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arxiv: 2412.06628 · v4 · submitted 2024-12-09 · 📊 stat.ME · math.ST· stat.TH

Partial identification of principal causal effects under violations of principal ignorability

Minxuan Wu , Joseph Antonelli This is my paper

Pith reviewed 2026-05-23 07:36 UTC · model grok-4.3

classification 📊 stat.ME math.STstat.TH
keywords principal stratificationprincipal ignorabilitypartial identificationcausal effectsprincipal strataparametric modelsassociation parameterscausal inference
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The pith

Even with known principal strata distributions and correctly specified parametric outcome models, principal causal effects remain only partially identified without the principal ignorability assumption.

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

The paper examines the principal ignorability assumption within principal stratification for causal effects involving post-treatment variables. It demonstrates that a common strategy of jointly modeling the outcome and principal strata parametrically, without principal ignorability, produces only partial identification of the causal effects. This partial identification persists even when the joint distribution of principal strata is known and the outcome models are simple and correctly specified. Principal ignorability instead delivers point identification, while weaker assumptions can generate informative partial identification regions. The authors further establish that association parameters for the strata distribution are identifiable only under violations of principal ignorability and strong parametric constraints, with extensions to semiparametric and nonparametric Bayesian models.

Core claim

Even if the joint distribution of principal strata is known, the strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability leads to point identification in this setting, alternative weaker assumptions can lead to informative partial identification regions. Association parameters that govern the joint distribution of principal strata are identifiable only if the principal ignorability assumption is violated, and only under strong parametric constraints.

What carries the argument

Principal stratification framework classifying units into strata by potential post-treatment variables, with principal ignorability as the conditional independence assumption between strata membership and outcomes given covariates, and parametric joint models for the outcome and strata.

If this is right

  • Parametric joint models without principal ignorability produce partial identification regions rather than point estimates for principal causal effects.
  • Weaker assumptions beyond principal ignorability can still yield informative bounds on the causal effects.
  • Association parameters for the joint distribution of principal strata become identifiable only when principal ignorability is violated.
  • Due to the partial identifiability of the causal effects, the association parameters themselves require strong parametric constraints to be identified.
  • The partial identification result continues to hold under semiparametric and nonparametric Bayesian extensions of the joint models.

Where Pith is reading between the lines

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

  • Analyses relying on joint parametric modeling should routinely report partial identification intervals when principal ignorability cannot be justified.
  • The necessity of parametric constraints for identifying strata association parameters suggests that fully nonparametric approaches will inherit the same partial identification issue.
  • These results point toward developing sensitivity analyses that vary the strength of departure from principal ignorability while tracking changes in the identification region.
  • In practice, the findings imply that researchers may need to collect richer covariate information or auxiliary data to tighten the partial identification bounds.

Load-bearing premise

The parametric forms chosen for the joint outcome-strata model are correctly specified and impose no additional identifying restrictions beyond that structure.

What would settle it

A finite-sample or asymptotic calculation in which the width of the partial identification region for a principal causal effect fails to collapse to a single point as the sample size grows, even when the strata distribution is treated as known and the outcome model is correctly specified.

read the original abstract

Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail in this manuscript. Our first key contribution is studying a commonly used strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption. We show that even if the joint distribution of principal strata is known, this strategy necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability leads to point identification in this setting, we discuss alternative, weaker assumptions and show how they can lead to informative partial identification regions. An additional contribution is that we provide theoretical support to strategies used in the literature for identifying association parameters that govern the joint distribution of principal strata. We prove that this is possible, but only if the principal ignorability assumption is violated. Additionally, due to partial identifiability of causal effects even when these association parameters are known, we show that these association parameters are only identifiable under strong parametric constraints. Lastly, we extend these results to more flexible semiparametric and nonparametric Bayesian models.

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

2 major / 2 minor

Summary. The manuscript examines violations of the principal ignorability (PI) assumption in principal stratification. It demonstrates that jointly modeling outcomes and principal strata via parametric models yields only partial identification of principal causal effects, even when the strata distribution is known and the outcome models are correctly specified and simple. PI itself produces point identification in the same setting. The paper explores weaker identifying assumptions that can produce informative partial-identification regions, supplies theoretical justification for estimating association parameters that govern the joint strata distribution (possible only when PI is violated), shows that such parameters remain only partially identifiable without strong parametric restrictions, and extends the analysis to semiparametric and nonparametric Bayesian models.

Significance. If the derivations are correct, the paper supplies a clear theoretical explanation for why common joint-modeling strategies in principal stratification cannot deliver point identification without PI, even under favorable conditions. It also supplies formal support for practices already used in the literature for recovering strata-association parameters and delineates the additional parametric constraints required. The extension to flexible models broadens the practical relevance of the partial-identification results.

major comments (2)
  1. [§3] The central claim that partial identification persists even when the joint distribution of principal strata is treated as known rests on the mixture structure induced by the latent strata; the manuscript should explicitly display the relevant likelihood or moment equations (likely in §3 or §4) that demonstrate why the causal-effect parameters remain unidentified without additional restrictions.
  2. [§5] The result that association parameters for the strata distribution are identifiable only under violation of PI and only under strong parametric constraints is load-bearing for the later semiparametric extension; the proof should be checked for any hidden identifying restrictions that might inadvertently restore point identification.
minor comments (2)
  1. Notation for the principal strata and the association parameters should be introduced once and used consistently; currently the abstract and later sections appear to employ slightly different symbols for the same quantities.
  2. The manuscript would benefit from a small simulation study (even a simple binary-outcome example) that numerically illustrates the width of the partial-identification intervals under the parametric models discussed in §3.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment and recommendation of minor revision. We address each major comment below and will incorporate clarifications to improve the manuscript.

read point-by-point responses

  1. Referee: [§3] The central claim that partial identification persists even when the joint distribution of principal strata is treated as known rests on the mixture structure induced by the latent strata; the manuscript should explicitly display the relevant likelihood or moment equations (likely in §3 or §4) that demonstrate why the causal-effect parameters remain unidentified without additional restrictions.

    Authors: We agree that explicitly presenting the likelihood or moment equations would clarify the mixture structure and the source of partial identification. In the revised manuscript, we will add these equations in Section 3, showing how the observed-data likelihood is a mixture over the latent strata even when the strata distribution is known, and why the principal causal effect parameters remain unidentified without further restrictions. revision: yes

  2. Referee: [§5] The result that association parameters for the strata distribution are identifiable only under violation of PI and only under strong parametric constraints is load-bearing for the later semiparametric extension; the proof should be checked for any hidden identifying restrictions that might inadvertently restore point identification.

    Authors: We have re-examined the proof in Section 5. The identification of the association parameters requires both the violation of principal ignorability and the strong parametric constraints on the outcome models; the derivation contains no hidden restrictions that would restore point identification. In the revision, we will add a short clarifying remark after the proof to explicitly state that the result relies only on the assumptions listed in the section. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central results establish partial identification of principal causal effects from the mixture structure of latent strata under correctly specified parametric joint models, even when the strata distribution is treated as known. This follows directly from the identification framework and mixture representation without reducing target quantities to fitted parameters by construction or relying on load-bearing self-citations. The derivations for weaker assumptions yielding informative bounds and the conditions under which association parameters are identifiable are presented as consequences of the model structure itself, with no evidence that any key step equates to its inputs via self-definition, renaming, or imported uniqueness theorems. The work is self-contained against external benchmarks of mixture identifiability.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the standard principal stratification framework and parametric modeling assumptions; no new entities are introduced and free parameters are the usual model coefficients estimated from data.

free parameters (1)
  • parameters of parametric outcome and strata models
    Coefficients in the joint parametric distributions are estimated from observed data and enter the identification analysis.
axioms (1)
  • standard math Standard axioms of probability and the potential-outcomes framework for principal stratification
    The entire analysis is conducted inside the principal stratification model that assumes well-defined potential outcomes and strata membership.

pith-pipeline@v0.9.0 · 5735 in / 1277 out tokens · 25956 ms · 2026-05-23T07:36:38.754984+00:00 · methodology

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