checking collinearity in a glm

Question

I'm new to checking the VIF value for a glm model so I just want to make sure i"m understanding this correctly.

I have 4 predictors for my count model and the model looks like this:

model1<-glm(Number~dts+dss+dtn+dsn, family=poisson, data=birds)

I then checked the collinearity on the model using the car::vif function and got this output;

dts         dss         dtn       dsn
2.261840    2.281326    2.016644  2.073556 

so from my understanding and reading online, due to all 4 being below vif of 3, then there is no multicollinearity and I can now proceed with finding the "simplest" model.

After I did this, i then performed the "summary" function, and found 3 out of the 4 to be significant, the model would then become;

dts, dss, dsn

Would that therefore mean that my best model would be;

glm(Numer~dts+dss+dsn, family=poisson, data=bird)

or am i completely misunderstanding the car:vif function

Answer 1

From what you describe, there's no reason to abandon the full four-predictor model.

Unless it's extreme, VIF isn't much of a criterion for evaluating a model. It describes the correlations among the coefficient estimates. A high VIF just means some imprecision in those estimates. See this page among many other for discussion on implications of VIFs. Things like goodness of fit and predictive performance are much more important.

There's little to be gained and potentially a lot to be lost if you remove the nominally "insignificant" predictor. There's a problem even in ordinary least-squares regression with omitted-variable bias: if you omit from a model any predictor that is correlated both with outcome and with another predictor, then the estimates of the coefficients for the retained predictors will be biased. In other types of regressions like logistic regression, you can have this problem even if the omitted predictor isn't correlated with the retained predictors.

So I don't see much reason to omit dtn from your model.