necessarily imply that a particular variable should be removed. Consider removing instead other (potencially less important) variables that are correlated with it, causing the high VIF; and see also the corSelect function.

Value

The function returns a matrix with one row per variable, the names of the variables as row names, and 3 columns: R-squared, Tolerance, and VIF.

Author(s)

A. Marcia Barbosa

References

Marquardt D.W. (1970) Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics 12: 591-612.

Mansfield E.R. & Helms B.P. (1982) Detecting multicollinearity. The American Statistician 36: 158-160.

Zuur A.F., Ieno E.N. & Elphick C.S. (2010) A protocol for data exploration to avoid common statistical problems. Methods in Ecology and Evolution 1: 3-14.

See Also

vif in package HH, vif in package usdm; package collinear

Examples

data(rotif.env)
names(rotif.env)


# compute multicollinearity among the predictor variables:

multicol(rotif.env[ , 5:17], reorder = FALSE)

multicol(rotif.env[ , 5:17])


# get also a plot of the results:

par(mar = c(11, 4, 2, 1))

multicol(rotif.env[ , 5:17], plot = TRUE,
ylab = "VIF", main = "VIF-selected variables", col = "orange2")


# select variables based on VIF:

multicol(rotif.env[ , 5:17], vif.thresh = 3, plot = TRUE,
ylab = "VIF", main = "VIF-selected variables", col = "orange2")


# you can also compute multicollinearity among variables included in a model:

mod <- step(glm(Abrigh ~ Area + Altitude + AltitudeRange +
HabitatDiversity + HumanPopulation + Latitude + Longitude +
Precipitation + PrecipitationSeasonality + TemperatureAnnualRange
+ Temperature + TemperatureSeasonality + UrbanArea,
data = rotif.env))

multicol(model = mod)


# more examples using R datasets:

multicol(trees)


# you'll get a warning and some NA results if any of the variables
# is not numeric:

multicol(OrchardSprays)


# so, define the subset of numeric 'vars' to calculate 'multicol' for:

multicol(OrchardSprays[ , 1:3])

fuzzySim documentation built on Dec. 19, 2025, 3:01 p.m.