Fall 2016 Q6.b - A little confused about offsets
So in the reading it says "We do this via an offset which is a predictor variable with the coefficient set equal to 1." However, in the solution they say we add the variable to the model as an offset, and that we would estimate B4. I would have thought that since that the prior claim count variable was being added as an offset, its coefficient should be 1, so B4=1 instead of estimating it.
To me, it seems like really every other variable is being added as an offset, that is, we have already modeled their coefficients, and now we're adding them with them to a new model where we're keeping their coefficients fixed and using them to estimate a new coefficient for the new prior claim count variable. Is this correct, and the issue is just that the language in the solution is a little loose, or is there something that I'm getting wrong?
Comments
Technically, the solution says "The result from the new business model can be added into the renewal model as an offset".
This means we set up another model ("the renewal model") which will reproduce the behavior of the new business model whenever a new business risk is input. We should interpret "the result" in this context to mean the coefficients of the variables within the new business model.
That is, the coefficients of the renewal model has the same coefficients as the new business model whenever the two models share a common variable. In fact, to correctly reproduce for new business within the renewal model, the renewal model must contain every variable within the new business model. I.e. we're offsetting each variable from the new business model within the renewal model.
When we do this, we only need to estimate the coefficients for any variables in the renewal model that aren't in the new business model, and re-estimate the coefficient. Notice by re-estimating the coefficient we're not guaranteeing the new business model and renewal model produce the same output for new business risks. However, they both behave the same way when you perturb the input characteristics of a new business risk. This is why in the question it says the coefficients should be consistent between the models rather than specifying the renewal model must output the same as the new business model when we input a new business risk.