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Consistently estimating network statistics using aggregated relational data.

Emily Breza1, Arun G Chandrasekhar2, Shane Lubold3

  • 1Department of Economics, Harvard University, Cambridge, MA 02138.

Proceedings of the National Academy of Sciences of the United States of America
|May 16, 2023
PubMed
Summary
This summary is machine-generated.

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Aggregated Relational Data (ARD) offers a cost-effective method for network analysis when complete data is unfeasible. This study establishes conditions for ARD to accurately estimate unobserved network features and parameters.

Area of Science:

  • Network Science
  • Sociology
  • Statistics
  • Data Analysis

Background:

  • Collecting comprehensive network data is often prohibitively expensive and time-consuming.
  • Aggregated Relational Data (ARD) offers a lower-cost alternative by asking about the number of contacts with specific traits, rather than direct dyadic connections.
  • A systematic understanding of ARD's accuracy in recovering unobserved network features is lacking.

Purpose of the Study:

  • To systematically characterize the conditions under which Aggregated Relational Data (ARD) can accurately recover features of unobserved networks.
  • To derive conditions for the consistent estimation of network statistics and model parameters using ARD.
  • To evaluate the efficacy of ARD for probabilistic network models including beta-models, stochastic block models, and latent geometric space models.
Keywords:
aggregated relational dataconsistencysocial networkssurvey methods

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Main Methods:

  • Derivation of conditions for consistent estimation of network statistics and model parameters from ARD.
  • Estimation of network model parameters for beta-models, stochastic block models, and latent geometric space models using ARD.
  • Simulation of networks based on fitted ARD models to analyze the estimation of unobserved network statistics (e.g., eigenvector centrality) and response functions (e.g., regression coefficients).

Main Results:

  • Established conditions under which statistics and parameters of unobserved networks can be consistently estimated using ARD.
  • Demonstrated that cross-group link probabilities are sufficient for estimating parameters in commonly used probabilistic network models.
  • Characterized when simulated networks from ARD facilitate consistent estimation of network statistics and regression coefficients.

Conclusions:

  • ARD provides a viable and statistically sound method for inferring network structures and statistics when complete data collection is infeasible.
  • The derived conditions offer guidance on the appropriate application and interpretation of results obtained from ARD.
  • This work bridges the gap in understanding the theoretical underpinnings and practical utility of ARD in network analysis.