A.F. Shapiro, R. Paul Gorman Insurance: Mathematics and Economics 26 2000 289–307 299
Another approach would be to use nonlinear com- pression, which is kind of the nonlinear correlate to
factor analysis
16
or principle components.
17
This can be accomplished, for example, with a four-layer au-
toassociative network, where the first and third hidden layers have sigmoidal nonlinear activation functions.
9. Domain segmentation
Domain segmentation involves the identification of segments within the decision space where the implicit
relationship between variables is constant. It is a very important step and has been demonstrated to provide
enormous amounts of value-added performance Kelly et al., 1995. Fig. 12 exemplifies the situation.
18
Traditionally, two approaches have been used for segmentation. One is to try to find segments in the pop-
ulation that have relatively constant behavior within a group and then to assign either a score or an output
to that entire group, assuming they have uniform be- havior. Another approach is to ignore the segmenta-
tion altogether and attempt to fit a model to the entire decision space.
Fig. 12 demonstrates that neither approach really gets at the underlying structure in the data since, in
Fig. 12 Domain segmentation.
16
In the current context, factor analysis may be thought of as a technique which uses measures of association correlations to
extract patterns latent structure in the data of association a dependence on common processes in complex data sets. To be
really useful and valid, factor analysis needs large data arrays as correlations can be found for spurious reasons.
17
Principal component analysis is a methodology for finding the structure of a cluster located in multidimensional space. Conceptu-
ally, it is equivalent to choosing that rotation of the cluster which best depicts its underlying structure.
18
Adopted from Gorman 1996, Slide 9.
both approaches, much of the resolution in the model is lost. Typically, what needs to be done is to isolate
the unique domains and model within them. This has the advantage of improving the ability of these adapted
technologies to extract the structure. In essence, the technique is allowed to focus in on relatively stationary
behavior, so that it has a better opportunity to extract the information.
9.1. Isotropic subdomains Domains that may be used in the development of
insurance models include the insurance companies themselves. In the area of consumer behavior models,
for example, it may turn out, as it has with credit bureaus Gorman, 1996, that each insurer actually
reflects relatively distinct characteristics of individual consumer behavior and so modeling within companies
rather than across them may have some advantages. Depending on the inquiry, one would also expect that
there are geographic regions that should be cordoned off. So, those groups can be isolated and modeled
within those domains to get a better resolution with regard to that behavior.
It also generally makes sense to classify clients by adverse selection characteristics and to model within
each of those classes. Moreover, as discussed below, certain aspects of temporal behavior are likely to be
much more important than cross-sectional behavior. Since the goal is to refine the detection of these types
of behavior the data could be segregated accordingly.
10. Variable selection and derivation
