Performance of combined models in discrete binary classification

Abstract

Diverse Discrete Discriminant Analysis (DDA) models perform differently in different samples. This fact has encouraged research in combined models which seems particularly promising when the a priori classes are not well separated or when small or moderate sized samples are considered, which often occurs in practice. In this study, we evaluate the performance of a convex combination of two DDA models: the First-Order Independence Model (FOIM) and the Dependence Trees Model (DTM). We use simulated data sets with two classes and consider diverse data complexity factors which may influence performance of the combined model -the separation of classes, balance, and number of missing states, as well as sample size and also the number of parameters to be estimated in DDA. We resort to cross-validation to evaluate the precision of classification. The results obtained illustrate the advantage of the proposed combination when compared with FOIM and DTM: it yields the best results, especially when very small samples are considered. The experimental study also provides a ranking of the data complexity factors, according to their relative impact on classification performance, by means of a regression model. It leads to the conclusion that the separation of classes is the most influential factor in classification performance. The ratio between the number of degrees of freedom and sample size, along with the proportion of missing states in the minority class, also has significant impact on classification performance. An additional gain of this study, also deriving from the estimated regression model, is the ability to successfully predict the precision of classification in a real data set based on the data complexity factors.