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Recovering Network Structure from Aggregated Relational Data using Penalized Regression

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  • Hossein Alidaee
  • Eric Auerbach
  • Michael P. Leung

Abstract

Social network data can be expensive to collect. Breza et al. (2017) propose aggregated relational data (ARD) as a low-cost substitute that can be used to recover the structure of a latent social network when it is generated by a specific parametric random effects model. Our main observation is that many economic network formation models produce networks that are effectively low-rank. As a consequence, network recovery from ARD is generally possible without parametric assumptions using a nuclear-norm penalized regression. We demonstrate how to implement this method and provide finite-sample bounds on the mean squared error of the resulting estimator for the distribution of network links. Computation takes seconds for samples with hundreds of observations. Easy-to-use code in R and Python can be found at https://github.com/mpleung/ARD.

Suggested Citation

  • Hossein Alidaee & Eric Auerbach & Michael P. Leung, 2020. "Recovering Network Structure from Aggregated Relational Data using Penalized Regression," Papers 2001.06052, arXiv.org.
    • Handle: RePEc:arx:papers:2001.06052
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    References listed on IDEAS

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    1. de Paula, Aureo & Rasul, Imran & Souza, Pedro, 2018. "Identifying Network Ties from Panel Data: Theory and an Application to Tax Competition," CEPR Discussion Papers 12792, C.E.P.R. Discussion Papers.
    2. Alexandre Belloni & Mingli Chen & Victor Chernozhukov, 2016. "Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk," Papers 1607.00286, arXiv.org, revised Oct 2019.
    3. Aureo de Paula & Imran Rasul & Pedro CL Souza, 2018. "Recovering social networks from panel data: Identification, simulations and an application," Documentos de Trabajo 16173, The Latin American and Caribbean Economic Association (LACEA).
    4. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    5. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    6. Belloni, Alexandre. & Chen, Mingli & Chernozhukov, Victor, 2016. "Quantile Graphical Models: Prediction and Conditional Independence with Applications to Financial Risk Management," The Warwick Economics Research Paper Series (TWERPS) 1125, University of Warwick, Department of Economics.
    7. Tyler H. McCormick & Tian Zheng, 2015. "Latent Surface Models for Networks Using Aggregated Relational Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1684-1695, December.
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    Cited by:

    1. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.
    2. Marko Mlikota, 2022. "Cross-Sectional Dynamics Under Network Structure: Theory and Macroeconomic Applications," Papers 2211.13610, arXiv.org, revised Sep 2024.
    3. Steven Wilkins Reeves & Shane Lubold & Arun G. Chandrasekhar & Tyler H. McCormick, 2024. "Model-Based Inference and Experimental Design for Interference Using Partial Network Data," Papers 2406.11940, arXiv.org.
    4. Ma, Shujie & Su, Liangjun & Zhang, Yichong, 2020. "Detecting Latent Communities in Network Formation Models," Economics and Statistics Working Papers 12-2020, Singapore Management University, School of Economics.
    5. Alejandro Sanchez-Becerra, 2022. "The Network Propensity Score: Spillovers, Homophily, and Selection into Treatment," Papers 2209.14391, arXiv.org.
    6. Yiren Wang & Liangjun Su & Yichong Zhang, 2022. "Low-rank Panel Quantile Regression: Estimation and Inference," Papers 2210.11062, arXiv.org.
    7. Mohamed Mostagir & James Siderius, 2023. "Social Inequality and the Spread of Misinformation," Management Science, INFORMS, vol. 69(2), pages 968-995, February.
    8. Candelaria, Luis E. & Ura, Takuya, 2023. "Identification and inference of network formation games with misclassified links," Journal of Econometrics, Elsevier, vol. 235(2), pages 862-891.

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