# Top-down Transformation Choice

## TL;DR

This paper proposes using transformation analysis with step-wise complexity reduction to identify simpler, interpretable models for understanding factors affecting body mass index, offering an alternative to traditional complexity-increasing methods.

## Contribution

It introduces a novel approach of complexity reduction through transformation models, including transformation trees and forests, for improved interpretability and understanding.

## Key findings

- Transformation models range from simple to highly flexible.
- A balance between model fit and interpretability is achieved.
- Flexible models reveal insights into BMI factors.

## 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.