More Flexible GLMs Zero-Inflated Models and Hybrid Models
Mathew Flynn, Louise A. Francis · 2009
Motivation: GLMs are widely used in insurance modeling applications. Claim or frequency models are a key component of many GLM ratemaking models. Enhancements to the traditional GLM that are described in this paper may by able to address practical issues that arise when fitting count models to insurance claims data. For modeling claims within the GLM framework, the Poisson distribution is a popular distribution choice. In the presence of overdispersion, the negative binomial is also sometimes used. The statistical literature has suggested that taking excess zeros into account can improve the fit of count models when overdispersion is present. In insurance excess zeros may arise when claims near the deductible are not reported to the insurer, thus inflating the number of zero policies when compared to the predictions of a Poisson or Negative Binomial distribution. In predictive modeling practice, data mining techniques such as neural networks and decision trees are often used to handle data complexities such as nonlinearities and interactions. Data mining techniques are sometimes combined with GLMs to improve the performance and/or efficiency of the predictive modeling analysis. One augmentation of GLMs uses decision tree methods in the data preprocessing step. An important preprocessing task reduces the number of levels on categorical variables so that sparse cells are eliminated and only significant groupings of the categories remain. Method: This paper addresses some common problems in fitting count models to data. These are: • Excess zeros