Assessing the Importance of Risk Factors in Distance-Based Generalized Linear Models

Predictions with distance-based linear and generalized linear models rely upon latent variables derived from the distance function. This key feature has the drawback of adding a non-linearity layer between observed predictors and response which shields one from the other and, in particular, prevents us from interpreting linear predictor coefficients as influence measures. In actuarial applications such as credit scoring or a priori rate-making we cannot forgo this capability, crucial to assess the relative leverage of risk factors. Towards the goal of recovering this functionality we define and study influence coefficients, measuring the relative importance of observed predictors. Unavoidably, due to inherent model non-linearities, these quantities will be local -valid in a neighborhood of a given point in predictor space.