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arxiv: 2606.18197 · v1 · pith:4NULKBNZnew · submitted 2026-06-16 · 📊 stat.AP · stat.ME

A Sensitivity Framework for Identifying Contagion under Latent Homophily for Fixed-in-Time Network Analyses, with an Application to U.S. House Congressional Voting

Duncan A. Clark This is my paper

Pith reviewed 2026-06-26 21:38 UTC · model grok-4.3

classification 📊 stat.AP stat.ME
keywords contagionlatent homophilysensitivity analysisnetwork datacausal inferenceselection biascongressional votingrisk ratio
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The pith

The gap between observed network contagion and true controlled direct effect is set by how strongly latent homophily changes which dyads connect.

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

The paper reframes the classic contagion-versus-homophily problem as a selection-bias question in the simple case of one fixed network observed at two time points with binary nodal outcomes. It defines a controlled direct effect that holds a tie fixed while intervening on an alter’s outcome, then shows that the difference between this effect and the raw connected-dyad risk ratio is fully determined by the strength of a latent homophily factor that shifts the composition of connected pairs. Nonparametric bounds on that strength are derived so that the original question “is there contagion?” becomes the concrete question “how large would latent homophily have to be to explain the entire observed association away?” A simulation study and an application to 2008 House votes on TARP illustrate when the bounds support or rule out contagion.

Core claim

We show that the gap between the CDE and the observed connected-dyad risk ratio is governed by how strongly a latent homophily variable shifts the composition of connected dyads. Inspired by Smith-style selection-bias sensitivity analysis and the risk-ratio bounding function of Ding and VanderWeele we develop interpretable nonparametric bounds. This translates the question 'is there contagion?' into the question 'how strong would latent homophily have to be to explain away the observed contagion?'

What carries the argument

A single sensitivity parameter that quantifies how strongly an unobserved homophily factor alters the composition of connected dyads, used to bound the difference between the controlled direct effect and the raw observed risk ratio.

If this is right

  • Under the derived bounds, contagion can be declared plausible once the homophily strength needed to explain the data away exceeds any value judged credible for that population.
  • The framework applies directly to any fixed network with two waves of binary nodal outcomes without requiring a parametric model of tie formation.
  • Simulation results show the bounds maintain nominal error control while retaining power to detect contagion when homophily is weak.
  • In the TARP vote data the method identifies the precise homophily threshold at which contagion remains credible.

Where Pith is reading between the lines

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

  • The same selection-bias reframing could be applied to directed or weighted networks once an appropriate dyad-composition parameter is defined.
  • Bounds derived here might be combined with measured covariates to tighten the required homophily threshold in empirical applications.
  • The approach suggests a design for future network studies: collect auxiliary data on potential homophily factors precisely to calibrate the sensitivity parameter.

Load-bearing premise

The only source of bias between the controlled direct effect and the observed association is latent homophily whose strength is captured by the sensitivity parameter.

What would settle it

Collect direct measures or proxies of the latent homophily variable in the same network setting and test whether its observed strength exceeds the value required by the bounds to nullify the contagion claim.

Figures

Figures reproduced from arXiv: 2606.18197 by Duncan A. Clark.

Figure 1
Figure 1. Figure 1: DAG showing latent U variables, with contagion and latent homophily for a single dyad; observed fixed covariates X are suppressed. We consider data generated from [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: Substantive sensitivity scenarios for CDE lower bounds among switchable egos ( [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Naturally connected CDE simulation heatmaps for no latent effect on outcome ( [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Forced-contact CDE simulation heatmaps for no latent effect on outcome ( [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Naturally connected CDE simulation heatmaps for strong latent effect on outcome ( [PITH_FULL_IMAGE:figures/full_fig_p029_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Forced-contact CDE simulation heatmaps for strong latent effect on outcome ( [PITH_FULL_IMAGE:figures/full_fig_p030_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Naturally connected CDE truth, Type I error, and Type II error heatmaps for no latent [PITH_FULL_IMAGE:figures/full_fig_p031_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Forced-contact CDE truth, Type I error, and Type II error heatmaps for no latent effect [PITH_FULL_IMAGE:figures/full_fig_p032_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Naturally connected CDE truth, Type I error, and Type II error heatmaps for moderate [PITH_FULL_IMAGE:figures/full_fig_p032_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Forced-contact CDE truth, Type I error, and Type II error heatmaps for moderate [PITH_FULL_IMAGE:figures/full_fig_p033_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Naturally connected CDE truth, Type I error, and Type II error heatmaps for strong [PITH_FULL_IMAGE:figures/full_fig_p033_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Forced-contact CDE truth, Type I error, and Type II error heatmaps for strong latent [PITH_FULL_IMAGE:figures/full_fig_p034_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Degree distribution for the primary clean cosponsorship network. Ties are signed [PITH_FULL_IMAGE:figures/full_fig_p035_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Empirical connected risk ratio, observed- [PITH_FULL_IMAGE:figures/full_fig_p037_16.png] view at source ↗
read the original abstract

Whether connected units are similar because influence spreads across ties or because similar units form ties, is a long-standing problem. Contagion or influence is generically unidentified from observational network data. We consider the minimal and common setting of a single network, fixed over time, with two waves of a binary nodal outcome. Rather than positing a parametric model for network formation, we reframe identification of contagion as a selection-bias problem and develop a sensitivity framework. We define a controlled direct effect (CDE) holding a tie present while intervening on an alter's outcome. We show that the gap between the CDE and the observed connected-dyad risk ratio is governed by how strongly a latent homophily variable shifts the composition of connected dyads. Inspired by Smith-style selection-bias sensitivity analysis and the risk-ratio bounding function of Ding and VanderWeele we develop interpretable nonparametric bounds. This translates the question "is there contagion?" into the question "how strong would latent homophily have to be to explain away the observed contagion?" A simulation study characterizes the bounds' error control and power. We apply the framework to the 2008 U.S. House votes on the Troubled Asset Relief Program, identifying under which assumptions contagion is plausible.

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 / 2 minor

Summary. The paper develops a sensitivity framework for contagion identification in a minimal setting of one fixed network observed at two time points with binary nodal outcomes. It reframes the problem as selection bias due to latent homophily, defines a controlled direct effect (CDE) holding ties fixed while intervening on alter outcomes, and derives nonparametric bounds (inspired by Smith-style selection-bias analysis and Ding-VanderWeele risk-ratio bounds) on the gap between the CDE and the observed connected-dyad risk ratio. The central translation is that assessing contagion reduces to assessing how strong latent homophily must be to explain away the observed association. The framework is evaluated in a simulation study on error control and power and applied to 2008 U.S. House TARP votes.

Significance. If the bounds derivation holds, the work supplies a practical, nonparametric sensitivity tool for distinguishing contagion from latent homophily without parametric network-formation models. Strengths include the explicit single sensitivity parameter, the simulation characterizing bound behavior, and the empirical demonstration; these make the contribution concrete and falsifiable in applied settings. The approach extends established selection-bias techniques to network contagion questions in a way that could see routine use in social-science network analyses.

minor comments (2)
  1. [Simulation study] The simulation section would benefit from an explicit table or figure reporting numerical power and coverage rates across the range of homophily strengths examined, to allow direct verification of the claimed error-control properties.
  2. [Methods] Notation for the bounding function and the latent-homophily sensitivity parameter should be introduced with a single consolidated definition early in the methods section rather than piecemeal.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their accurate summary of the manuscript and for recognizing its potential contribution. The recommendation for minor revision is noted. No specific major comments appear in the report, so there are no individual points requiring rebuttal or revision at this stage. We will incorporate any editorial or minor changes in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained sensitivity analysis

full rationale

The paper reframes contagion identification as a selection-bias problem under a fixed network with two binary outcome waves, defines the CDE, and derives nonparametric bounds on the gap to the observed risk ratio using the strength of latent homophily as the sensitivity parameter. This directly follows established external techniques (Smith-style selection-bias analysis and Ding-VanderWeele risk-ratio bounds) without any reduction of the target quantity to a fitted parameter defined by the same equations, without self-citation load-bearing on the central claim, and without ansatz smuggling or renaming. The result is explicitly a sensitivity framework (not point identification), with the single parameter acknowledged as the modeling choice; the logic remains internally consistent and independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the definition of the controlled direct effect, the fixed-network two-wave setting, and the single sensitivity parameter that governs the gap between the CDE and the observed risk ratio.

free parameters (1)
  • latent homophily sensitivity parameter
    The nonparametric bounds are expressed as functions of this parameter that quantifies the shift in connected-dyad composition due to unobserved homophily.
axioms (2)
  • domain assumption Single fixed network with two waves of binary nodal outcome
    Described as the minimal and common setting under consideration.
  • domain assumption No parametric model for network formation is posited
    The problem is instead reframed entirely as a selection-bias problem.

pith-pipeline@v0.9.1-grok · 5763 in / 1500 out tokens · 29921 ms · 2026-06-26T21:38:47.899968+00:00 · methodology

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