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Personal Lines Actuarial Research Department
Generalized Linear Models
CAGNY
Wednesday, November 28, 2001
Keith D. Holler
Ph.D., FCAS, ASA, ARM, MAAA
Personal Lines Actuarial Research Department
High Level
Given Characteristics:
e.g.
Eye Color
Age
Weight
Coffee Size
Predict Response:
e.g. Probability someone takes Friday off, given it’s
sunny and 70°+
e.g. Expected amount spent on lunch
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Personal Lines Actuarial Research Department
Insurance Examples
Personal auto or H.O. class plans
Deductible or ILF severity models
Liability non-economic claim settlement amount
Hurricane damage curves*
Direct mail response and conversion*
Policyholder retention*
WC transition from M.O. to L.T.*
Auto physical damage total loss identification*
Claim disposal probabilities*
* Logistic Regression
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Personal Lines Actuarial Research Department
Example – Personal Auto
Log (Loss Cost) = Intercept + Driver + Car
Age
Size
Factor i Factor j
Parameters
Intercept
6.50
Driver Age
Young
Older
.75
0
Small
Car Size
Medium
Large
.50
.20
0
e.g. Young Driver, Large Car
Loss Cost = exp (6.50 + .75 + 0) = $1,408
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Personal Lines Actuarial Research Department
Technical Bits
Exponential families – gamma, poisson, normal, binomial
Fit parameters via maximum likelihood
Solve MLE by IRLS or Newton-Raphson
Link Function (e.g. Log Loss Cost)
i. 1-1 function
ii. Range Predicted Variable  ( - ,  )
iii. LN  multiplicative model, id  additive model
logit  binomial model (yes/no)
5. Different means, same scale
1.
2.
3.
4.
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Personal Lines Actuarial Research Department
Personal Auto Class Plan Issues:
1.
2.
3.
4.
5.
6.
7.
Territories or other many level variables
Deductibles and Limits
Loss Development
Trend
Frequency, Severity or Pure Premium
Exposure
Model Selection – penalized likelihood an option
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Personal Lines Actuarial Research Department
Why GLMS?
1. Multivariate – adjusts for presence of other variables. No
overlap.
2. For non-normal data, GLMS better than OLS.
3. Preprogrammed – easy to run, flexible model structures.
4. Maximum likelihood allows testing importance of variables.
5. Linear structure allows balance between amount of data and
number of variables.
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Personal Lines Actuarial Research Department
Software and References
Software:
References:
SAS, GLIM, SPLUS, EMBLEM,
GENSTAT, MATLAB, STATA, SPSS
Part 9 paper bibliography
Greg Taylor (Recent Astin)
Stephen Mildenhall (1999)
Hosmer and Lemeshow
Farrokh Guiahi (June 2000)
Karl P. Murphy (Winter 2000)
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