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Detecting Latent Communities in Network Formation Models

Author

Listed:
  • Ma, Shujie

    (University of California, Riverside)

  • Su, Liangjun

    (School of Economics, Singapore Management University)

  • Zhang, Yichong

    (School of Economics, Singapore Management University)

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

  • 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.
    • Handle: RePEc:ris:smuesw:2020_012
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    Cited by:

    1. 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.
    2. Yiren Wang & Peter C B Phillips & Liangjun Su, 2023. "Panel Data Models with Time-Varying Latent Group Structures," Papers 2307.15863, arXiv.org.
    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. 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.
    6. 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).
    7. Yiren Wang & Liangjun Su & Yichong Zhang, 2022. "Low-rank Panel Quantile Regression: Estimation and Inference," Papers 2210.11062, arXiv.org.

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    More about this item

    Keywords

    Community detection; homophily; spectral clustering; strong consistency; unobserved heterogeneity;
    All these keywords.

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