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Old 06-15-2018, 12:09 PM
2pac Shakur 2pac Shakur is offline
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Default GLM for mortality

The applied statistics module uses a poisson distribution with a log-link to model mortality.

Why would that be more appropriate than using logistic regression?

Is there a good online (free) resource for guidance on GLM parameters by use case? By parameters - I am referring to distribution and link function.

Thank you
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Old 06-15-2018, 12:35 PM
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If by "model mortality" you mean "model expected time (from now) until death" . . . then logistic regression isn't the correct set up as it generally models binary results (e.g., will you die in the next x years where x is a fixed value).

I've found the following material (from CAS MAS-I exam) to be helpful:
http://www-bcf.usc.edu/~gareth/ISL/I...20Printing.pdf
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Old 06-15-2018, 12:51 PM
2pac Shakur 2pac Shakur is offline
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Yea - I'm not looking at a classification model - I am looking to model a qx - which is between 0 and 1. Seems like a perfect candidate for logistic - but maybe the interpretation is difficult to model projections?

Anyway - thanks for the material - I will have a look...
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Old 06-15-2018, 01:48 PM
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You can do Binomial distribution where X ~ Bi(N, p) and use the logistic regression to get "p". It's just with a high N and low p, it converges to a Poisson anyway. From Wikipedia:

Quote:
The Poisson distribution can be derived as a limiting case to the binomial distribution as the number of trials goes to infinity and the expected number of successes remains fixed — see law of rare events below. Therefore, it can be used as an approximation of the binomial distribution if n is sufficiently large and p is sufficiently small. [21]
There is also negative binomial which is more flexible than poisson. The poisson distribution has the mean/variance equal whereas the negative binomial does not. There are also zero-inflated poisson models as well. These are going to be more difficult to implement though.

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Old 06-15-2018, 02:00 PM
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Also, if you want to run this as a logistic model, you would have to change your data from the number of people in one column and number of deaths in another to all 1's and 0's. So if you have 10000 people and 100 deaths and want the deaths to be zeros, then you need 100 0's and 9900 1's in your dataset instead with the predictors that you'll be using for each member.
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Old 06-15-2018, 02:09 PM
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Thank you.

Do any of you use a GLM for modeling mortality and/or lapse?
Do you use (quasi)Poisson with log-link for everything?
Does it vary by case?
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Old 06-15-2018, 02:40 PM
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I've supervised interns doing lapse models with a GLM . . . logistic regression.

But the question was looking at what were some key indicators of new business not renewing with the company; so GLM was the route of choice.

However, if you're just looking at a "final answer," you could use some additional "data science" type analysis as outlined in the reference I linked above.
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Old 06-19-2018, 01:01 PM
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I believe the primary advantage of using a Poisson model with a log link for mortality is that then the modeled mortality naturally decomposes as a product of factors, which is consistent with how mortality assumptions have traditionally been expressed (e.g. preferred mortality is x% of standard mortality).

It's theoretically unreasonable, of course -- you're using a model that says that it's possible for a cell that contains N lives to experience more than N deaths. But practically speaking the mortality rates being considered are rather small, and in that case there isn't really that much difference between a Poisson distribution with mean Nq and a binomial distribution N events with probability q.
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Old 06-19-2018, 01:46 PM
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Quote:
Originally Posted by 2pac Shakur View Post
Thank you.

Do any of you use a GLM for modeling mortality and/or lapse?
Do you use (quasi)Poisson with log-link for everything?
Does it vary by case?
Hi,

Is there a reason why you're limiting yourself to GLMs? I think there are many reasons why this occurs, but just wanted to see what your constraints are (regulatory, software, etc).

I personally don't use GLMs very often for modeling mortality, churn, retention, etc. I'm guessing you mention quasi-Poisson because there are overdispersion problems. In those cases, I think a decent fix is to switch over to a negative binomial distribution where you can set up differing means/variances.

Another typical approach outside of GLMs is going to be a survival model, such as proportional hazards, which feels similar to a Poisson regression and is a little more computationally heavy, but should give you better results.

State of the art stuff for "time-to-event" is something like this: https://ragulpr.github.io/2016/12/22...hurn-modeling/

But this requires more data at different times than what you're probably working with.

-Riley
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