Exploring credit data

Credit scoring methods aim to assess the default risk of a potential borrower. This involves typically the calculation of a credit score and the estimation of the probability of default. One of the standard approaches is logistic discriminant analysis, also referred to as logit model. This model maps explanatory variables for the default risk to a credit score using a linear function. Nonlinearity can be included by using polynomial terms or piecewise linear functions. This may give however only a limited reflection of a truly nonlinear relationship. Moreover, an additional modeling step may be necessary to determine the optimal polynomial order or the optimal interval classification. This paper presents semiparametric extensions of the logit model which directly allow for nonlinear relationships to be part of the explanatory variables. The technique is based on the theory generalized partial linear models. We illustrate the advantages of this approach using a consumer retail banking data set.