Order Dependence in Regression by Composition: Discussion on "Regression by Composition'' by Farewell, Daniel, Stensrud, and Huitfeldt

TL;DR

This paper discusses how the sequential nature of the regression-by-composition framework leads to order dependence, affecting model interpretation and inference.

Contribution

It highlights the implications of order dependence in regression-by-composition, emphasizing its impact on model specification and interpretation.

Findings

Reordering flows can change the implied conditional distribution.

Order dependence affects parameter interpretation.

Reordering influences the estimation problem.

Abstract

We discuss the regression-by-composition framework of Farewell, Daniel, Stensrud and Huitfeldt, highlighting a key consequence of its sequential construction: order dependence. Reordering the flows may change the implied conditional distribution, the interpretation of model parameters, and the associated estimation problem, with consequences for model specification, interpretation, and inference.