Case weighted logistic regression

Question

I'm looking at a few logistic regression issues. ("regular" and "conditional").

Ideally, I'd like to weight each of the input cases so that the glm will focus more on predicting the higher weighted cases correctly at the expense of possibly misclassifying the lower weighted cases.

Surely this has been done before. Can anyone point me toward some relevant literature (Or possibly suggest a modified likelihood function.)

Thanks!

Answer 1

glm holds a parameter weights exactly for this purpose. You provide it with a vector of numbers on any scale, that holds the same number of weights as you have observations.

I only now realize that you may not be talking R. If not, you might want to.

Answer 2

If you have access to SAS, this is very easily accomplished using PROC GENMOD. As long as each observation has a weight variable, the use of the weight statement will allow you do perform the kind of analysis you're looking for. I've mostly used it using Inverse-Probability-of-Treatment weights, but I see no reason why you couldn't assign weights to your data to emphasize certain types of cases, so long as you make sure your N remains constant. You'll also want to make sure to include some sort of ID variable, because technically the upweighted cases are repeated observations. Example code, with an observation ID of 'id' and a weight variable of 'wt':

proc genmod data=work.dataset descending;
    class id;
    model exposure = outcome covariate / dist=bin link=logit;
    weight wt;
    repeated subject=id/type=ind;
run;