Using Discrete Loss Functions and Weighted Kappa for Classification: An Illustration Based on Bayesian Network Analysis

In certain data analyses (e.g., multiple discriminant analysis and multinomial log-linear modeling), classification decisions are made based on the estimated posterior probabilities that individuals belong to each of several distinct categories. In the Bayesian network literature, this type of classification is often accomplished by assigning individuals to the modal state, based on the estimated posterior probabilities. This procedure is not satisfactory, however, when various types of classification errors have different costs. For example, Lenaburg used Bayesian network methods to forecast students’ grades in a college statistics course to identify students who were likely to benefit from extra tutoring, and was most concerned with incorrectly predicting students would pass. We recommend a simple post hoc classification method, based on discrete loss functions, that can lead to improved classification. We further propose that Cohen’s weighted kappa statistic be used to evaluate the quality of the classification decisions. We illustrate the approach using Lenaburg’s data.