[R] Multicollinearty in logistic regression models

[cberry at tajo.ucsd.edu]

David Winsemius <dwinsemius at comcast.net> writes:

> On Dec 15, 2011, at 11:34 AM, Mohamed Lajnef wrote:
>
>> Dear All,
>>
>> Is there a method to diagnostic multicollinearty in logistic
>> regression
>> models  like vif indicator in linear regression ( variance inflation
>> Factor ...) ?
>>
>
> Wouldn't matrix representation of the predictor "side" of the
> regression be the same? Couldn't you just use the same methods you
> employ for linear regression?

Trouble is that in logistic regression the Fisher Information for each
case has a factor of p[i]*(1-p[i]) (where 'p' is the vector of success
probabilites and 'i' indexes which case).

If the value of p[i] is very near one or zero, then the information
provided is scant. And this will happen if you have a really good
predictor in the mix.

Even with an orthogonal design, you can wind up with huge variances. And
you can have an ill-conditioned var-cov matrix for the coefficients
depending on how different cases get weighted. Thus, you could get the
equivalent of multicollinearity even with an orthogonal design.

And the diagnostics for linear regresson would not be all
that helpful if you have a good predictor.

OTOH, if the predictors were collectively pretty weak, the linear
regression diagnostics might be OK.

Mu advice: Google Scholar 'pregibon logistic regression', click where it
says 'cited by ...' and page through the results to find good leads on
this topic.

HTH,

Chuck

>
>> Thank you in advance
>> M
>>
>> --
>> ####################################
>> Mohamed Lajnef,IE INSERM U955 eq 15#
>
>
> David Winsemius, MD
> West Hartford, CT
>

-- 
Charles C. Berry                            Dept of Family/Preventive Medicine
cberry at ucsd  edu			    UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901