Source-linked AI summary
Peer Effects in Signed Networks: Separating Influence Through Positive and Negative Ties
Xiaojing Du, Jiuyong Li, Lin Liu, Debo Cheng, Jixue Liu, Thuc Duy Le
TL;DR
Counting treated neighbors without distinguishing tie signs can assign the same exposure to different signed-neighbor compositions and yield an estimate near zero despite opposing influences. The paper defines four signed peer-effect contrasts and proposes SiDE, a doubly robust estimator combining sign-specific outcome models with exposure probabilities induced by individual treatment assignment. The positive-tie effect is the effect of one more treated positive-tie neighbor, averaged over the compositions an ego reaches at total k.
Problem
Counting treated neighbors without distinguishing tie signs can assign the same exposure to different signed-neighbor compositions and yield an estimate near zero despite opposing influences.
Source: §1 · p. 1Method
The paper defines four signed peer-effect contrasts and proposes SiDE, a doubly robust estimator combining sign-specific outcome models with exposure probabilities induced by individual treatment assignment.
Source: §1 · p. 2Results
The positive-tie effect is the effect of one more treated positive-tie neighbor, averaged over the compositions an ego reaches at total k.
Source: §3.4 · p. 5Takeaways & Limitations
The sign-composition effect indicates whether a program designer should treat a trusted or avoided neighbor when the number of treated neighbors is fixed.
Source: §6 · p. 9Approximate positive-tie intervals undercover in some evaluated networks: coverage is 0.850, and the two Bitcoin networks have coverage 0.880 and 0.840.
Source: §5.4 · p. 9
Abstract
from arXiv · showhide
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.
1 INTRODUCTION
Signed peer effects distinguish influence through trusted and avoided neighbors, including what happens when treatment shifts between tie types while the total stays fixed. The paper defines and identifies these contrasts, proposes SiDE, and studies how unsigned analyses combine tie-specific effects.
1 INTRODUCTION
- The paper defines positive- and negative-tie effects, their interaction, and a sign-composition effect that reallocates treatment between tie types at a fixed total.The sign-composition contrast compares treatment of a trusted rather than an avoided neighbor while four neighbors remain treated.Source: §1 · p. 1, Figure 1 · p. 2
- Counting treated neighbors without tie signs gives households with different signed exposures the same state, so opposing influences can produce an estimate near zero.The paper’s example contrasts exposures (3, 1) and (4, 0), each with four treated neighbors.Source: §1 · p. 1
- SiDE combines separate positive- and negative-neighborhood encoders with exposure probabilities induced by individual treatment assignment to estimate the signed contrasts.The paper also establishes double robustness of its score and evaluates approximate intervals accounting for overlapping neighborhoods.Source: §1 · p. 2
- The paper evaluates SiDE against eleven baselines on semi-synthetic data from six real signed networks and reanalyzes a school field experiment.The reanalysis separates peer effects through students’ spend-time and conflict ties.Source: §1 · p. 2
2 RELATED WORK
The paper builds on causal-inference methods for network interference and research on signed ties, defining effects that distinguish tie types and treatment reallocation.
2 RELATED WORK
- Prior interference methods use exposure mappings, covariate adjustment, targeted learning, graph neural models, and doubly robust estimators to study peer effects.Earlier work also distinguishes tie strength, edge type, and multiple networks.Source: §2 · p. 2
- Research on signed networks examines trust, conflict, diffusion, and social influence; this paper formalizes effects by tie type, their interaction, and fixed-total treatment reallocation.Prior findings include that disliking a source need not reverse its influence.Source: §2 · p. 3
3 PROBLEM SETTING
The framework represents peer exposure with treated-neighbor counts split by tie sign, defines four contrasts over reachable exposure states, and identifies them under stated assumptions. Under sign-blind assignment, an unsigned increment averages positive- and negative-tie increments, which can cancel.
3 PROBLEM SETTING
- A directed signed network separates each unit’s positive- and negative-tie neighborhoods; signed exposure counts record treated neighbors of each type alongside own treatment and covariates.An unsigned analysis retains only the total treated-neighbor count and cannot distinguish exposures such as (3, 1) and (4, 0).Source: §3 · p. 3
3.1 ASSUMPTIONS
- Identification assumes neighbor treatments affect outcomes through signed exposure counts, consistency, conditional exchangeability given ego and neighbor covariates, and positive probability for compared states.The effects are defined for a common nonempty population able to reach the compared exposure states.Source: §3.1 · p. 3, §3.2 · p. 4
3.2 THE FOUR EFFECTS
- The four contrasts are positive-tie and negative-tie increments, their interaction, and a sign-composition effect that shifts treatment from a negative- to a positive-tie neighbor at fixed total.A negative interaction means the positive-tie increment is smaller when negative-tie exposure is higher.Source: §3.2 · p. 4
3.3 IDENTIFICATION
- Under the stated assumptions, each potential-outcome mean is identified by averaging the conditional observed-outcome regression over covariates in the target population.The four effects follow by substituting this regression for the potential outcomes in their definitions.Source: §3.3 · p. 4
3.4 WHAT AN UNSIGNED ANALYSIS ESTIMATES
- Under sign-blind assignment, an unsigned increment is a degree-share-weighted average of positive- and negative-tie increments averaged over their exposure compositions.The weighted sum can vanish when the two weighted increments cancel, even if both tie types have large effects.Source: §3.4 · p. 5
4 ESTIMATION AND INFERENCE
SiDE estimates signed-exposure contrasts with propensity-weighted residual correction and held-out predictions, then estimates uncertainty using overlapping neighborhoods.
4.1 EXPOSURE PROPENSITIES AND DOUBLY ROBUST SCORE
- Exposure propensities use individual treatment probabilities and positive- and negative-neighbor counts, while inverse-probability weights correct outcome-prediction errors.The assignment model relies on disjoint ego and signed-neighbor sets; the count probabilities use Poisson–binomial probabilities.Source: §4.1 · p. 5
- Under the stated assumptions, the score has the target conditional mean if either the outcome model or the exposure-propensity model is correct.Averaging scores over the common reachable population gives the conditional contrast.Source: §4.1 · p. 5
4.2 SIGN-SPECIFIC NEIGHBORHOOD ENCODER AND ESTIMATOR
- Separate sign-specific encoders feed the outcome and assignment models; SiDE scores held-out egos, normalizes each partition estimate, and reports their median.The assignment head predicts individual treatment probabilities, which are converted into exposure propensities.Source: §4.2 · p. 6
4.3 VARIANCE ESTIMATION AND INFERENCE
- Variance estimation assumes residuals for unlinked egos are conditionally independent, then estimates variance from linked pairs, including each ego paired with itself.Linked egos have intersecting closed neighborhoods; the variance estimate uses held-out residuals and the normalized inverse-probability weights.Source: §4.3 · p. 6
5 EXPERIMENTS
Experiments evaluate SiDE against network-interference baselines on six real signed networks and assess effect estimation, sensitivity, ablations, interval coverage, and a school-data reanalysis. SiDE leads on average MAE and absolute bias, while interval coverage and the exploratory school estimates have important qualifications.
5 EXPERIMENTS
- The experiments repeat semi-synthetic analyses 10 times and report averages and standard deviations; data are generated on six observed networks so true effects are known.The main interaction comparison excludes the two Bitcoin networks because few egos reach the compared exposure states.Source: §5 · p. 6, §5.1 · pp. 6–7
5.2 RESULTS ON SEMI-SYNTHETIC DATA
- SiDE has the lowest MAE averaged over four networks and four effects, and ranks first in average absolute bias across all six networks and four effects.It has the lowest MAE for all four effects on Epinions, while individual baselines are more accurate for some effects on other networks.Source: Table 1 · p. 7, §5.2 · p. 7
5.1 EXPERIMENTAL SETUP
- The evaluation compares SiDE with eleven baselines from regression, neural treatment-effect, graph-neural, and generalized AIPW families.The six networks include Bitcoin-Alpha, Bitcoin-OTC, Wiki-Elec, Slashdot, Epinions, and Reddit.Source: §5.1 · pp. 6–7
5.2 RESULTS ON SEMI-SYNTHETIC DATA
- Across hidden widths of 32, 64, and 128, SiDE retains the lowest average MAE, with each effect changing by less than two Monte Carlo standard errors on four main networks.With network depth fixed, each training epoch costs O(|E|H + nH2); a complete run takes 11–94 seconds after preprocessing on one NVIDIA RTX 6000 Ada GPU.Source: §5.2 · pp. 7–8
- Removing tie signs attenuates the negative-tie estimate on Wiki-Elec, Slashdot, and Epinions, reverses its average sign on Reddit, and makes the sign-composition effect zero.The unsigned estimator pools positive and negative neighbors; the two composition states have the same total treated-neighbor count.Source: §5.2 · p. 7, Figure 3 · p. 8
5.3 ABLATION STUDY
- Dropping the outcome model or Poisson-binomial exposure probabilities raises MAE for every network and effect; dropping residual correction raises average absolute bias to 0.054 from 0.020, while standard deviation rises to 0.084 from 0.055 for SiDE.SiDE’s bias stays within two Monte Carlo standard errors of zero for every network-effect pair except the negative-tie effect on Wiki-Elec.Source: Table 2 · p. 8, §5.3 · p. 8
5.4 COVERAGE OF APPROXIMATE INTERVALS
- Coverage is at least 0.919 except for positive-tie intervals on Epinions and Reddit; positive-tie coverage is 0.850, and the two Bitcoin networks have positive-tie coverage of 0.880 and 0.840.The evaluation uses 200 datasets on each of four main networks and nominal 95% intervals.Source: §5.4 · pp. 8–9, Table 3 · p. 9
5.5 CASE STUDY
- The spend-time peer-effect estimate is 3.3 percentage points (95% interval [0.5, 6.1]), but after Bonferroni adjustment its interval is [−0.3, 6.9], so the analysis is exploratory.The conflict-tie estimate is −0.9 points with interval [−7.2, 5.5], too wide to determine its direction.Source: §5.5 · p. 9
6 CONCLUSION
The paper defines and identifies four signed peer effects, shows how ignoring tie signs can mask opposing influences, and proposes SiDE to estimate effects and account for overlapping neighborhoods.
6 CONCLUSION
- The four signed peer-effect contrasts are identified from observational data as contrasts of outcome regressions over their reachable sets.They comprise positive-tie and negative-tie effects, their interaction, and the sign-composition effect.Source: §6 · p. 9
- Under sign-blind assignment, an unsigned increment is a weighted average of positive- and negative-tie increments, so opposing influences can cancel.The sign-composition effect helps a program designer choose between treating a trusted or avoided neighbor when the number of treated neighbors is fixed.Source: §6 · p. 9
- SiDE estimates the four effects with a doubly robust score combining sign-specific outcome models and exposure probabilities, and constructs approximate intervals accounting for overlapping neighborhoods.Semi-synthetic evaluation used six real signed networks; an exploratory school-experiment reanalysis associates a positive peer effect on wristband wearing with spend-time ties. Extending the effects to networks that change in response to treatment is future work.Source: §6 · p. 9