Using Bayesian networks for bankruptcy prediction: Some methodological issues

This study provides operational guidance for using naïve Bayes Bayesian network (BN) models in bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors from a pool of potential variables. The method is based upon the assumption that the joint distribution of the variables is multivariate normal. Variables are selected based upon correlations and partial correlations information. A naïve Bayes model is developed using the proposed heuristic method and is found to perform well based upon a tenfold analysis, for both samples with complete information and samples with incomplete information. Second, we analyze whether the number of states into which continuous variables are discretized has an impact on a naïve Bayes model performance in bankruptcy prediction. We compare the model’s performance when continuous variables are discretized into two, three, ..., ten, fifteen, and twenty states. Based upon a relatively large training sample, our results show that the naïve Bayes model’s performance increases when the number of states for discretization increases from two to three, and from three to four. Surprisingly, when the number of states increases to more than four, the model’s overall performance neither increases nor decreases. It is possible that the relative large size of training sample used by this study prevents the phenomenon of over fitting from occurring. Finally, we experiment whether modeling continuous variables with continuous distributions instead of discretizing them can improve the naïve Bayes model’s performance. Our finding suggests that this is not true. One possible reason is that continuous distributions tested by this study do not represent well the underlying distributions of empirical data. More importantly, some results of this study could also benefit the implementation of naïve Bayes models in business decision contexts other than bankruptcy prediction.