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Old 03-09-2018, 09:15 AM
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Default GLM ? - time variable

If using 'year' or any other datetime variable as a control for trends/development/etc., do you include it as an actual variable and then ignore the output with respect to relativities, or use it as an offset so that there's no output to begin with? The couple texts I've read aren't specifically clear, and the two approaches appear to provide different results. In the particular sample data I'm working with the deviance is almost halved by using it as a variable as opposed to an offset, so that makes sense in this particular case, but I can't find anything to specify if it is generally better to do it one way vs. the other.
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Old 03-09-2018, 09:41 AM
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When you way "use it as an offset," do you mean use the actual time variable itself (such as accident year) as the offset, or a factor that reflects the assumed effect of time (e.g., the development factor multiplied by trend factor) as the offset? If the former, that's wrong -- an offset constrains the coefficient on the variable to be one, and there's no reason your target variable should vary directly with time. If the latter, and your deviance is halved when you use time as a variable, there's probably some major deficiency in your assumed trend/development factors you may want to look into.

Best approach IMO is to use time as a variable to control for time-related effects (so they don't affect your other modeled relativities) and ignore the output.
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Old 03-09-2018, 09:58 AM
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Got it. Was doing the former, and your explanation makes sense. I'm assuming it should be logged as a 'continuous variable' as well? (tweedie w/ log link)

Some of my results still look weird: intercept almost 0 (2e-29), with the 'year' coefficient being relatively large. This makes it difficult to map the coefficients to the fitted values, even though the remaining relativities make sense. Does it make sense to use 'year-2000', 'year/earliest year' or some other transform to temper that variation?
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Old 03-09-2018, 11:26 AM
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Include year as a categorical variable. It may make sense to then model year continuously if the coefficients from the categorical approach show some simple monotonic linear effect of year, but chances are they won't.
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Old 03-09-2018, 11:29 AM
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Originally Posted by ALivelySedative View Post
Got it. Was doing the former, and your explanation makes sense. I'm assuming it should be logged as a 'continuous variable' as well? (tweedie w/ log link)

Some of my results still look weird: intercept almost 0 (2e-29), with the 'year' coefficient being relatively large. This makes it difficult to map the coefficients to the fitted values, even though the remaining relativities make sense. Does it make sense to use 'year-2000', 'year/earliest year' or some other transform to temper that variation?
Yes, subtract 2000 or earliest year, otherwise the silly scale of some numbers is going to be distracting.
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Old 03-09-2018, 11:40 AM
MoralHazard MoralHazard is offline
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If you're going to go with the continuous variable approach, and the year variable is meant to pick up trend (and not other effects such as development) it may be best to leave the variable unlogged. This is because trend is usually modeled as a year-over-year percentage increase, and and unlogged variable in a log link model gives you that. Just subtract the earliest year out of the variable, as Heywood said -- this won't make any difference to your modeled relativities or predictions, but will get rid of that silly low intercept.
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Old 03-09-2018, 11:50 AM
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All very helpful, thank you both.
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Old 03-09-2018, 12:16 PM
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Whoops...one more thing regarding offsets/logging...

Among other things I need baserates and deductibles to be fixed/offset. Goldburd et al monograph indicates to log the offsets in a log-link model to put them on the same scale as the linear predictor, which makes sense. Baserates seem straightforward in this regard, but I'm hesitant on deductible. Seems more accurate to use the relativities associated with higher deductibles than the actual dollar deductible amount for this? Relativities seem more linear and numerically related than the actual dollar amounts, which I could almost see being included as categorical instead. Or is this another case of 'try it both ways and see which one works better'?
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Old 03-09-2018, 12:33 PM
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You offset for the log of relativity, the other way is just wrong. Offset is a predictive variable that you force to have a coefficient of one. It is logical to force a coefficient of one on the current deductible relativity, but it is not logical to force a coefficient of one on the deductible amount, however you put it in the model.
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Old 03-09-2018, 01:28 PM
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Offset logging depend on the software - In Emblem, you put the rating factor ( 1.0 for no credit or debit) into the offset. For SAS and R (and probably most other applications), you would use the log of the factor (0.0 for no credit or debit).
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