Abstract
With GLMs, mean responses are modeled as monotonic functions of linear scores. The assumed linearity of the score is not restrictive for categorical features coded by means of binary variables. However, this assumption becomes questionable for continuous features which may have a nonlinear effect on the score scale. This chapter is devoted to Generalized Additive Models (GAMs) which keep the additive decomposition of the score but allow the actuary to discover nonlinear effects of features like policyholder’s age or place of residence (geographic effect), for instance. Contrarily to the prior categorization of continuous features (banding into pre-defined classes), GAMs offer a flexible, data-driven procedure to identify the optimal transformation of continuous features for inclusion on the score scale. Precisely, continuous features enter the model in a semi-parametric additive predictor. Typical applications in insurance include the graduation of mortality and morbidity or the analysis of risk variation by age or geographic area, for instance.
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Notes
- 1.
It turns out that this phenomenon is not an isolated case and has led to a theory known as the Wisdom of Crowds.
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Denuit, M., Hainaut, D., Trufin, J. (2019). Generalized Additive Models (GAMs). In: Effective Statistical Learning Methods for Actuaries I. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25820-7_6
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