Preview of the Chapter. We start with a discussion of model families for multilevel data outside the Gaussian framework. We continue with generalized linear mixed models (GLMMs), which enable generalized linear modeling with multilevel data. The chapter includes highlights of estimation techniques for GLMMs in the frequentist as well as Bayesian context. We continue with a discussion of nonlinear mixed models (NLMMs). The chapter concludes with an extensive case study using a selection of R packages for GLMMs.

Introduction

Chapter 8 (Section 3) motivates predictive modeling in actuarial science (and in many other statistical disciplines) when data structures go beyond the cross-sectional design. Mixed (or multilevel) models are statistical models suitable for the analysis of data structured in nested (i.e., hierarchical) or non-nested (i.e., cross-classified, next to each other, instead of hierachically nested) clusters or levels. Whereas the focus in Chapter 8 is on linear mixed models, we now extend the idea of mixed modeling to outcomes with a distribution from the exponential family (as in Chapter 5 on generalized linear models (GLMs)) and to mixed models that generalize the concept of linear predictors. The first extension leads to the family of generalized linear mixed models (GLMMs), and the latter creates nonlinear mixed models (NLMMs). The use of mixed models for predictive modeling with multilevel data is motivated extensively in Chapter 8.