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Generalized linear models (GLM)

Although both are known now, there is a time element involved in  
which one, max.loss was fixed at the time of underwriting and loss was  
unknown at that time. This *is* an insurance question is it not?

Wouldn't the question be: Can one use the group variable to estimate  
the proportion of max.loss actually lost following underwriting?

I would vote "no" on all of those offered solutions. If you believe  
otherwise, you should write an explanation to a hypothetical professor  
what the output of any of the models actually means.