A case study on using generalized additive models to fit credit rating scores

We consider the estimation of credit scores by means of semiparametric logit models. In credit scoring, the fitted rating score shall not only provide an optimal classification result but serves also as a modular component of a (typically quite complex) rating system. This means in particular that a rating score should be given by a linearly weighted sum of rating factors. That way the rating procedure can be easily interpreted and understood also by non-statisticians. For that reason the logit model or the logistic regression approach is one of the most popular models for estimating credit rating scores. The first step in fitting the rating model is usually a nonlinear transformation of the raw variables in order to obtain a linear predictor (rating score) in the final estimation. As an alternative to this two-step approach, generalized additive models (GAM) would allow for a simultaneous estimation of both the initial transformation and final logit fit. In this study we compare GAM estimating approaches with a focus on the specific structure of credit data: small default rates, mixed discrete and continuous explanatory variables, possibly nonlinear dependencies between the regressors.