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In-Depth Information
Chevy Blazer,
Chevy Citation,
Ford Ram
,
Ford Contour, and
Dodge Intrepid.
he good news from both analyses is that no obvious outliers are found among
vehicles newer than the
model year.
Car Insurance Rates - Poisson Regression
7.6
he data are from Statlib. A subset of them is given in Andrews and Herzberg (
,
pp.
-
). he original data consist of information on more than two million
third-party automobile insurance policies in Sweden for the
year. For each pol-
icytheannualmileage,bonusclass(onaseven-pointscale),geographicalzone(seven
categories), and make of car (nine categories) were recorded. Annual mileage is dis-
cretized into five categories: (
) less than
,
km/year, (
)
-
km/year,
(
)
-
km/year, (
)
-
km/year, and (
) more than
km/year (Hallin and Ingenbleek,
).hesefour explanatory variables yield
a
table with
possible cells. For each cell, the following quantities
were obtained:
. Total insured time in years,
. Total number of claims,
. Total monetary value of the claims.
Twenty-three cells are empty.
Wewill model claim ratehere. According toAndrewsand Herzberg(
,p.
),
aSwedishAnalysis ofRiskgroupdecidedthat amultiplicative model(i.e.,anadditive
Poisson loglinear model) for claim rate is fairly good, and that any better model is
too complicated to administer. To challenge this conclusion, we will use GUIDE to
fit a piecewise-additive Poisson loglinear model for number of claims, using the log
of number of claims as offset variable. Bonus class and mileage class are treated as
continuous, and zone and make as categorical variables.
Figure
.
.
GUIDE multiple linear Poisson regression tree for car insurance data. At each intermediate
node, a case goes to the let child node if and only if the condition is satisfied. he number in italics
beneath each leaf node is the sample claim rate
