Assessing Multi-collinearity

multicollinearity.R

library(car)
library(Hmisc)
library(perturb)

n <- 200

x0 <- rnorm(n)
x1 <- rnorm(n)
x2 <- x1 + rnorm(n)/2
x3 <- x2 + rnorm(n)/1.25
x4 <- x3 + rnorm(n)
x5 <- x4 + rnorm(n)/.8
x6 <- x5 + rnorm(n)/.25
x7 <- x1 + rnorm(n, m=0, sd=.2)

m <- cbind(x0,x1,x2,x3,x4,x5,x6,x7)

Hmisc::rcorr(m)

## Note that in this example, x0, is a throw-away variable. It does
## not enter into the calculation of vif or condition number. (DVs, 
## generally, do not).
m.lm <- lm(x0~., data=data.frame(m))

car::vif(m.lm) # variance inflation factors

## The VIF is probably the most common means to test for the presence of 
## multicollinearity (MCL). But a key problem with VIFs is that they do not
## afford easy diagnosis of the sources of MCL for a given variable. An 
## alternative is to use the condition index (kappa) together with variance
## decomposition proportions for the purpose (Belsley, 1991).  

dgn <- perturb::colldiag(m.lm, add.intercept=F) # condition indices

## The result of colldiag() is a list of 2 elements, a vector of condition 
## numbers and a matrix of variance decomposition proportions. 

dgn$condindx

dgn$pi

## each column of pi shows the distribution of variance proportion for the 
## named variable. Therefore, each column of pi will sum to 1.

apply(dgn$pi, 2, sum)


## Generally speaking, if MCL is a concern, you should
## standardize your variables, or at least center them.

Should x0 be included in m? It doesn't affect the VIFs, but there will be one additional condition index if x0 is included (although the values of the rest of the condition indices won't differ).