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Estimating Spatial Autocorrelation With Sampled Network Data


  • Jing Zhou
  • Yundong Tu
  • Yuxin Chen
  • Hansheng Wang


Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first-order Taylor’s expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large-scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.

Suggested Citation

  • Jing Zhou & Yundong Tu & Yuxin Chen & Hansheng Wang, 2017. "Estimating Spatial Autocorrelation With Sampled Network Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 130-138, January.
  • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:1:p:130-138
    DOI: 10.1080/07350015.2015.1061437

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    References listed on IDEAS

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    Cited by:

    1. Lan, Jing & Liu, Zhen, 2019. "Social network effect on income structure of SLCP participants: Evidence from Baitoutan Village, China," Forest Policy and Economics, Elsevier, vol. 106(C), pages 1-1.
    2. Zhu, Xuening & Wang, Weining & Wang, Hansheng & Härdle, Wolfgang Karl, 2019. "Network quantile autoregression," Journal of Econometrics, Elsevier, vol. 212(1), pages 345-358.
    3. Yan Chen & Youran Qi & Qing Liu & Peter Chien, 2018. "Sequential sampling enhanced composite likelihood approach to estimation of social intercorrelations in large-scale networks," Quantitative Marketing and Economics (QME), Springer, vol. 16(4), pages 409-440, December.
    4. Schintler, Laurie A. & Fischer, Manfred M., 2018. "Big Data and Regional Science: Opportunities, Challenges, and Directions for Future Research," Working Papers in Regional Science 2018/02, WU Vienna University of Economics and Business.
    5. Zhu, Xuening & Huang, Danyang & Pan, Rui & Wang, Hansheng, 2020. "Multivariate spatial autoregressive model for large scale social networks," Journal of Econometrics, Elsevier, vol. 215(2), pages 591-606.
    6. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    7. Zhu, Xuening & Chang, Xiangyu & Li, Runze & Wang, Hansheng, 2019. "Portal nodes screening for large scale social networks," Journal of Econometrics, Elsevier, vol. 209(2), pages 145-157.

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