Re: st: RE: Multicollinerity test in IV regression

[Marcello Pagano <pagano@hsph.harvard.edu>]

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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