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RE: st: RE: Multicollinerity test in IV regression


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Multicollinerity test in IV regression
Date   Wed, 13 Oct 2004 22:38:36 +0100

Excellent advice. I did say "often", not always. 

Nick 
n.j.cox@durham.ac.uk 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Marcello
> Pagano
> Sent: 13 October 2004 22:34
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: Multicollinerity test in IV regression
> 
> 
> I agree somewhat with what Nick says, but I would like to take
> it one step further. Indeed, mathematically one can think of the
> predictors, over this particular sample region, as defining a linear
> space.  If the space is not of full rank, then there is 
> multicollinearity.
> That means that a linear combination of two, or more of the
> predictor variables, or even linear combinations of two or more of
> the predictor variables, equal zero.
> 
> In the finite precision world we live in with computers, zero is
> interpreted to be relatively small. This is especially important
> in the statistical world we live in where the predictors themselves
> (big secret) may be known with error.
> 
> These linear combinations are not unique, but, and here is where
> I disagree with Nick, they are informative.  Possibly because it is
> not clear that the solution is the simple one implied by Nick: 
> drop one, or more, variables until we get rid of the problem. 
> A better solution might be to replace all offending predictors
> by (a) linear combination(s) that make sense.  For example if
> X1+X2=0, then drop both X1 and X2 and replace them with the
> new variable X1+X2. You can extend this to the more general
> situation.
> 
> 
> Just a thought.
> 
>  m.p.
> 
> 
> 
> Nick Cox 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. 
> >
> >You can look at the structure of relationships 
> >with -graph matrix-; get numerical summaries 
> >by using -correlate-; and use -_rmcoll- to 
> >look further. 
> >
> >Whether there is some omnibus test of multicollinearity 
> >I do not know. If there were, it wouldn't necessarily 
> >be helpful in indicating what to do. 
> >
> >I have always found it most useful 
> >to think about the meanings of variables and the 
> >roles they play in terms of the underlying science.  
> >That is, reflection often makes it seem unsurprising
> >that two or more variables are highly correlated, 
> >so that they tell the same story and only one 
> >need be recorded. 
> >
> >However, there are other issues particularly where 
> >lots of dummies are included. 
> >
> >Nick 
> >n.j.cox@durham.ac.uk 
> >
> >Rozilee Asid
> > 
> >  
> >
> >>Just to ask one simple question, how do I test for the existence of
> >>multicollinearity after using ivreg2 command.
> >>
> >>    
> >>
> >
> >*
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> >  
> >
> 
> -- 
> ______________________________________________________________________
> 
> Marcello Pagano 
> Biostatistics Department			Tel: 1-617-432-4911
> Harvard School of Public Health		        Fax: 
> 1-617-432-5619 
> 655 Huntington Avenue            		
> email:pagano@biostat.harvard.edu
> Boston, MA  02115                 		
http://biosun1.harvard.edu/~bio200
USA

eppur si muove


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