Filing at a Glance General Information - Delaware Insurance ...

Methodology
ALLSTATE INDEMNITY COMPANY
PRIVATE PASSENGER AUTOMOBILE
DELAWARE
GENERALIZED LINEAR MODELS PROCEDURE
Attachment IV
Page 1
A multivariate analysis using Generalized Linear Models (GLMs) is used to determine indicated factors for
each coverage. GLMs provide regression-like modeling of the response variable of pure premium, but
provide more flexibility versus linear regression, as GLMs allow the response variable to come from an
exponential family of distributions, including normal, Poisson, binomial, negative binomial, gamma and
Tweedie distributions. Six models are developed for this analysis; one GLM for each of Bodily Injury,
Property Damage, Medical, Personal Injury Protection, Collision and Comprehensive coverages.
For more information on GLMs and usage in insurance ratemaking, please see the following references:
1. Anderson, D.; Feldblum, S; Modlin, C; Schirmacher, D. Schirmacher, E.; and Thandi, N., “A
Practitioner’s Guide to Generalized Linear Models” (Third Edition), CAS Study Note, February
2007.
http://www.casact.org/library/studynotes/anderson9.pdf
2. McCullagh, P. and Nelder, J., Generalized Linear Models (Second Edition), Chapman and Hall,
London, 1989.
Data
The data used in the analysis is countrywide nonstandard automobile policies that have been with Allstate for
five years or less, from accident years 2005-2008, evaluated at March 31, 2009. Note that policy data from
nine states (CA, HI, MA, MI, MN, ND, NJ, NC and SD) are excluded, as these states either do not have a
distinct nonstandard auto company or do not have all of the data fields necessary for the GLM analysis.
In preparing the data, the following variables are fixed in advance of running the GLMs:
Bodily Injury increased limit factors
Property Damage increased limit factors
Medical increased limit factors
Personal Injury Protection increased limit factors or deductible
Model Year and Deductible by Price Group Symbol for Collision and Comprehensive coverages
Vehicle Surcharge factors
Standard practice to assemble data for a GLM is to utilize a Development Dataset to create the model and a
Holdout Dataset to validate the model. Once this was completed, we established our model structure. We
then updated our data and used the established model to run the GLMs.
Model and Variables Structure
For each coverage, indicated rating plan factors are produced by fitting a GLM using a Tweedie 1 distribution
with a log link function 2 to predict the response variable of pure premium.
1. The Tweedie distribution is commonly used in practice for modeling automobile insurance pure
premiums.
2. The log link function is commonly used in practice for modeling automobile insurance as it has the
appealing property of producing factors that are intended to be multiplied together rather than added.
This is consistent with how the factors are applied in the rate calculation.