Top-down Transformation Choice
This work addresses the challenge of model selection for researchers and practitioners in statistics and data science, offering an incremental improvement over classical bottom-up methods by focusing on interpretability and complexity reduction.
The paper tackles the problem of balancing model simplicity and interpretability against complexity and fit by proposing a top-down transformation choice approach, which uses step-wise complexity reduction to identify simpler, better-interpretable models, as demonstrated by modeling body mass index distributions in Switzerland with transformation models ranging from normal linear regression to novel flexible methods like transformation trees and forests.
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.