Multi-Level Factors and Credibility Theory

Abstract

Here we introduce the term multi-level factor (MLF) for a rating factor with a large number of levels without an inherent ordering, with car model as an example. These variables can not be analyzed by GLMs, since such a large number of parameters cannot be estimated with reasonable accuracy. This kind of variables are studied in the branch of insurance mathematics called credibility theory. After having introduced the classical Bühlmann-Straub model for a MLF, we show how credibility theory and GLMs may be combined to analyze models containing both MLFs and standard rating factors such as age or gender. This is then extended to hierarchical credibility. The results are applied to the problem of car model classification for private cars. The chapter ends by a case study on bus insurance.