Pros/Cons of recoding ordinal/nominal variables to target mean for logistic regression?

Question

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.

Answer 1

If I understand you correctly you are assigning values to categories of your explanatory/independent/right-hand-side/x variable based on average values of your explained/dependent/left-hand-side/y variable. I suspect that the purpose of that excercise is to assign values to the categories of verx_s such that the linear effect of the resulting variable in your model is (close to) maximal. If that is the case then what you are looking for is a sheaf coefficient (Heise 1972). However, for one categorical or ordinal variable this just boils down to a different way of presenting your results when you added your variable to the model as a set of indicator (dummy) variables. If all you care about is out of sample predictions, then the easiest way to achieve your goal is to just add verx_s as a set of indicator variables.

As Peter Flom already suggested, you could try and do some programming to impose monotonicity, but the resulting program will in all likelihood fail to converge or converge at unreasonable values when the pattern in the data is not monotonic.

Heise, David R. 1972. "Employing nominal variables, induced variables, and block variables in path analysis." Sociological Methods & Research 1(2): 147-173.

Answer 2

You can use dummy codes with ordinal independent variables. The effect may not be monotonic, but that's OK; in fact, it may be revealing.

I am not aware of any standard methods that impose a monotonic relationship with an ordinal independent variable; there may be some. You could also probably write some function that would do it, if you are ingenious enough (e.g. if in SAS, using PROC NLMIXED' or programming something inR`. I wouldn't recommend that, however.

Recoding an ordinal variable to a continuous one is possible, too, but it needs substantive justification (and should probably be tested with sensitivity analysis). I have done this, e.g. with specified Likert variables such as

0 - Never
1 - Once a week
2 - 2 or 3 x a week
3 - Daily
4 - Twice a day

or something like that, which could be recoded to "times per week" and then 0 = 0, 1 = 1, 2 = 2.5, 3 = 7 and 4 = 14.

Answer 3

This approach seems more futile than wrong. Why not go the whole hog & recode the independent variable as the log-odds of the dependent variable in each category? Then you have a perfect linear relationship, with all coefficients unity & zero intercept. But you haven't actually gained anything over using dummy variables; you've just re-described the relationship in a confusing way, & any apparent parsimony is only apparent.

I can't follow the argument about monotonicity. If the DV should (in whatever sense of 'should') change monotonically with the IV as originally coded, & doesn't, it's simply evading the issue to create a different coding which re-orders the IV's categories. And of course if it does change monotonically with the IV as originally coded, there's no problem in using dummy variables.