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st: RE: multicollinearity test for probit?


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: multicollinearity test for probit?
Date   Wed, 10 Dec 2003 22:12:00 -0000

As I understand it, multicollinearity on the right-hand side 
is much the same irrespective of what is on the left-hand 
side or what link function is contemplated. So I don't 
see that you are obliged to do it retrospectively. 

The world divides here into those who think in terms of 
some test (e.g. through an omnibus or portmanteau test statistic)
and those who want to examine structure or look for potential 
problems in an exploratory way. As someone firmly in the 
latter camp, I've no idea if there's some overall test 
which supposedly maps all pertinent information into a single 
statistic. If they tell you there is one, its merits
are probably exaggerated. 

Three things spring to mind. There are probably thirty others, 
and my three may not even be among the most important. 

1. -_rmcoll- 
============ 

Check it out. 

2. -pca-
========

One of the best general ways of looking for structure 
is to look at the principal components of the predictors. 
The eigenvalues give a quick guide to whether you have clusters of 
variables. Perhaps the best single diagnostic is not 
among the standard outputs: it is the correlations 
between the original variables and the components. 
-makematrix- on SSC gives a relatively painless
way of getting those concisely and directly. 

Sometimes you look at the principal components
and see some structure that you then realise 
could be presented and explained in some other
way, say directly in terms of the correlation
matrix. It's like climbing up the North Face 
with pitons and ropes and goodness knows what, 
but when you get to the top you see that there
was an easier way to climb up there all the time. 
(I've never done this, but I saw Clint Eastwood do it once.
Principal components, that is.) 

3. scatterplot matrix
=====================

This can be a good way of scanning a few dozen 
predictors. You are just on the look out for scatter plots
with strongly diagonal patterns. (But watch out 
for outliers too.) 

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

Matt A. Barreto
 
> Is there a similar command to vif following regress when 
> using probit or
> oprobit (or logit/ologit) to test for multicollinearity 
> among independent
> variables in a probit equation?

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