When Interference Graphs Evolve: Doubly Robust Estimation of Dynamic Peer Effects

Xiaojing Du

cs.LGAug 27, 2026

When Interference Graphs Evolve: Doubly Robust Estimation of Dynamic Peer Effects

Authors: Xiaojing Du

Organizations: Adelaide University

Abstract

Peer effects are difficult to estimate when interaction graphs evolve because pre-assignment network history, dynamic peer exposure, and post-assignment network change have distinct causal roles. We introduce a controlled contrast framework that indexes potential outcomes by own treatment, temporally aggregated peer exposure, and a post-assignment evolution summary. Differences between the resulting means define own-treatment, peer-exposure, controlled network-evolution, and joint controlled contrasts rather than a mediation decomposition. We develop the Dynamic Network Doubly Robust estimator, DynaNet-DR, which combines a temporally factorized propensity with normalized augmentation. Under consistency, summary sufficiency, sequential exchangeability, positivity, nuisance convergence, and weak dependence, its canonical estimator is consistent when either the outcome regression or the propensity estimator is consistent. The reported implementation adds representative-score prediction, fixed clipping, and finite-sample stabilization. Semi-synthetic benchmarks on fixed real temporal graph sequences show favorable estimation accuracy among methods targeting the full profile. These benchmarks assess summary-indexed contrasts rather than counterfactual edge generation, and the MathOverflow study is an observational illustration under the stated assumptions.

Figures & tables

Figure 1: Controlled comparisons for focal unit $i$ . Each panel varies one highlighted feature while holding the others fixed.

Figure 2: Time ordering. Peer treatments are aggregated over pre-assignment graphs into

Z_{it}

. The post-assignment summary

M_{i,t+1}

precedes the outcome. The generated trait

U_{i}

is included by default and withheld in the sensitivity analysis.

Dataset	Method	DE	PE	CNE	JCC	Coverage
CollegeMsg	Naive-A	0.722 $\pm$ 0.042	0.552 $\pm$ 0.000	0.326 $\pm$ 0.000	0.157 $\pm$ 0.043	0.00
	Static-Z OR	0.099 $\pm$ 0.043	0.354 $\pm$ 0.029	0.326 $\pm$ 0.000	0.591 $\pm$ 0.055	0.01
	Static-Z DR	0.103 $\pm$ 0.024	0.279 $\pm$ 0.051	0.326 $\pm$ 0.000	0.503 $\pm$ 0.054	0.10
	GPS †	0.147 $\pm$ 0.025	0.417 $\pm$ 0.044	0.326 $\pm$ 0.000	0.878 $\pm$ 0.056	0.00
	DynInt †	0.069 $\pm$ 0.032	0.062 $\pm$ 0.026	0.326 $\pm$ 0.000	0.254 $\pm$ 0.053	0.04
	TL †	0.056 $\pm$ 0.021	0.053 $\pm$ 0.034	0.049 $\pm$ 0.028	0.044 $\pm$ 0.029	0.17

Table 1: RMSE by contrast family and empirical coverage of node-clustered nominal intervals. Bold marks the lowest RMSE among full-target implementations, and

\dagger

denotes adaptations. Restricted designs have different targets, and coverage is descriptive.

Variant	College	Email	Primary	High
Full	.047 $\pm$ .011	.052 $\pm$ .021	.126 $\pm$ .045	.083 $\pm$ .027
$\lambda=1$	.052 $\pm$ .022	.077 $\pm$ .021	.206 $\pm$ .123	.110 $\pm$ .040
Plug-in	.064 $\pm$ .019	.056 $\pm$ .020	.125 $\pm$ .045	.111 $\pm$ .050
No $M$	.199 $\pm$ .005	.203 $\pm$ .006	.231 $\pm$ .041	.202 $\pm$ .010
No $M$ + plug-in	.206 $\pm$ .007	.204 $\pm$ .007	.231 $\pm$ .040	.219 $\pm$ .017
No- $M$ IPW	.288 $\pm$ .058	.318 $\pm$ .044	.341 $\pm$ .111	.371 $\pm$ .088

Table 2: Mean

\pm

SD overall RMSE across seven contrasts. Full denotes DynaNet-DR with its adaptive gate. Bold marks the dataset minimum. The

\lambda=1

and plug-in rows share the full target; the other variants have target mismatch.

	CollegeMsg			email-Eu
Method	Default	Outcome	Prop.	Default	Outcome	Prop.
OR	.064 (.019)	.421 (.047)	.064 (.019)	.056 (.020)	.474 (.094)	.056 (.020)
No- $M$ IPW	.288 (.058)	.288 (.058)	.305 (.050)	.318 (.044)	.318 (.044)	.403 (.042)
TL	.054 (.022)	.205 (.069)	.052 (.023)	.093 (.026)	.170 (.050)	.101 (.030)
GML-DR	.053 (.023)	.242 (.060)	.051 (.020)	.081 (.023)	.222 (.052)	.088 (.027)
DynaNet	.047 (.011)	.213 (.069)	.046 (.014)	.052 (.021)	.277 (.047)	.053 (.018)

Table 3: Mean overall RMSE, with SD in parentheses. OR is the full-target plug-in outcome regression, and DynaNet denotes DynaNet-DR. Bold marks each minimum. Outcome and Prop. restrict one nuisance model; only No-

M

IPW has target mismatch.

Figure 3: Mean estimates and benchmark truths for seven contrasts on CollegeMsg and email-Eu. Error bars are one standard deviation across replications, not confidence intervals. Appendix defines the targets; Appendix reports the other networks.

Figure 4: DynaNet-DR overall RMSE and empirical coverage by clip bound. Bands show one standard deviation; dashed line marks

c=0.02

Causal Effect Estimation

Causal effect estimation measures how outcomes would change under interventions, using experiments or observational data and explicit assumptions.

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Causal Effect Estimation Causal Inference Social Network Analysis Doubly Robust Estimation

Open paper AskPDF arXiv

Evaluating network interventions requires understanding how treatment affects people through their social relationships. Counting treated neighbors without distinguishing supportive and antagonistic ties can conceal opposing influences. We define effects through positive and negative ties, their interaction, and a sign-composition effect of reallocating treatment between the two types at a fixed total, and give their identification formulas. Under sign-blind assignment, we show how ignoring signs mixes the effects of the two tie types. We propose SiDE (Signed-exposure Doubly robust Estimator), which combines sign-specific outcome models with exposure probabilities induced by individual treatment assignment. We establish double robustness of its score and assess approximate intervals that account for overlapping neighborhoods. Semi-synthetic experiments on six real signed networks demonstrate accurate effect estimation and examine the limits of interval coverage. An exploratory reanalysis of published school-experiment data yields a positive estimate of the peer effect through spend-time ties on wristband wearing, but the intervals for all four effects include zero after adjustment for multiple comparisons. This framework can inform network intervention design by showing when influences through the two tie types reinforce or offset one another.

Abstract

Causal Effect Estimation

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