Tree-Structured Scale Effects in Binary and Ordinal Regression

Abstract: In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity. In particular since it has been demonstrated that misleading effects can occur if one ignores the presence of a scaling component it is important to account for potential scaling effects in the regression model, which is not possible in available recursive partitioning methods. The proposed recursive partitioning method yields two trees, one for the location and one for the scaling. They show in a simple interpretable way how variables interact to determine the binary or ordinal response. The developed algorithm controls for the global significance level and automatically selects the variables that have an impact on the response. The modelling approach is illustrated by several real-world applications.