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8 - Linear Mixed Models

from II - Predictive Modeling Methods

Published online by Cambridge University Press:  05 August 2014

By
Katrien Antonio  and
Yanwei Zhang
Edited by
Edward W. Frees ,
Richard A. Derrig  and
Glenn Meyers
Katrien Antonio
Affiliation:
University of Amsterdam and KU Leuven
Yanwei Zhang
Affiliation:
University of Southern California
Edward W. Frees
Affiliation:
University of Wisconsin, Madison
Richard A. Derrig
Affiliation:
Temple University, Philadelphia
Glenn Meyers
Affiliation:
ISO Innovative Analytics, New Jersey
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Summary

Chapter Preview. We give a general discussion of linear mixed models and continue by illustrating specific actuarial applications of this type of model. Technical details on linear mixed models follow: model assumptions, specifications, estimation techniques, and methods of inference. We include three worked-out examples with the R lme4 package and use ggplot2 for the graphs. Full code is available on the book's website.

Mixed Models in Actuarial Science

8.1.1 What Are Linear Mixed Models?

A First Example of a Linear Mixed Model. As explained in Chapter 7, a panel dataset follows a group of subjects (e.g., policyholders in an insurance portfolio) over time. We therefore denote variables (e.g., yit, xit) in a panel dataset with double subscripts, indicating the subject (say, i) and the time period (say, t). As motivated in Section 1.2 of Chapter 7, the analysis of panel data has several advantages. Panel data allow one to study the effect of certain covariates on the response of interest (as in usual regression models for cross–sectional data), while accounting appropriately for the dynamics in these relations. For actuarial ratemaking the availability of panel data is of particular interest in a posteriori ratemaking. An a posteriori tariff predicts the current year loss for a particular policyholder, using (among other factors) the dependence between the current year's loss and losses reported by this policyholder in previous years.

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Predictive Modeling Applications in Actuarial Science , pp. 182 - 216
Publisher: Cambridge University Press
Print publication year: 2014

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