multicollinearity in a logistic mutlilevel model: testing and implications

[Sid Molloy]

Hi all:

I've put together a multilevel (binomial) logistic model using 'meqrlogit'. The model appears to have a very good fit, and the coefficient standard errors are all more than acceptability small for the purposes of the model (and all p-values are <0.001).

However, the model includes an interaction term and this seems to be causing multicollinearity. Of note, this is not because the standard errors grew large when I added the interaction term (they remained small), but rather because of some prelimary VIFs I calculated (which was ~40 for the interaction term and one of the predictors).

Theory suggests the model would not be correctly specified if the interaction term were dropped.

I have two related questions:

1) How to test for mutlicollinearity when using meqrlogit?

Searching this forum, I see that multicollinearity is a property of the data (here), meaning I can just run a series of single level linear regressions (using 'regress') and calculate the VIFs for each using R^2.

Is this correct if I'm using multilevel logistic regression (meqrlogit)? Or do I need to do an equivalent single-level test using logistic regression?


2) Do I have a multicollinearity problem?

Despite the high VIFs (for now assuming I've calculated these correctly), and based on another previous discussion on this forum (here), my understanding is that I don't have a problem.

As I understand it, multicollinearity may affect individual coefficients in the model, but I am not trying to assess the separate effects of each variable in the model.

Rather, the purpose of the model is to make predictions: as I understand it, multicollinearity does not significantly affect model predictions. Is that correct?

If this is correct, I'll need to chase down a reference supporting it. I've found a few online blogs/discussions on multicollinearity and prediction, but I have not come across a textbook or paper. If anyone knows of any, please do let me know.

Thanks.

[Clyde Schechter]

The bottom line is that you don't have a multicolinearity problem--your standard errors are sufficiently small--end of story. If you have nothing better to waste your time on than running some VIF's, go ahead and be my guest. Just promise me that if you come out with some "large" VIF's you won't waste even more time wondering why or what to do about them. It's not just that multicollinearity does not "significantly" affect model predictions: it doesn't affect them at all.

Arthur Goldberg's A Course in Econometrics, Harvard University Press 1991 has an entertaining chapter (Chapter 23) on why multicolinearity is a bogus issue.

[Sid Molloy]

Thanks a lot for the reply Clyde, and for also including a reference. I agree with you on this entirely. The issue has come up in peer review of a paper so I need to make a strong case: your advice and the reference certainly provide this!

[Bruce Weaver]

Goldberg's comments on micronumerosity can be seen here.

• http://davegiles.blogspot.ca/2011/09...umerosity.html

[Sid Molloy]

Thanks Bruce. Much appreciated. I've now read Goldberger's chapter and found it both enlightening and amusing (esp on 'micronumerosity'). I will certainly recommend it to anyone tangling with multicollinearity...