Multicollinearty in logistic regression models
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