A Generalized Additive Model for Binary Rare Events Data: An Application to Credit Defaults

We aim at proposing a new model for binary rare events, i.e. binary dependent variable with a very small number of ones. We extend the Generalized Extreme Value (GEV) regression model proposed by Calabrese and Osmetti (Journal of Applied Statistics 40(6):1172–1188, 2013) to a Generalized Additive Model (GAM). We suggest to consider the quantile function of the GEV distribution as a link function in a GAM, so we propose the Generalized Extreme Value Additive (GEVA) model. In order to estimate the GEVA model, a modified version of the local scoring algorithm of GAM is proposed. Finally, to model default probability, we apply our proposal to empirical data on Italian Small and Medium Enterprises (SMEs). The results show that the GEVA model has a higher predictive accuracy to identify the rare event than the logistic additive model.