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#1




What do you do with the intercept in a GLM?
Couldn't find any clarification on this in the CAS Monograph 5. We're not using software to implement the model. The factors get put into SQL. I present the factors to the underwriters with a confidence interval and they make selections within that interval.
For continuous variables, we determine a base rate, and bin the continuous data. For each bin, we take the midpoint to calculate the factor. So if it's a bin of property value [0, $1M] the formula is ($500K/Base Rate)^Factor. I know this degrades the model, but the underwriters would rather have bins than for me to put the formula into SQL. Some of the intercept values are very different. One model has a logged value of 9.68, so is .00006 on linear scale which has a large impact on the final value. So how do you handle that? Excluding it causes the factors to look unrealistic. My guess is that you treat it like a control variable and ignore it since I'm really only interested in the relativity, but curious what others do. 
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However note that having control variables in the model that aren't included in the scoring will make your intercept not make sense, so you will need to manually reset your base rate to bring the predictions in balance. 
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I've been poking around old GLM posts on here and see the same people that answer my questions are the same people that still answer. Thanks to you guys for continuing to answer my basic questions! 
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You should read through the Ratemaking material for CAS Exam 5 to address the fundamentals of your question regarding "base rate".
There really is too much to address in posts here that already is captured rather well (if I may say so) elsewhere.
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That was the exam I stopped at before deciding not to be an actuary, only to end up back in insurance. I'll give it a read; hopefully doesn't give me PTSD. I guess I have no choice, but to learn ratemaking if I want to fully understand how to implement a model. Would be much easier if I could just create an API lol. 
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For anyone else in the same boat as me, this article is pretty useful:
https://www.casact.org/pubs/forum/00wforum/00wf107.pdf 
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After binning my continuous variables, I ran the frequency models using MoralHazard's advice.
Is this the correct way to do it? I ran the model with continuous variables, took the predictions of that, attached it to my training data, and then ran the model with the same variables except binned versions. Since the predictions are continuous, I switched to the Gamma distribution. The residuals look random, so I think that's a safe move. If this is correct, I have some additional questions. Is the reason this works is because the original model did all the work, so if you keep all the original variables, it's just regressing toward the mean of each bin and adjusting the other variables to account for that? Where would I get the standard errors from to create confidence intervals? Use the continuous version standard error for every bucket? 
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Interesting question. This procedure really just produces restated model factors, but not standard errors. If you do need standard errors for the restated model, one thing you can try is bootstrapping this whole procedure. That is, take a random sampling of your training data with replacement, fit the first model, fit the second model on top of that, and save the resulting factors. Repeat 1000 times (or 10,000, or whatever is practical) and use the +/ 95% range of the distribution of the factors as your confidence interval. (Though I imagine there's probably some simpler way to get CIs.) 
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