StATS: Multicollinearity is not a violation of assumptions (created 2006-01-20)
A colleague from my days at the National Institute for Occupational Safety and Health emailed me a question. Apparently, one of the co-authors of a paper he is writing is in a bit of a panic because the linear regression model that they are using has multicollinearity. She calls this a violation of assumptions and wonders if she should look at certain transformations that are difficult to interpret but which remove much of the multicollinearity. To me this seems like jumping from the frying pan into the fire.
The first thing to recognize is that the presence of multicollinearity is not a violation of assumptions. It is worth repeating, MULTICOLLINEARITY IS NOT A VIOLATION OF ASSUMPTIONS. All of the tests and confidence intervals in a regression model are valid in the presence of multicollinearity.
Multicollinearity does lead to a loss of precision and power, so you have to look at the overall findings. If they are positive, then say "In spite of severe multicollinearity, we were able to establish an association between our exposure variable and our outcome." If the results are negative, then say "Although these results are negative, we need to be cautious about our findings, since the presence of multicollinearity may have led to a serious loss in precision for our estimate of the exposure effect."
Another thing to keep in mind is that the multicollinearity is often just a factor among your covariates and it may not directly involve your exposure variable. In this case, you may have some difficulty figuring out which covariates are more important than the others, but who cares. As long as you adjust for all the relevant covariates, your estimate of the exposure effect should still be good.
Some people advocate tossing out some of the covariates if there is multicollinearity, and this is a defensible course of action. The latest word, as I understand it, though, is that you are still better off keeping all your covariates in. There are a lot of opportunities for mischief if you start tinkering with the covariate list. I'll try to write more about this when I have time.
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