Re: Multicollinearity !!!!!

On Wed, 06 Aug 2008 18:27:40 -0400, Paul Rubin <rubin@xxxxxxx> wrote:

Richard Startz wrote:

What is your problem? Multicollinearity does not bias the coefficients
of a regression. Statistical inference is fine.


Multicollinearity tends to inflate the variances of some or all
coefficients, so drawing inferences gets tricky. Consider the extreme
case (one predictor is literally a linear combination of the other
predictors): there's a unique set of predictions that minimizes total
squared error over the sample, but there's an uncountable number of
coefficient vectors that produce those predictions (and no way to pick a
winner among them).

/Paul

Paul:

[This must be a frequently argued question :)]

When there is multicollinearity, the variances of the coefficients are
larger than if there were not multicollinearity. All the standard
inference procedures are correct.

I agree completely with the extreme example you give. The problem is
that unless there is external information, there is--as you say--no
way to pick a winner. So the right cure for multicollinearity is to
get more data, better data, or to have prior information about the
coefficients. Unfortunately, people want to find an algorithm to "get
around" multicollinearity.

-***

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