colldiag {VisCollin}

Collinearity Diagnostics

Description

Calculates condition indexes and variance decomposition proportions in order to test for collinearity among the independent variables of a regression model and identifies the sources of collinearity if present.

Usage

colldiag(mod, scale = TRUE, center = FALSE, add.intercept = FALSE)

## S3 method for class 'colldiag'
print(x, dec.places = 3, fuzz = NULL, fuzzchar = ".", ...)

Arguments

mod

A model object, such as computed by lm or glm, or a data-frame to be used as predictors in such a model.

scale

If FALSE, the data are left unscaled. If TRUE, the data are scaled, typically to mean 0 and variance 1 using scale. Default is TRUE.

center

If TRUE, data are centered. Default is FALSE.

add.intercept

if TRUE, an intercept is added. Default is FALSE.

x

A colldiag object

dec.places

Number of decimal places to use when printing

fuzz

Variance decomposition proportions less than fuzz are printed as fuzzchar

fuzzchar

Character for small variance decomposition proportion values

...

arguments to be passed on to or from other methods (unused)

Details

colldiag is an implementation of the regression collinearity diagnostic procedures found in Belsley, Kuh, and Welsch (1980). These procedures examine the “conditioning” of the matrix of independent variables.

It computes the condition indexes of the model matrix. If the largest condition index (the condition number) is large (Belsley et al suggest 30 or higher), then there may be collinearity problems. All large condition indexes may be worth investigating.

colldiag also provides further information that may help to identify the source of these problems, the variance decomposition proportions associated with each condition index. If a large condition index is associated two or more variables with large variance decomposition proportions, these variables may be causing collinearity problems. Belsley et al suggest that a large proportion is 50 percent or more.

Note that such collinearity diagnostics are often provided by other software for the model matrix including the constant term for the intercept (e.g., SAS PROC REG, with the option COLLIN). However, these are generally useless and misleading unless the intercept has some real interpretation and the origin of the regressors is contained within the prediction space, as explained by Fox (1997, p. 351). The default values for scale, center and add.intercept exclude the constant term, and correspond to the SAS option COLLINNOINT.

Value

A "colldiag" object, containing:

condindx

A one-column matrix of condition indexes

pi

A square matrix of variance decomposition proportions. The rows refer to the principal component dimensions, the columns to the predictor variables.

print.colldiag prints the condition indexes as the first column of a table with the variance decomposition proportions beside them. print.colldiag has a fuzz option to suppress printing of small numbers. If fuzz is used, small values are replaces by a period “.”. Fuzzchar can be used to specify an alternative character.

Note

Missing data is silently omitted in these calculations

Author(s)

John Hendrickx

Source

These functions were taken from the (now defunct) perturb package by John Hendrickx. He credits the Stata program coldiag by Joseph Harkness [e-mail], Johns Hopkins University.

References

Belsley, D.A., Kuh, E. and Welsch, R. (1980). Regression Diagnostics, New York: John Wiley & Sons.

Belsley, D.A. (1991). Conditioning diagnostics, collinearity and weak data in regression. New York: John Wiley & Sons.

Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. thousand Oaks, CA: Sage Publications.

Friendly, M., & Kwan, E. (2009). Where’s Waldo: Visualizing Collinearity Diagnostics. The American Statistician, 63, 56–65.

See Also

lm, scale, svd, [car]vif, [rms]vif

Examples

data(cars)
cars.mod <- lm (mpg ~ cylinder + engine + horse + weight + accel + year,
                data=cars)
car::vif(cars.mod)

# SAS PROC REG / COLLIN option, including the intercept
colldiag(cars.mod, add.intercept = TRUE)

# Default settings: scaled, not centered, no intercept, like SAS PROC REG / COLLINNOINT
colldiag(cars.mod)

(cd <- colldiag(cars.mod, center=TRUE))

# fuzz small values
print(cd, fuzz = 0.5)

# Biomass data
data(biomass)

biomass.mod <- lm (biomass ~ H2S + sal + Eh7 + pH + buf + P + K +
                             Ca + Mg + Na + Mn + Zn + Cu + NH4,
                   data=biomass)
car::vif(biomass.mod)

cd <- colldiag(biomass.mod, center=TRUE)
# simplified display
print(colldiag(biomass.mod, center=TRUE), fuzz=.3)

# None yet