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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Multicollinerity test in IV regression |

Date |
Wed, 13 Oct 2004 14:56:13 -0400 |

On Wed, 13 Oct 2004 18:10:10 +0100, Nick Cox <n.j.cox@durham.ac.uk> wrote: > I assert that multicollinearity is a property of the > predictors and does not depend on what > you do with them before, during or > after any examination of multicollinearity. Indeed, multicollinearity has nothing to do with the estimation method, but rather an intrinsic property of the regressor configuration. Any good regression book (not an econometric book!) would have a discussion of multicollinearity. One of the basic references (actually, written by economists) is Belsley, Kuh and Welsh; other books to look at are Fox (it seems to me he is in psychology, although I am not sure, hence his examples are more pertinent for social sciences), or a classic text by Draper and Smith. My advisor at UNC, Richard Smith, has compiled a very modern and comprehensive text on regression, but just does not seem to have time to polish it for a publication; otherwise, this would be the default reference I would provide. There are no "formal" tests on collinearity; all the measures are ad-hoc. The most advanced one is to use singular value decomposition of the regressor matrix and look at the singular values close to zero -- they would correpond to the linear combinations that do not have much variability, and thus cannot be estimated with sufficient precision. Principal component analysis of the regressor matrix serves the same purpose. Stata has -vif- (variance inflation factors) command that shows by how much the variance of the estimated coefficients goes up compared to the imaginary case should regressors be orthogonal to each other. The methods to deal with collinearity are tighlty related to the variable selection methods, and regularization approaches, such as ridge regression, principal components' regression, lasso, etc. Again, Richard Smith's unpublished manuscript deals with them quite nicely, and among the published sources, I would recommend Hastie, Tibshirani and Friedman's book "The Elements of Statistical Learning". -- Stas Kolenikov http://stas.kolenikov.name * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: Multicollinerity test in IV regression***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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