mSHAP: SHAP Values for Two-Part Models

Abstract: Two-part models are important to and used throughout insurance and actuarial science. Since insurance is required for registering a car, obtaining a mortgage, and participating in certain businesses, it is especially important that the models which price insurance policies are fair and non-discriminatory. Black box models can make it very difficult to know which covariates are influencing the results. SHAP values enable interpretation of various black box models, but little progress has been made in two-part models. In this paper, we propose mSHAP (or multiplicative SHAP), a method for computing SHAP values of two-part models using the SHAP values of the individual models. This method will allow for the predictions of two-part models to be explained at an individual observation level. After developing mSHAP, we perform an in-depth simulation study. Although the kernelSHAP algorithm is also capable of computing approximate SHAP values for a two-part model, a comparison with our method demonstrates that mSHAP is exponentially faster. Ultimately, we apply mSHAP to a two-part ratemaking model for personal auto property damage insurance coverage. Additionally, an R package (mshap) is available to easily implement the method in a wide variety of applications.