Predictive Modeling Applications in Actuarial Science

Chapter 9 - Credibility and Regression Modeling


Vytaras Brazauskas | University of Wisconsin - Milwaukee

Harald Dornheim | KPMG AG Switzerland

Ponmalar Ratnam | University of Wisconsin - Milwaukee

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This chapter introduces the reader to credibility and related regression modeling. The first section provides a brief overview of credibility theory, regression-type credibility, and discusses historical developments. The next section shows how some well-known credibility models can be embedded within the linear mixed model framework. Specific procedures on how such models can be used for prediction and standard ratemaking are given as well. Further, in Section 9.3, a step-by-step numerical example, based on the widely-studied Hachemeister's data, is developed to illustrate the methodology. All computations are done using the statistical software package R. The fourth section identifies some practical issues with the standard methodology. In particular, its lack of robustness against various types of outliers is mentioned. Possible solutions that have been proposed in the statistical and actuarial literatures are discussed. Performance of the most effective proposals is illustrated on the Hachemeister's data set and compared to that of the standard methods. Suggestions for further reading are made in Section 9.5.

Data R Code
How to read a dataset Hachem Revised