Predictive Modeling Applications in Actuarial Science
 Volume 1
 Introduction
 Predictive Modeling Foundations
 Predictive Modeling Methods
 Bayesian and Mixed Modeling
 Longitudinal Modeling
 Volume 2
 Generalized Linear Model
 Extensions of the Generalized Linear Model
 Unsupervised Predictive Modeling Methods

Applications on Current Problems in Actuarial Science
 Chapter 8  The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
 Chapter 9  Finite Mixture Model and Workersâ€™ Compensation LargeLoss Regression Analysis
 Chapter 10  A Framework for Managing Claim Escalation Using Predictive Modeling
 Chapter 11  Predictive Modeling for UsageBased Auto Insurance
Chapter 9  Credibility and Regression Modeling
Authors
Vytaras Brazauskas  University of Wisconsin  Milwaukee
vytaras@uwm.edu
Harald Dornheim  KPMG AG Switzerland
bavaria_harry@gmx.de
Ponmalar Ratnam  University of Wisconsin  Milwaukee
psratnam@uwm.edu
Chapter Preview
This chapter introduces the reader to credibility and related regression modeling. The first section provides a brief overview of credibility theory, regressiontype credibility, and discusses historical developments. The next section shows how some wellknown 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 stepbystep numerical example, based on the widelystudied 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 