Non-linearity of scorecard log-odds

The use of linear and log-linear models for scorecard construction is nearly universal. In this paper we address the question of non-linearity in the distribution of a scorecard’s inferred log-odds to score relationship. Linear scorecards are excellent and robust ranking tools, but the inferred default probabilities are increasingly used in day-to-day business operations — within account-level strategies, for cutoff setting, and for capital allocation. All of these uses are dependent upon the accurate estimation of the probability of default, which is a quality independent of a model’s ranking performance.