Comparing Logistic Regression, Multinomial Regression, Classification Trees and Random Forests Applied to Ternary Variables Three-Way Genitive Variation in English

The authors apply logistic regression, multinomial regression, classification trees and random forests to a ternary outcome variable: the variation between the ’s-genitive, the of-genitive and functionally equivalent noun + noun combinations. The statistical approaches discussed fall into regression models on the one hand and classification trees on the other. Specifically, as an alternative to successive binomial regression analyses, the authors implement a multinomial model, which can analyse the entire dataset with three outcome categories simultaneously. Further, a basic classification tree is calculated alongside a more complex (and more robust) random forest. The chapter does not only weigh advantages and shortcomings of all four models, but it also explicates the different rationales and interpretations that come with them. As a major insight, it emerges that the nature of the dataset, the analytic purpose and the statistical model are interdependent and condition each other in several non-trivial respects.