Condition indexes and variance decomposition proportions

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

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

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

Arguments

mod

A model object or data-frame

scale

If FALSE, the data are left unscaled. Default is TRUE

center

If TRUE, data are centered. Default is FALSE

add.intercept

if TRUE, an intercept is added. Default is TRUE

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

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.

Colldiag computes the condition indexes of the 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.

Value

A colldiag object

condindx

A vector of condition indexes

pi

A matrix of variance decomposition proportions

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

Colldiag is based on the Stata program coldiag by Joseph Harkness joe.harkness@jhu.edu, Johns Hopkins University.

Author(s)

John Hendrickx John_Hendrickx@yahoo.com

References

D. Belsley, E. Kuh, and R. Welsch (1980). Regression Diagnostics. Wiley.

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

See Also

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

Examples

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# Belsley (1991). "Conditioning Diagnostics"
# The Consumption Function (pp. 149-154)
data(consumption)

ct1 <- with(consumption, c(NA,cons[-length(cons)]))

# compare (5.3)
m1 <- lm(cons ~ ct1+dpi+rate+d_dpi, data = consumption)
anova(m1)
summary(m1)

# compare exhibit 5.11
with(consumption, cor(cbind(ct1, dpi, rate, d_dpi), use="complete.obs"))

# compare exhibit 5.12
cd<-colldiag(m1)
cd
print(cd,fuzz=.3)

## Not run: 
# Example of reading UCLA data files from 
# http://www.ats.ucla.edu/stat/r/dae/rreg.htm
library(foreign)
elemapi <- read.dta("http://www.ats.ucla.edu/stat/data/elemapi2.dta")
attach(elemapi)

# Example of SAS collinearity diagnostics from
# http://www.ats.ucla.edu/stat/sas/webbooks/reg/chapter2/sasreg2.htm
# 2.4 Tests for Collinearity
m2 <- lm(api00 ~ acs_k3+avg_ed+grad_sch+col_grad+some_col)
summary(m2)
library(car)
vif(m2)

library(perturb)
cd2<-colldiag(m2,add.intercept=FALSE,center=TRUE)
print(cd2,dec.places=5)

# Same data, SPSS example at
# http://www.ats.ucla.edu/stat/spss/webbooks/reg/chapter2/spssreg2.htm
colldiag(m2,add.intercept=TRUE)

## End(Not run)