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Estimating Policy Effects in a Social Network with Independent Set Sampling

Eugene Ang, Prasanta Bhattacharya, Andrew Lim

TL;DR

A novel empirical strategy that combines network sampling based on the identification of independent sets with a stochastic actor-oriented model (SAOM) to infer the direct and net effects of a policy is proposed.

Abstract

Evaluating the impact of policy interventions on respondents who are embedded in a social network is often challenging due to the presence of network interference within the treatment groups, as well as between treatment and non-treatment groups throughout the network. In this paper, we propose a novel empirical strategy that combines network sampling based on the identification of independent sets with a stochastic actor-oriented model (SAOM) to infer the direct and net effects of a policy. By assigning respondents from an independent set to the treatment, we are able to block direct spillover of the treatment among the treated respondents for an extended period of time, during which the direct effect of the treatment can be isolated from the associated network interference. We empirically demonstrate this using a simulation-based evaluation of a fictitious policy implementation using both real-life and generated networks, and use a counterfactual approach to estimate the treatment effect of the policy. Our results highlight the effectiveness of our proposed empirical strategy, and notably, the role of network sampling techniques in influencing the evaluation of policy effects. The findings from this study have the potential to help researchers and policymakers with planning, designing, and anticipating policy responses in a networked society.

Estimating Policy Effects in a Social Network with Independent Set Sampling

TL;DR

A novel empirical strategy that combines network sampling based on the identification of independent sets with a stochastic actor-oriented model (SAOM) to infer the direct and net effects of a policy is proposed.

Abstract

Evaluating the impact of policy interventions on respondents who are embedded in a social network is often challenging due to the presence of network interference within the treatment groups, as well as between treatment and non-treatment groups throughout the network. In this paper, we propose a novel empirical strategy that combines network sampling based on the identification of independent sets with a stochastic actor-oriented model (SAOM) to infer the direct and net effects of a policy. By assigning respondents from an independent set to the treatment, we are able to block direct spillover of the treatment among the treated respondents for an extended period of time, during which the direct effect of the treatment can be isolated from the associated network interference. We empirically demonstrate this using a simulation-based evaluation of a fictitious policy implementation using both real-life and generated networks, and use a counterfactual approach to estimate the treatment effect of the policy. Our results highlight the effectiveness of our proposed empirical strategy, and notably, the role of network sampling techniques in influencing the evaluation of policy effects. The findings from this study have the potential to help researchers and policymakers with planning, designing, and anticipating policy responses in a networked society.
Paper Structure (16 sections, 2 theorems, 15 equations, 4 figures, 9 tables, 3 algorithms)

This paper contains 16 sections, 2 theorems, 15 equations, 4 figures, 9 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Policy Evaluation in Networked Contexts
  3. Proposed Method
  4. Independent set sampling
  5. Specifying a stochastic actor-oriented model
  6. Estimating policy effects using SAOM
  7. Policy Intervention Analysis under Network Interference
  8. Illustrative study using a real-world social network
  9. Illustrative study using random graph-based models
  10. Discussion and Conclusion
  11. Summary of key findings
  12. Limitations and future extensions
  13. Selection of Independent Set
  14. Structural Preservation of Maximal Independent Sets
  15. Graph Visualization of the Samples
  16. ...and 1 more sections

Key Result

Theorem 1

Let $G$ be a graph on $n$ vertices with $e$ edges and let $\Delta$ be the maximum vertex degree. Then, the independence number $\alpha(G)$, which is the size of the largest independent set of $G$, has the following upper bound,

Figures (4)

  • Figure 1: Selecting the shaded nodes from a $C_6$ graph to form different independent sets
  • Figure 2: Smoothed adoption rate for different sampling strategies
  • Figure 3: Common network descriptives of the maximal independent sets from dataset
  • Figure 4: Graphs generated using different sampling strategies

Theorems & Definitions (4)

  • Definition 1: Independent Set
  • Theorem 1: Kwok Bound
  • Theorem 2: Caro-Wei Bound
  • Definition 2