The best of two worlds: Balancing model strength and comprehensibility in business failure prediction using spline-rule ensembles

Numerous organizations and companies rely upon business failure prediction to assess and minimize the risk of initiating business relationships with partners, clients, debtors or suppliers. Advances in research on business failure prediction have been largely dominated by algorithmic development and comparisons led by a focus on improvements in model accuracy. In this context, ensemble learning has recently emerged as a class of particularly well-performing methods, albeit often at the expense of increased model complexity. However, in practice, model choice is rarely based on predictive performance alone. Models should be comprehensible and justifiable to assess their compliance with common sense and business logic, and guarantee their acceptance throughout the organization. A promising ensemble classification algorithm that has been shown to reconcile performance and comprehensibility are rule ensembles. In this study, an extension entitled spline-rule ensembles is introduced and validated in the domain of business failure prediction. Spline-rule ensemble complement rules and linear terms found in conventional rule ensembles with smooth functions with the aim of better accommodating nonlinear simple effects of individual features on business failure. Experiments on a large selection of 21 datasets of European companies in various sectors and countries (i) demonstrate superior predictive performance of spline-rule ensembles over a set of well-established yet powerful benchmark methods, (ii) show the superiority of spline-rule ensembles over conventional rule ensembles and thus demonstrate the value of the incorporation of smoothing splines, (iii) investigate the impact of alternative term regularization procedures and (iv) illustrate the comprehensibility of the resulting models through a case study. In particular, the ability of the technique to reveal the extent and the way in which predictors impact business failure, and if and how variables interact, are exemplified.