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  #51  
Old 02-21-2019, 08:48 AM
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JohnLocke JohnLocke is offline
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Originally Posted by FactuarialStatement View Post
That’s not what I tried to prove and you missed the point by a mile. Go look at output again.



Of course the predictions are the same. You also missed the point.

The level of analysis on my code here is really proving that (most) Actuaries should stay away from ever trying to do statistical inference..
It's almost like you intentionally make every post as vague as possible so you can follow-up with a smug "gee, why didn't these dum-dums get the point (that I never made)?" Dude, all you did was throw up some code vomit. If you have good points, make them. If you are half as smart as you act we would all be blessed to have even a fraction of your wisdom bestowed upon us. You do an awful job of communicating (hey, communicating can be hard, I get that) but then lace every response with condescension (to what end? If you are getting frustrated that people don't get "your point" then may you could try more clearly elucidating your point?). This is a fun topic that you are making not-fun.
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  #52  
Old 02-21-2019, 08:50 AM
Actuarially Me Actuarially Me is offline
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Originally Posted by ShundayBloodyShunday View Post
Sorry. I just started posting recently and it gets frustrating when my topics/questions get derailed by him.
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  #53  
Old 02-21-2019, 09:06 AM
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ShundayBloodyShunday ShundayBloodyShunday is offline
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Originally Posted by FactuarialStatement View Post
Thatís not what I tried to prove and you missed the point by a mile. Go look at output again.



Of course the predictions are the same. You also missed the point.

The level of analysis on my code here is really proving that (most) Actuaries should stay away from ever trying to do statistical inference..
The level of your explanation is like a college professor trying to teach 2nd graders how to subtract by borrowing.
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  #54  
Old 02-21-2019, 09:51 AM
Actuarially Me Actuarially Me is offline
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This thread got a bit distracted. Here's what I've gathered from user response and other readings I have done.

Per the "Practitioners Guide to GLMS (I'd link it, but it links to a direct pdf):

Page 3: log linked Poisson GLMs are equivalent to multiplicative balance principles of minimum bias estimations (minimum bias estimation goes all the way back to the 1960s and were used when computing power was limited)

Page 19: Log-linked Poisson is commonly used for Frequencies because the log link makes it a multiplicative model (much easier to implement and compare factors) and because it is invariant to measures of time: modeling frequencies per year will yield the same results as per month.

Page 20: Log-linked Gamma is commonly used for Severities because the log link makes it multiplicative and Gamma is invariant to measures of currency. Measuring severity in dollars and cents will yield same results.

The log linked Tweedie distribution w/ p in (1,2) is considered a compound Poisson-Gamma distribution. The closer to 1, it acts more like Poisson, and closer to 2, it acts more like Gamma. Common values are 1.5-1..65. It also makes the assumption that frequency and severity are highly correlated. I'm not too familiar with the Tweedie distribution likelihood function, but due to its complexity, it's a bit harder to grab some metrics.


It really depends on your data if it is appropriate. When you select a family, you're choosing the mean-variance relationship. For Poisson GLMs, the mean-variance relationship is the identity. Despite the warnings that most statistical software gives you, it's completely reasonable to model a relationship in continuous data in which the relationship between two variables is linear on the log scale, and the variance increases in accordance with the mean.

If you look at the residuals, you can determine whether the Poisson mean-variance relationship is accurate. If not, may be better to use Gamma whose mean-variance is x^2.

Back to my original question: Is there any major disadvantages of using Poisson over Tweedie? No, but it's worth also checking Gamma.
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  #55  
Old 02-21-2019, 09:54 AM
MoralHazard MoralHazard is offline
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Originally Posted by FactuarialStatement View Post
Thatís not what I tried to prove and you missed the point by a mile. Go look at output again.



Of course the predictions are the same. You also missed the point.
So what was the point? That the significance statistics are different? But when you swap in quasipoisson, the significance statistics are similar too. So what precisely were you trying to demonstrate with that code?
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  #56  
Old 02-21-2019, 07:12 PM
magillaG magillaG is offline
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Originally Posted by Actuarially Me View Post
This thread got a bit distracted. Here's what I've gathered from user response and other readings I have done.

Per the "Practitioners Guide to GLMS (I'd link it, but it links to a direct pdf):

Page 3: log linked Poisson GLMs are equivalent to multiplicative balance principles of minimum bias estimations (minimum bias estimation goes all the way back to the 1960s and were used when computing power was limited)

Page 19: Log-linked Poisson is commonly used for Frequencies because the log link makes it a multiplicative model (much easier to implement and compare factors) and because it is invariant to measures of time: modeling frequencies per year will yield the same results as per month.

Page 20: Log-linked Gamma is commonly used for Severities because the log link makes it multiplicative and Gamma is invariant to measures of currency. Measuring severity in dollars and cents will yield same results.

The log linked Tweedie distribution w/ p in (1,2) is considered a compound Poisson-Gamma distribution. The closer to 1, it acts more like Poisson, and closer to 2, it acts more like Gamma. Common values are 1.5-1..65. It also makes the assumption that frequency and severity are highly correlated. I'm not too familiar with the Tweedie distribution likelihood function, but due to its complexity, it's a bit harder to grab some metrics.


It really depends on your data if it is appropriate. When you select a family, you're choosing the mean-variance relationship. For Poisson GLMs, the mean-variance relationship is the identity. Despite the warnings that most statistical software gives you, it's completely reasonable to model a relationship in continuous data in which the relationship between two variables is linear on the log scale, and the variance increases in accordance with the mean.

If you look at the residuals, you can determine whether the Poisson mean-variance relationship is accurate. If not, may be better to use Gamma whose mean-variance is x^2.

Back to my original question: Is there any major disadvantages of using Poisson over Tweedie? No, but it's worth also checking Gamma.
Another way to think about it is how the errors scale.

For a true poisson distribution, the error is proportional to the square root of the mean. So if you measured value is 110, and your model thinks the true value is 100, then you are like 1 sigma off. And if your measured value is 1032 and your model thinks the true value is 1000, then that is also 1 sigma off. It weights the two errors appropriately relative to each other.

For gamma, the error is proportional to the mean. So if 110 vs 100 is equivalent to 1100 vs 1000.

The variances add in your pure premium: the variance from the poisson process that is probably driving your claims, plus some severity distribution's variance. So the poisson model probably doesn't assume enough variance, and your model will give to much weight to the data point at 1000.

Just how much does that matter? You mileage will vary.

The other problem is that the poisson will get our standard errors wrong as well. The over dispersed poisson model helps with that part.
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  #57  
Old 02-22-2019, 09:07 AM
Actuarially Me Actuarially Me is offline
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Originally Posted by magillaG View Post
Another way to think about it is how the errors scale.

For a true poisson distribution, the error is proportional to the square root of the mean. So if you measured value is 110, and your model thinks the true value is 100, then you are like 1 sigma off. And if your measured value is 1032 and your model thinks the true value is 1000, then that is also 1 sigma off. It weights the two errors appropriately relative to each other.

For gamma, the error is proportional to the mean. So if 110 vs 100 is equivalent to 1100 vs 1000.

The variances add in your pure premium: the variance from the poisson process that is probably driving your claims, plus some severity distribution's variance. So the poisson model probably doesn't assume enough variance, and your model will give to much weight to the data point at 1000.

Just how much does that matter? You mileage will vary.

The other problem is that the poisson will get our standard errors wrong as well. The over dispersed poisson model helps with that part.
Thanks! So poisson standard errors will always be lower since it doesn't assume enough variance.
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  #58  
Old 02-22-2019, 10:10 AM
Heywood J Heywood J is offline
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Originally Posted by Actuarially Me View Post
Thanks! So poisson standard errors will always be lower since it doesn't assume enough variance.
That's not the reason. Standard errors are more a function of the estimate of your dispersion parameter; the higher the dispersion, the higher the standard error.

For standard Poisson, dispersion is not even estimated, as it's assumed to be 1. In practice, dispersion is higher than 1, and way higher than 1 if you're using Poisson to model pure premium. As long as you're using Pearson estimate of dispersion, your standard errors should be more or less in the same ballpark regardless of distribution you pick, but if you use something like a deviance estimate, then you may be off by a mile if your distribution is off by a mile.
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