I have changed my modelling technique. Instead of continuing with logistic regression, I am going with a total least squares approach instead. For those serious number crunchers out there, see:
(http://en.wikipedia.org/wiki/Total_least_squares).
Why change the approach? Well, I am a bit worried about the error in this model. In particular, this should satisfy those who belive in the potential sub-levels theory since it allows for error in both the response and dependent variables. I can now drop that assumption from my (long) list of assumptions. It is certainly more complex but that is another story.
In any case, in order to program this I had to go back to my university days and re-learn non-linear programming. This allowed me to put certain constraints on the model parameters (so, for example, no coefficient becomes negative, which I was having a problem with under logistic regression).
I would still like to put additional constraints but I think I have reached the limit of my skills. If anyone knows anything about non-linear programming, and in particular how to program it in SAS, please contact me.
Run of the Mill Canadian Manager