Generalized Linear Models CAGNY

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Generalized Linear ModelsCAGNY

• Wednesday, November 28, 2001

Keith D. Holler Ph.D., FCAS, ASA, ARM, MAAA
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High Level
Given Characteristics

• e.g. Eye Color
• Age
• Weight
• Coffee Size

Predict Response e.g. Probability someone takes
Friday off, given its sunny and 70 e.g.
Expected amount spent on lunch
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Personal auto or H.O. class plansDeductible or
ILF severity models Liability non-economic claim
settlement amountHurricane damage curves
Direct mail response and conversionPolicyholder
retentionWC transition from M.O. to L.T.Auto
physical damage total loss identificationClaim
disposal probabilities
Insurance Examples
Logistic Regression
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Example Personal Auto
Log (Loss Cost) Intercept Driver
Car Age Size Factor i
Factor j
Parameters
e.g. Young Driver, Large Car Loss Cost exp
(6.50 .75 0) 1,408
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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)
• 1-1 function
• Range Predicted Variable ? ( -? , ? )
• LN ? multiplicative model, id ? additive model
  logit ? binomial model (yes/no)
• Different means, same scale

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Personal Auto Class Plan Issues

• 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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Why GLMS?

• Multivariate adjusts for presence of other
  variables. No overlap.
• For non-normal data, GLMS better than OLS.
• Preprogrammed easy to run, flexible model
  structures.
• Maximum likelihood allows testing importance of
  variables.
• Linear structure allows balance between amount of
  data and number of variables.

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Software and References
Software SAS, GLIM, SPLUS, EMBLEM, GENSTAT,
MATLAB, STATA, SPSS References Part 9 paper
bibliography Greg Taylor (Recent
Astin) Stephen Mildenhall (1999) Hosmer and
Lemeshow Farrokh Guiahi (June 2000) Karl P.
Murphy (Winter 2000)