We aim at proposing a new model for binary rare events, i.e. binary depen- dent variable with a very small number of ones.We extend the Generalized Extreme Value (GEV) regression model proposed by Calabrese and Osmetti [5] to a Gener- alized 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.
Calabrese, R., Osmetti, S. A., A Generalized Additive Model for Binary Rare Events Data: an Application to Credit Defaults., in Vicari, D., Okada, A., Ragozini, G., Weihs, C. (ed.), Analysis and Modeling of Complex Data in Behavioural and Social Sciences, Springer, Milano 2014: <<STUDIES IN CLASSIFICATION, DATA ANALYSIS, AND KNOWLEDGE ORGANIZATION>>, 73- 81. 10.1007/978-3-319-06692-9_9 [http://hdl.handle.net/10807/56463]
A Generalized Additive Model for Binary Rare Events Data: an Application to Credit Defaults.
Calabrese, Raffaella;Osmetti, Silvia Angela
2014
Abstract
We aim at proposing a new model for binary rare events, i.e. binary depen- dent variable with a very small number of ones.We extend the Generalized Extreme Value (GEV) regression model proposed by Calabrese and Osmetti [5] to a Gener- alized 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.
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