Top-down Transformation Choice

Abstract: Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model diagnostics. Eventually, one increases the complexity of this initial overly simple model and obtains a better-fitting model. I illustrate how transformation analysis can be used as an alternative approach to model choice. Instead of adding complexity to simple models, step-wise complexity reduction is used to help identify simpler and better-interpretable models. As an example, body mass index distributions in Switzerland are modelled by means of transformation models to understand the impact of sex, age, smoking and other lifestyle factors on a person's body mass index. In this process, I searched for a compromise between model fit and model interpretability. Special emphasis is given to the understanding of the connections between transformation models of increasing complexity. The models used in this analysis ranged from evergreens, such as the normal linear regression model with constant variance, to novel models with extremely flexible conditional distribution functions, such as transformation trees and transformation forests.