Classification-relevant Importance Measures for the West German Business Cycle

When analyzing business cycle data, one observes that the relevant predictor variables are often highly correlated. This paper presents a method to obtain measures of importance for the classification of data in which such multicollinearity is present. In systems with highly correlated variables it is interesting to know what changes are inflicted when a certain predictor is changed by one unit and all other predictors according to their correlation to the first instead of a ceteris paribus analysis. The approach described in this paper uses directional derivatives to obtain such importance measures. It is shown how the interesting directions can be estimated and different evaluation strategies for characteristics of classification models are presented. The method is then applied to linear discriminant analysis and multinomial logit for the classification of west German business cycle phases.