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

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.