I am trying to explain the housing sales prices and need for it to include the squared terms of some variables, for instance distance to the nearest forest, in order to capture the real effect. This lead my GVIF (generalized variance inflation factor) to exceed 10. I have read in the litterature that multicolinearity is not an issue when it concerns a variable and its squared term, so I moved on.
However, when I've tried to run a wald test of significance of my model, that contains heteroskedasticity robust standard error, I've got an error message telling that there's a singularity problem. I know that it is induced by the inclusion of some squared term, since when they are removed the problem disappear. I've tried "poly(x, 2, raw = TRUE)" and "poly(x, 2, raw = FALSE)" but the problem still remains.
So my questions are :
- Is it indispensable to conduct a Wald test at this stage if the F-test of my initial model was good ?
- How can I run a significance test of the model in the presence of heteroskedasticity and multicollinearity between x and x square ?
Thank you !