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 5  Generalized Linear Models
Authors
Curtis Gary Dean  Ball State University
CGDEAN@bsu.edu
Chapter Preview
Generalized linear models (GLMs) generalize linear regression in two important ways: (1) the response variable y can be linked to a linear function of predictor variables x_{j} with a nonlinear link function and (2) the variance in the response variable y is not required to be constant across observations but can be a function of y's expected value. For example, if y represents the number of claims, then the variance in y may depend on the expected value of y as in a Poisson distribution. In linear regression the normal distribution plays a key role but with GLMs the response variable y can have a distribution in a linear exponential family. These include distributions important to actuaries: Poisson, binomial, normal, gamma, inverse Gaussian, and compound Poissongamma. Actuaries can model frequency, severity, and loss ratios with GLMs as well as probabilities of events such as customers renewing policies.
The likelihood function has a key role in GLMs. Maximum likelihood estimation replaces least squares in the estimation of model coefficients. The loglikelihood function is used to perform statistical tests.