Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

62 Actuarial Modelling of Claim Counts
The reader has always to keep in mind that it is often not possible to disentangle a true
effect of a rating factor from an apparent effect resulting from correlation with unobservable
characteristics.
2.3 Poisson Regression Model
2.3.1 Coding Explanatory Variables
All the explanatory variables presented above are categoric (or nominal). A categoric variable
with k levels partitions the portfolio into k classes (for instance, 4 classes for Age in Portfolio
A). It is coded with the help of k − 1 binary variables, being all zero for the reference level.
The reference level is usually selected as the most populated class in the portfolio. The
following example illustrates this coding methodology.
Example 2.2 In Portfolio A, reference levels are ‘31–60’ for Age, ‘Male’ for Gender,
‘Urban’ for District, ‘Premium paid once a year’ for Split and ‘Private’ for Use. Policyholder
i is then represented by a vector of dummies giving the values of
{ 1 if policyholder i is less than 24
x i1 =
0 otherwise
{ 1 if policyholder i is 25–30
x i2 =
0 otherwise
{ 1 if policyholder i is over 60
x i3 =
0 otherwise
{ 1 if policyholder i is a female
x i4 =
0 otherwise
{ 1 if policyholder i lives in a rural area
x i5 =
0 otherwise
{ 1 if policyholder i splits his premium payment
x i6 =
0 otherwise
{ 1 if policyholder i uses his car for professional reasons
x i7 =
0 otherwise.
The results are interpreted with respect to the reference class (for which all the x ij s
are equal to 0) corresponding to a man aged between 31 and 60, living in an urban area,
paying the premium once a year and using the car for private purposes only. The sequence
(1,0,0,0,0,0,1) represents a man aged less than 24, living in an urban area, paying the premium
once a year and using the car for professional reasons.
In case two covariates interact, a new variable is created by combining the levels of each
of the interacting covariates, as shown in the following example.