Collinearity after accounting for random/mixed effects

Question

could two/more predictors become more/less collinear after accounting for random effects?

In my case I have tested for collinearity prior to modelling, e.g. using VIF, and everything checks out. However, the ranking (using IC) of different models makes me uncertain whether it truly can separate between the predictors.

Any ideas?

ps! Can someone with higher rep than I add a more relevant tag such as collinearity?

Answer 1

There are some solutions listed at this blog post. They use some code to create a function that will calculate VIFs for lmer and lme model objects from the lmer and nlme R packages, respectively. I have copied the code for the function below.

vif.lme <- function (fit) {
    ## adapted from rms::vif
    v <- vcov(fit)
    nam <- names(fixef(fit))
    ## exclude intercepts
    ns <- sum(1 * (nam == "Intercept" | nam == "(Intercept)"))
    if (ns > 0) {
        v <- v[-(1:ns), -(1:ns), drop = FALSE]
        nam <- nam[-(1:ns)] }
    d <- diag(v)^0.5
    v <- diag(solve(v/(d %o% d)))
    names(v) <- nam
    v }

Once you run that code once, you will be able to execute a new function, vif.lme within the R environment. I give an example below using a random data set, and an uninformative random effect. I use an uninformative random effect so that the results of lme within nlme will generate the same parameter values for predictors as lm in base R. Then, I use the above code to calculate variance inflation factors, as well as the vif functino from the car package used to calculate VIFs for linear models, to show that they give the same output.

#make 4 vectors- c is used as an uninformative random effect for the lme model
a<-c(1:10)
b1<-c(2,4,6,8,10,100,14,16,18,20)
b2<-c(1,9,2,4,5,6,4,3,2,-1)
c<-c(1,1,1,1,1,1,1,1,1,1)
test<-data.frame(a,b1,b2,c)

#model a as a function of b1 and b2, and c as a random effect
require(nlme)
fit<-lme(a~b1+b2, random=~1|c,data=test)
#see how the model fits
summary(fit)
#check variance inflation factors
vif.lme(fit)

#create a new regular linear regression model and check VIF using the car package.
#answers should be the same, as our random effect above was totally uninformative
require(car)
fit2<- lm(a~b1+b2,data=test)
#check to see that parameter fits are the same.
summary(fit2)
#check to see that variance inflation factors are the same
vif(fit2)