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Multivariate spatial autoregressive model for large scale social networks

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  • Zhu, Xuening
  • Huang, Danyang
  • Pan, Rui
  • Wang, Hansheng

Abstract

The rapid growth of social network platforms generates a large amount of social network data, where multivariate responses are frequently collected from users. To statistically model such type of data, the multivariate spatial autoregressive (MSAR) model is studied. To estimate the model, the quasi maximum likelihood estimator (QMLE) is obtained under certain technical conditions. However, it is found that the computational cost of QMLE is expensive. To fix this problem, a least squares estimator (LSE) is developed. The corresponding identification conditions and asymptotic properties are investigated. To gauge the finite sample performance of various estimators, a number of simulation studies are conducted. Lastly, a Sina Weibo dataset is analyzed for illustration purpose.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:215:y:2020:i:2:p:591-606
    DOI: 10.1016/j.jeconom.2018.11.018
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    as
    1. Badi H. Baltagi, 2015. "Seemingly Unrelated Regressions," Springer Texts in Business and Economics, in: Solutions Manual for Econometrics, edition 3, chapter 0, pages 233-257, Springer.
    2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    3. Liu, Xiaodong, 2013. "Estimation of a local-aggregate network model with sampled networks," Economics Letters, Elsevier, vol. 118(1), pages 243-246.
    4. Thomas de Graaff & Frank G. van Oort & Raymond J.G.M. Florax, 2012. "Regional Population–Employment Dynamics Across Different Sectors Of The Economy," Journal of Regional Science, Wiley Blackwell, vol. 52(1), pages 60-84, February.
    5. Xiaodong Liu & Eleonora Patacchini & Edoardo Rainone, 2017. "Peer effects in bedtime decisions among adolescents: a social network model with sampled data," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 103-125, October.
    6. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    7. Ethan Cohen‐Cole & Xiaodong Liu & Yves Zenou, 2018. "Multivariate choices and identification of social interactions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(2), pages 165-178, March.
    8. Xiaodong Liu, 2014. "Identification and Efficient Estimation of Simultaneous Equations Network Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 516-536, October.
    9. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    10. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    11. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    12. James P. Lesage, 2008. "An Introduction to Spatial Econometrics," Revue d'économie industrielle, De Boeck Université, vol. 0(3), pages 19-44.
    13. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
    14. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    15. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    16. Badi H. Baltagi & Ying Deng, 2015. "EC3SLS Estimator for a Simultaneous System of Spatial Autoregressive Equations with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 659-694, December.
    17. Aaron Sojourner, 2013. "Identification of Peer Effects with Missing Peer Data: Evidence from Project STAR," Economic Journal, Royal Economic Society, vol. 123(569), pages 574-605, June.
    18. 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.
    19. Baltagi, Badi H. & Bresson, Georges, 2011. "Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris," Journal of Urban Economics, Elsevier, vol. 69(1), pages 24-42, January.
    20. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    21. Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
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    Cited by:

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    3. Dong, Ruipeng & Li, Daoji & Zheng, Zemin, 2021. "Parallel integrative learning for large-scale multi-response regression with incomplete outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    4. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    5. Valentin Courgeau & Almut E. D. Veraart, 2022. "Likelihood theory for the graph Ornstein-Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 227-260, July.
    6. Ando, Tomohiro & Li, Kunpeng & Lu, Lina, 2023. "A spatial panel quantile model with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 232(1), pages 191-213.
    7. Xuan Liang & Tao Zou, 2023. "Quasi-Score Matching Estimation for Spatial Autoregressive Model with Random Weights Matrix and Regressors," Papers 2305.19721, arXiv.org.
    8. Christis Katsouris, 2024. "Robust Estimation in Network Vector Autoregression with Nonstationary Regressors," Papers 2401.04050, arXiv.org.
    9. Wu, Shihao & Li, Zhe & Zhu, Xuening, 2023. "A distributed community detection algorithm for large scale networks under stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).

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    More about this item

    Keywords

    Least squares estimator; Quasi maximum likelihood estimator; Multivariate responses; Social network; Network autoregression;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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