Motor insurance claim modelling with factor collapsing and Bayesian model averaging

Abstract

While generalized linear models have become the insurance industry's standard approach for claim modelling, the approach of utilizing a single best model on which predictions are based ignores model selection uncertainty. An additional feature of insurance claim data sets is the common presence of categorical variables, within which the number of levels is high, and not all levels may be statistically significant. In such cases, some subsets of the levels may be merged to give a smaller overall number of levels for improved model parsimony and interpretability. Hence, clustering of the levels poses an additional model uncertainty issue. A method is proposed for assessing the optimal manner of collapsing factors with many levels into factors with smaller numbers of levels, and Bayesian model averaging is used to blend model predictions from all reasonable models to account for selection uncertainty. This method will be computationally intensive when the number of factors being collapsed or the number of levels within factors increases. Hence, a stochastic approach is used to quickly identify the best collapsing cases across the model space.1. Should a categorical predictor be included? 2. When included, should certain levels be merged together? 3. When included and with certain levels merged, how much confidence should be placed on this clustering of levels and this model?Therefore, factor collapsing (FC) and BMA are considered to improve model predictions, with a focus on clustering categorical levels within factors so that the number of levels can be reduced, and thus, model parsimony and interpretability improved. The structure of this article is as follows: in Section 2 data sets used are introduced; Section 3 briefly reviews BMA, introduces the method of FC incorporated within BMA (FC-BMA) and discusses how to select the optimal clustering of categories in a computationally efficient way; Section 4 tests and compares the different

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