I attempted this on my own and didn't get very far and having looked at the answer to piece together my understanding.. it hasn't helped. I've tried to use the example on p658 of CMP to follow along, though I'm lost where model A becomes [1] I'm putting together the linear function, but this is where I'm struggling I think. I take the claim numbers for each class as variables and the class of each policy as factors. I don't know where to go from here in terms of creating a linear predictors for the variables and the factors. I believe this is the predictor for the variables: α*SUM(1,10): y_i + β*SUM(11:15): y_i + γ*SUM(16:35): y_i And this is the predictor for the factors: – 10*exp(α) – 5*exp(β) – 20*exp(γ) How are these constructed? η = log(μ_i) = -n1*α - n2*β - n3*γ which becomes μ_i = -n1*exp(α) - n2*exp(β) - n3*exp(γ) I'm very confused with this initial bit, thanks.
The linear predictor is just \(\alpha\) for the 1st 10 values of i, \(\beta\) with the next 5 values of i and then \(\gamma\) for the last 20 values. Then we use the given link function of \(log\mu\) to replace the \(\mu\)'s. Essentially, in the log-likelihood you should substitute \(\mu \) with \(exp{\alpha}\) for the 1st 10 values of i, \(exp{\beta}\) with the next 5 values of i and then \(exp{\gamma}\) for the last 20 values. Then you differentiate with respect to \(\alpha\) and set that equal to zero, which will give you your estimate for \(\alpha\). Then differentiate with respect to \(\beta\) and set that equal to zero, which will give you your estimate for \(\beta\) and so on. Does that help?
