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# RE: st: RE: Multicollinerity test in IV regression

 From "Nick Cox" To 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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```

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