st: collinear categorical variable identification

[Buzz Burhans <wsb2@cornell.edu>]

Dear Stata listers, especially epidemiologists,

I have a question related identification and removal of collinear 
categorical variables  My question(s) are about use of coldiag or other 
methods to identify collinear dichotomous variables for logistic regression.

I have replaced the nominal and ordinal independent variables with 
dichotomous indicator variables.   The dataset contains a fairly large 
number of factors which are collinear independent variables, and I am 
uncertain of the best way to identify and eliminate collinearity in the 
case of categorical variables.

I have used coldiag, with a cut off of 30, accompanied by theoretical 
plausibiity, to identify candidates for removal from independent variables 
due to collinearity.  However, I find that there is still some instability 
in the model, indicated by large CIs for the odds ratios.  I then looked at 
the correlation matrix for the regressors, and  using a combination of 
identification by a lower singular value (10), and by what is suggested by 
the independent variable correlations, I identify candidates for further 
removal. In making the identification I consider the correlation of two 
independent variables (if > 0.35, strong consideration for removal) and the 
contribution to variance decomposition (> 0.5 sugests removal), and the 
strength of the correlation to the dependant variable ( the stronger of two 
variables suggests it should be retained when there are competing 
candidates), and theoretical plausibility.

My understanding is that using the correlation matrix when the regressor 
matrix includes dichotomous variables is not appropriate.  However, the 
models are stable and sensible, and improved (more stable) from my earlier 
runs when I used simply the coldiag and a higher  condition number as a 
cutoff. when I go back and tabulate the competing variables the in 2 way 
tables my decisions seem to be reasonable.  When they are two dichotomous 
variables the odds ratios seem to support the decisions, and visual 
inspection of the tables for categorical variables with several categories 
seem consistent with the decisions70740buz
 for retention or exclusion I made. ( the dataset is relatively small, and 
there are not uncommonly empty cells in the twoway tabulations.


Can you comment on my strategy, in particular on the appropriateness of 
coldiag approach in this case, and on the appropriateness of using a 
correlation assessment for categorical variables? Can you suggest a better 
strategy?

Thanks very much for any help you can offer.



Buzz Burhans
wsb2@cornell.edu



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