Generalized Linear Mixed Models for Ratemaking: A Means of Introducing Credibility into a Generalized Linear Model Setting

GLMs that include explanatory classification variables with sparsely populated levels assign large standard errors to these levels but do not otherwise shrink estimates toward the mean in response to low credibility. Accordingly, actuaries have attempted to superimpose credibility on a GLM setting, but the resulting methods do not appear to have caught on. The Generalized Linear Mixed Model (GLMM) is yet another way of introducing credibility-like shrinkage toward the mean in a GLM setting. Recently available statistical software, such as SAS PROC GLIMMIX, renders these models more readily accessible to actuaries. This paper offers background on GLMMs and presents a case study displaying shrinkage towards the mean very similar to Buhlmann-Straub credibility.

Keywords: Credibility, Generalized Linear Models (GLMs), Linear Mixed Effects (LME) models, Generalized Linear Mixed Models (GLMMs).