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 colldiag
print(x, dec.places = 3, fuzz = NULL, fuzzchar = ".", ...)Source
These functions were taken from the (now defunct) perturb package by John Hendrickx.
He credits the Stata program coldiag by Joseph Harkness joe.harkness@jhu.edu, Johns Hopkins University.
Arguments
- mod
A model object, such as computed by
lmorglm, or a data-frame to be used as predictors in such a model.- scale
If
FALSE, the data are left unscaled. IfTRUE, the data are scaled, typically to mean 0 and variance 1 usingscale. Default isTRUE.- center
If TRUE, data are centered. Default is
FALSE.- add.intercept
if
TRUE, an intercept is added. Default isFALSE.- x
A
colldiagobject- 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)
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.
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.
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.
Examples
data(cars)
cars.mod <- lm (mpg ~ cylinder + engine + horse + weight + accel + year,
data=cars)
car::vif(cars.mod)
#> cylinder engine horse weight accel year
#> 10.633049 19.641683 9.398043 10.731681 2.625581 1.244829
# SAS PROC REG / COLLIN option, including the intercept
colldiag(cars.mod, add.intercept = TRUE)
#> Condition
#> Index Variance Decomposition Proportions
#> intercept cylinder engine horse weight accel year
#> 1 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 2 4.821 0.000 0.001 0.013 0.004 0.001 0.012 0.001
#> 3 16.620 0.003 0.023 0.065 0.270 0.006 0.078 0.003
#> 4 25.625 0.008 0.273 0.002 0.088 0.199 0.170 0.017
#> 5 36.384 0.007 0.548 0.914 0.001 0.271 0.021 0.013
#> 6 37.447 0.006 0.134 0.004 0.444 0.468 0.598 0.068
#> 7 91.281 0.976 0.020 0.002 0.191 0.055 0.122 0.898
# Default settings: scaled, not centered, no intercept, like SAS PROC REG / COLLINNOINT
colldiag(cars.mod)
#> Condition
#> Index Variance Decomposition Proportions
#> cylinder engine horse weight accel year
#> 1 1.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 2 4.757 0.001 0.013 0.005 0.000 0.023 0.007
#> 3 15.896 0.027 0.085 0.435 0.003 0.054 0.031
#> 4 24.742 0.379 0.004 0.036 0.229 0.157 0.168
#> 5 34.020 0.221 0.666 0.110 0.675 0.285 0.004
#> 6 35.464 0.372 0.230 0.414 0.093 0.480 0.790
(cd <- colldiag(cars.mod, center=TRUE))
#> Condition
#> Index Variance Decomposition Proportions
#> cylinder engine horse weight accel year
#> 1 1.000 0.005 0.003 0.005 0.004 0.009 0.010
#> 2 2.252 0.004 0.002 0.000 0.007 0.022 0.787
#> 3 2.515 0.004 0.001 0.002 0.010 0.423 0.142
#> 4 5.660 0.309 0.014 0.306 0.087 0.063 0.005
#> 5 8.342 0.115 0.000 0.654 0.715 0.469 0.052
#> 6 10.818 0.563 0.981 0.032 0.176 0.013 0.004
# fuzz small values
print(cd, fuzz = 0.5)
#> Condition
#> Index Variance Decomposition Proportions
#> cylinder engine horse weight accel year
#> 1 1.000 . . . . . .
#> 2 2.252 . . . . . 0.787
#> 3 2.515 . . . . . .
#> 4 5.660 . . . . . .
#> 5 8.342 . . 0.654 0.715 . .
#> 6 10.818 0.563 0.981 . . . .
# 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)
#> H2S sal Eh7 pH buf P K Ca
#> 3.027456 3.387615 1.977447 62.080846 34.431748 1.895804 7.367110 16.662146
#> Mg Na Mn Zn Cu NH4
#> 23.764229 10.351043 6.185628 11.626479 4.829203 8.376506
cd <- colldiag(biomass.mod, center=TRUE)
# simplified display
print(colldiag(biomass.mod, center=TRUE), fuzz=.3)
#> Condition
#> Index Variance Decomposition Proportions
#> H2S sal Eh7 pH buf P K Ca Mg Na Mn Zn Cu
#> 1 1.000 . . . . . . . . . . . . .
#> 2 1.154 . . . . . . . . . . . . .
#> 3 1.750 . . . . . . . . . . . . .
#> 4 1.921 . . . . . . . . . . . . .
#> 5 2.668 . . . . . 0.426 . . . . . . .
#> 6 3.136 . . 0.360 . . . . . . . . . .
#> 7 3.574 . . . . . . . . . . . . .
#> 8 3.596 . . . . . . . . . . . . .
#> 9 5.447 . . . . . . . . . . . . .
#> 10 5.868 . . . . . . . . . . . . .
#> 11 7.529 . . . . . . . . . . . 0.320 .
#> 12 10.427 . . . . . . . . . . . . 0.426
#> 13 12.843 . . . . . . . . 0.671 . . 0.453 .
#> 14 22.775 . . . 0.955 0.697 . . 0.596 . . 0.338 . .
#> NH4
#> 1 .
#> 2 .
#> 3 .
#> 4 .
#> 5 .
#> 6 .
#> 7 .
#> 8 .
#> 9 .
#> 10 .
#> 11 .
#> 12 .
#> 13 .
#> 14 .
# None yet