Stratification Before Discriminant Analysis: A Must?

Abstract

It could be said as a tautology that, if we want to make a discriminant analysis between two or more populations and if we are able to divide these populations and training sets into some homogeneous subsets, it will be more efficient to make it on each of these subsets and then to combine the results. This can be done using one or two variables highly correlated with the one we want to predict. Our point of view will be a bit different: we will use a classification tree on all the available variables. We will first recall the first attempt (presented at IFCS2002 in Krakow). This one allowed us to obtain on an example of prediction of failure of the enterprises a gain of 5% of well classified data, using, after and before stratification, the classical Fisher’s linear discriminant rule or the logistic regression. We intend to present a new method, still a classification tree, but with a multivariate criterion and in an agglomerative way. We compare both methods. In the same conditions and with the same data set, the gain is as high as 20%! Results will obviously also be presented when the methods are applied to test sets. Finally, we will conclude.