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arxiv: 2604.18388 · v1 · submitted 2026-04-20 · 📊 stat.ME

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

Mei Dong , Linbo Wang , Lin Liu , Oliver Dukes This is my paper

Pith reviewed 2026-05-10 03:39 UTC · model grok-4.3

classification 📊 stat.ME
keywords regression by compositionorder dependenceconditional distributionmodel specificationparameter interpretationstatistical inferencesequential construction
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The pith

Reordering the component regressions in the composition framework changes the implied conditional distributions and parameter interpretations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This discussion paper examines the regression-by-composition framework proposed by Farewell and colleagues. It shows that the sequential construction of the framework makes results depend on the order in which the flows are arranged. A sympathetic reader would care because different orderings of the same regressions can produce non-equivalent models, altering what conditional distributions are represented and how parameters are to be understood. The point matters for anyone using the framework to specify models or draw inferences from data.

Core claim

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.

What carries the argument

The sequential construction of the regression-by-composition framework, in which the order of composing conditional regressions determines the overall structure.

If this is right

  • Model specification must select an order that matches the intended data-generating process.
  • Parameter interpretations become tied to the specific sequence chosen.
  • Estimation and inference steps need to be adjusted according to the ordering used.
  • Conclusions drawn from the model may not be stable across different valid orderings of the flows.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Users of the framework should justify their chosen order using substantive knowledge of the process under study.
  • Sensitivity checks that vary the ordering could reveal whether conclusions depend on this choice.
  • The observation points to a broader need for order-invariant alternatives in sequential regression modeling.

Load-bearing premise

That the sequential construction of the framework inherently produces order-dependent results for distributions, interpretations, and estimation.

What would settle it

A concrete example in which permuting the order of the same set of component regressions leaves the implied conditional distribution, parameter interpretations, and estimation problem unchanged.

Figures

Figures reproduced from arXiv: 2604.18388 by Linbo Wang, Lin Liu, Mei Dong, Oliver Dukes.

Figure 1
Figure 1. Figure 1: Implied conditional probabilities under Model 1 (left panel) and Model 2 (right panel) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The manuscript discusses 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.

Significance. If the central observation holds, the discussion is significant because it draws attention to the non-commutativity inherent in sequential compositions of conditional distributions, a standard probabilistic property that directly affects modeling choices in this framework. This provides practitioners with a clear reminder that order is a substantive modeling decision rather than an incidental detail, with downstream effects on interpretation and inference.

minor comments (1)
  1. [Abstract] The abstract is self-contained but the discussion would be strengthened by including at least one concrete numerical example or small simulation showing how reordering changes a fitted conditional distribution or parameter interpretation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. We appreciate the recognition that the discussion highlights a substantive modeling consideration in the regression-by-composition framework.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central observation—that reordering sequential compositions of conditional distributions alters the implied joint, parameter interpretations, and estimation—follows directly from the non-commutativity of conditional factorization, a standard property of probability models. No equations, fitted parameters, or self-citations are invoked to derive this; the reference to Farewell et al. provides context only. The discussion is self-contained and does not reduce any claim to a definition, fit, or prior result by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a discussion paper critiquing an existing framework, no new free parameters, axioms, or invented entities are introduced by the authors.

pith-pipeline@v0.9.0 · 5356 in / 1119 out tokens · 58706 ms · 2026-05-10T03:39:19.855944+00:00 · methodology

discussion (0)

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Reference graph

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6 extracted references · 6 canonical work pages

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