Say I have an independent variable with the following relationship to the binary dependent variable, DV:
___________________________________________________________________________
|verx_s | # Recs | % Recs | # DV | DV Rt |
|________________________________|_________|_____________|_________|________|
|0 | 75,700| 6.4467%| 941| 1.243% |
|1 | 277,129| 23.6009%| 1,471| .5308% |
|2 | 51,662| 4.3996%| 219| .4239% |
|3 | 769,737| 65.5526%| 2,269| .2948% |
|All |1,174,228| 100.0000%| 4,900| .4173% |
|________________________________|_________|_____________|_________|________|
It's common practice at my company to recode the values of verx_s to the value of DV Rt and treat it as a continuous variable when modeling logistic regression. Confidence intervals are not important. All we care about is whether the model validations on an out-of-time sample. Is there anything inherently wrong with taking this shortcut?
It should also be mentioned that in most cases the independent variable is crafted in such a way that it makes intuitive sense to our customers. Therefore the ordering of the target mean is important. Hence, why we can't use simple dummy vars.
verx_s
variable is the result of several crossings and interactions with other fields. It is a compound attribute that has been created in an intuitive manner (for the consumer credit risk world). The relationship HAS to be monotonic for legal reasons. A person has a right to know why they are denied credit, for example, and the monotonic relationship supports that kind of disclosure. Your point about recoding as odds is one I've brought up to my colleagues. The pros/cons of such choices is what I'm interested in from a theoretical perspective. THanks! $\endgroup$