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Detecting Latent Communities in Network Formation Models

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  • Shujie Ma
  • Liangjun Su
  • Yichong Zhang

Abstract

This paper proposes a logistic undirected network formation model which allows for assortative matching on observed individual characteristics and the presence of edge-wise fixed effects. We model the coefficients of observed characteristics to have a latent community structure and the edge-wise fixed effects to be of low rank. We propose a multi-step estimation procedure involving nuclear norm regularization, sample splitting, iterative logistic regression and spectral clustering to detect the latent communities. We show that the latent communities can be exactly recovered when the expected degree of the network is of order log n or higher, where n is the number of nodes in the network. The finite sample performance of the new estimation and inference methods is illustrated through both simulated and real datasets.

Suggested Citation

  • Shujie Ma & Liangjun Su & Yichong Zhang, 2020. "Detecting Latent Communities in Network Formation Models," Papers 2005.03226, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2005.03226
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    1. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
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    9. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    10. Koen Jochmans, 2023. "Modified-likelihood estimation of fixed-effect models for dyadic data," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(3), pages 417-433, December.
    11. Leung, Michael P., 2015. "Two-step estimation of network-formation models with incomplete information," Journal of Econometrics, Elsevier, vol. 188(1), pages 182-195.
    12. Belloni, Alexandre & Chen, Mingli & Madrid Padilla, Oscar Hernan & Wang, Zixuan (Kevin), 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," The Warwick Economics Research Paper Series (TWERPS) 1230, University of Warwick, Department of Economics.
    13. Ting Yan & Binyan Jiang & Stephen E. Fienberg & Chenlei Leng, 2019. "Statistical Inference in a Directed Network Model With Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 857-868, April.
    14. Ting Yan & Jinfeng Xu, 2013. "A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices," Biometrika, Biometrika Trust, vol. 100(2), pages 519-524.
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    Cited by:

    1. Wang, Yiren & Phillips, Peter C.B. & Su, Liangjun, 2024. "Panel data models with time-varying latent group structures," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Miao, Ke & Phillips, Peter C.B. & Su, Liangjun, 2023. "High-dimensional VARs with common factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 155-183.
    3. Churchill, Brandyn F., 2021. "How important is the structure of school vaccine requirement opt-out provisions? Evidence from Washington, DC's HPV vaccine requirement," Journal of Health Economics, Elsevier, vol. 78(C).
    4. Lu, Xun & Su, Liangjun, 2023. "Uniform inference in linear panel data models with two-dimensional heterogeneity," Journal of Econometrics, Elsevier, vol. 235(2), pages 694-719.
    5. Wyrwich, Michael & Steinberg, Philip J. & Noseleit, Florian & de Faria, Pedro, 2022. "Is open innovation imprinted on new ventures? The cooperation-inhibiting legacy of authoritarian regimes," Research Policy, Elsevier, vol. 51(1).
    6. Yiren Wang & Liangjun Su & Yichong Zhang, 2022. "Low-rank Panel Quantile Regression: Estimation and Inference," Papers 2210.11062, arXiv.org.
    7. 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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