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CN 34-1054/N

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Open AccessOpen Access JUSTC Management 18 August 2023

Estimation of peer pressure in dynamic homogeneous social networks

  • 1.

    International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

  • 2.

    School of Economics and Management, Anhui University of Science and Technology, Huainan 232001, China

Cite this:
https://doi.org/10.52396/JUSTC-2023-0035
More Information
  • Author Bio:

    Jie Liu is an Associate Professor at the University of Science and Technology of China (USTC). He received his Bachelor’s degree and Ph.D. degree in Statistics from USTC in 2003 and 2008, respectively. His major research interests include random networks, statistical modelling, and network analysis

    Jiayang Zhao is currently a Ph.D. student at the University of Science and Technology of China (USTC). His research interests focus on network data modelling and subgroup analysis

  • Corresponding author: E-mail: zhaojy19@mail.ustc.edu.cn
  • Received Date: 09 March 2023
  • Accepted Date: 26 May 2023
    • Available Online: 18 August 2023
    Abstract

  • Abstract

    Social interaction with peer pressure is widely studied in social network analysis. Game theory can be utilized to model dynamic social interaction and one class of game network models assumes that peopleos decision payoff functions hinge on individual covariates and the choices of their friends. However, peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model. For this reason, we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks. The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios. To estimate peer pressure in the model, we first present two algorithms based on the initialize expand merge method and the polynomial-time two-stage method to estimate homogeneity parameters. Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure. Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error. We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.

    Graphical abstract

    A novel network game model is proposed to quantify social interaction with peer pressure in dynamic networks. New algorithms are designed to identify homogeneity. The NPLE method is introduced to estimate the model parameters.

    Abstract

    Social interaction with peer pressure is widely studied in social network analysis. Game theory can be utilized to model dynamic social interaction and one class of game network models assumes that peopleos decision payoff functions hinge on individual covariates and the choices of their friends. However, peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model. For this reason, we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks. The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios. To estimate peer pressure in the model, we first present two algorithms based on the initialize expand merge method and the polynomial-time two-stage method to estimate homogeneity parameters. Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure. Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error. We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.

    • Public Summary

    • This paper introduces the Generalized Constant Peer Effect (GCPE) model, a novel network game model that quantifies social interactions within dynamic networks.
    • The proposed model can efficiently mitigate estimation inaccuracies related to peer pressure by integrating homogeneity.
    • We design innovative algorithms to accurately identify homogeneity. Then we apply the Nested Pseudo-Likelihood Estimation (NPLE) method to obtain consistent estimators of parameters.

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    • References(28)
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    Durlauf S N, Ioannides Y M. Social interactions. Annual Review of Economics, 2010, 2 (1): 451–478. doi: 10.1146/annurev.economics.050708.143312
    [2]
    Kim J, Kim M, Choi J, et al. Offline social interactions and online shopping demand: Does the degree of social interactions matter? Journal of Business Research, 2019, 99: 373–381. doi: 10.1016/j.jbusres.2017.09.022
    [3]
    Poutvaara P, Siemers L R. Smoking and social interaction. Journal of Health Economics, 2008, 27 (6): 1503–1515. doi: 10.1016/j.jhealeco.2008.06.005
    [4]
    Yin J, He X, Yang Y, et al. Outcome-based evaluations of social interaction valence in a contingent response context. Frontiers in Psychology, 2019, 10: 2557. doi: 10.3389/fpsyg.2019.02557
    [5]
    Sirakaya S. Recidivism and social interactions. Journal of the American Statistical Association, 2006, 101: 863–877. doi: 10.1198/016214506000000177
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    Blume L E, Brock W A, Durlauf S N, et al. Linear social interactions models. Journal of Political Economy, 2015, 123 (2): 444–496. doi: 10.1086/679496
    [7]
    Xu H. Social interactions in large networks: A game theoretic approach. International Economic Review, 2018, 59 (1): 257–284. doi: 10.1111/iere.12269
    [8]
    Lin Z, Xu H. Estimation of social-influence-dependent peer pressure in a large network game. The Econometrics Journal, 2017, 20 (3): S86–S102. doi: 10.1111/ectj.12102
    [9]
    Sun Z, Du Y, Chen X, et al. Implicit community discovery based on microblog theme homogeneit. IOP Conference Series: Materials Science and Engineering, 2020, 790 (1): 012045. doi: 10.1088/1757-899X/790/1/012045
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    Shalizi C R, Thomas A C. Homophily and contagion are generically confounded in observational social network studies. Sociological Methods & Research, 2011, 40 (2): 211–239. doi: 10.1177/0049124111404820
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    Davin J P, Gupta S, Piskorski M J. Separating homophily and peer influence with latent space. Boston, MA: Harvard Business School, 2014.
    [14]
    Hill S, Provost F, Volinsky C. Network-based marketing: Identifying likely adopters via consumer networks. Statistical Science, 2006, 21 (2): 256–276. doi: 10.1214/088342306000000222
    [15]
    Worrall H. Community detection as a method to control for homophily in social networks. Corpus ID: 15409339, 2014.
    [16]
    McFowland III E, Shalizi C R. Estimating causal peer influence in homophilous social networks by inferring latent locations. Journal of the American Statistical Association, 2023, 118: 707–718. doi: 10.1080/01621459.2021.1953506
    [17]
    Aguirregabiria V, Mira P. Sequential estimation of dynamic discrete games. Econometrica, 2007, 75 (1): 1–53. doi: 10.1111/j.1468-0262.2007.00731.x
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    Egesdal M, Lai Z, Su C-L. Estimating dynamic discrete-choice games of incomplete information. Quantitative Economics, 2015, 6 (3): 567–597. doi: 10.3982/QE430
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    Manski C F. Identification of endogenous social effects: The reflection problem. The Review of Economic Studies, 1993, 60 (3): 531–542. doi: 10.2307/2298123
    [20]
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    [21]
    Han Q, Xu K, Airoldi E. Consistent estimation of dynamic and multi-layer block models. In: Proceedings of the 32nd International Conference on Machine Learning. Lille, France: JMLR, 2015, 37: 1511–1520.
    [22]
    Pensky M, Zhang T. Spectral clustering in the dynamic stochastic block model. Electronic Journal of Statistics, 2019, 13: 678–709. doi: 10.1214/19-EJS1533
    [23]
    Chunaev P. Community detection in node-attributed social networks: A survey. Computer Science Review, 2020, 37: 100286. doi: 10.1016/j.cosrev.2020.100286
    [24]
    Liu M, Guo J, Chen J. Community discovery in weighted networks based on the similarity of common neighbors. Journal of Information Processing Systems, 2019, 15 (5): 1055–1067. doi: 10.3745/JIPS.04.0133
    [25]
    Gao C, Ma Z, Zhang A Y, et al. Achieving optimal misclassification proportion in stochastic block models. The Journal of Machine Learning Research, 2017, 18 (1): 1980–2024. doi: 10.5555/3122009.3153016
    [26]
    Bickel P J, Chen A. A nonparametric view of network models and Newman–Girvan and other modularities. 2009. Proceedings of the National Academy of Sciences, 2009, 106 (50): 21068–21073. doi: 10.1073/pnas.0907096106
    [27]
    Zhao Y, Levina E, Zhu J. Consistency of community detection in networks under degree-corrected stochastic block models. Annals of Statistics, 2012, 40: 2266–2292. doi: 10.1214/12-AOS1036
    [28]
    Kasahara H, Shimotsu K. Sequential estimation of structural models with a fixed point constraint. Econometrica, 2012, 80 (5): 2303–2319. doi: 10.3982/ECTA8291
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    Figure  1.  Average community misclassification rate for Algorithm 1, which is based on the average of 50 replications.

    Figure  2.  Average community misclassification rate for Algorithms 1 and 2, which is based on the average of 50 replications.

    Figure  3.  The standard deviation and mean square error of the estimated peer pressure parameter.

    [1]
    Durlauf S N, Ioannides Y M. Social interactions. Annual Review of Economics, 2010, 2 (1): 451–478. doi: 10.1146/annurev.economics.050708.143312
    [2]
    Kim J, Kim M, Choi J, et al. Offline social interactions and online shopping demand: Does the degree of social interactions matter? Journal of Business Research, 2019, 99: 373–381. doi: 10.1016/j.jbusres.2017.09.022
    [3]
    Poutvaara P, Siemers L R. Smoking and social interaction. Journal of Health Economics, 2008, 27 (6): 1503–1515. doi: 10.1016/j.jhealeco.2008.06.005
    [4]
    Yin J, He X, Yang Y, et al. Outcome-based evaluations of social interaction valence in a contingent response context. Frontiers in Psychology, 2019, 10: 2557. doi: 10.3389/fpsyg.2019.02557
    [5]
    Sirakaya S. Recidivism and social interactions. Journal of the American Statistical Association, 2006, 101: 863–877. doi: 10.1198/016214506000000177
    [6]
    Blume L E, Brock W A, Durlauf S N, et al. Linear social interactions models. Journal of Political Economy, 2015, 123 (2): 444–496. doi: 10.1086/679496
    [7]
    Xu H. Social interactions in large networks: A game theoretic approach. International Economic Review, 2018, 59 (1): 257–284. doi: 10.1111/iere.12269
    [8]
    Lin Z, Xu H. Estimation of social-influence-dependent peer pressure in a large network game. The Econometrics Journal, 2017, 20 (3): S86–S102. doi: 10.1111/ectj.12102
    [9]
    Sun Z, Du Y, Chen X, et al. Implicit community discovery based on microblog theme homogeneit. IOP Conference Series: Materials Science and Engineering, 2020, 790 (1): 012045. doi: 10.1088/1757-899X/790/1/012045
    [10]
    Favre G, Figeac J, Grossetti M, et al. Social distance in France: Evolution of homogeneity within personal networks from 2001 to 2017. Social Networks, 2022, 68: 70–83. doi: 10.1016/j.socnet.2021.05.001
    [11]
    Liu L, Wang X, Zheng Y, et al. Homogeneity trend on social networks changes evolutionary advantage in competitive information diffusion. New Journal of Physics, 2020, 22 (1): 013019. doi: 10.1016/j.socnet.2021.05.001
    [12]
    Shalizi C R, Thomas A C. Homophily and contagion are generically confounded in observational social network studies. Sociological Methods & Research, 2011, 40 (2): 211–239. doi: 10.1177/0049124111404820
    [13]
    Davin J P, Gupta S, Piskorski M J. Separating homophily and peer influence with latent space. Boston, MA: Harvard Business School, 2014.
    [14]
    Hill S, Provost F, Volinsky C. Network-based marketing: Identifying likely adopters via consumer networks. Statistical Science, 2006, 21 (2): 256–276. doi: 10.1214/088342306000000222
    [15]
    Worrall H. Community detection as a method to control for homophily in social networks. Corpus ID: 15409339, 2014.
    [16]
    McFowland III E, Shalizi C R. Estimating causal peer influence in homophilous social networks by inferring latent locations. Journal of the American Statistical Association, 2023, 118: 707–718. doi: 10.1080/01621459.2021.1953506
    [17]
    Aguirregabiria V, Mira P. Sequential estimation of dynamic discrete games. Econometrica, 2007, 75 (1): 1–53. doi: 10.1111/j.1468-0262.2007.00731.x
    [18]
    Egesdal M, Lai Z, Su C-L. Estimating dynamic discrete-choice games of incomplete information. Quantitative Economics, 2015, 6 (3): 567–597. doi: 10.3982/QE430
    [19]
    Manski C F. Identification of endogenous social effects: The reflection problem. The Review of Economic Studies, 1993, 60 (3): 531–542. doi: 10.2307/2298123
    [20]
    Seim K. An empirical model of firm entry with endogenous product-type choices. The RAND Journal of Economics, 2006, 37 (3): 619–640. doi: 10.1111/j.1756-2171.2006.tb00034.x
    [21]
    Han Q, Xu K, Airoldi E. Consistent estimation of dynamic and multi-layer block models. In: Proceedings of the 32nd International Conference on Machine Learning. Lille, France: JMLR, 2015, 37: 1511–1520.
    [22]
    Pensky M, Zhang T. Spectral clustering in the dynamic stochastic block model. Electronic Journal of Statistics, 2019, 13: 678–709. doi: 10.1214/19-EJS1533
    [23]
    Chunaev P. Community detection in node-attributed social networks: A survey. Computer Science Review, 2020, 37: 100286. doi: 10.1016/j.cosrev.2020.100286
    [24]
    Liu M, Guo J, Chen J. Community discovery in weighted networks based on the similarity of common neighbors. Journal of Information Processing Systems, 2019, 15 (5): 1055–1067. doi: 10.3745/JIPS.04.0133
    [25]
    Gao C, Ma Z, Zhang A Y, et al. Achieving optimal misclassification proportion in stochastic block models. The Journal of Machine Learning Research, 2017, 18 (1): 1980–2024. doi: 10.5555/3122009.3153016
    [26]
    Bickel P J, Chen A. A nonparametric view of network models and Newman–Girvan and other modularities. 2009. Proceedings of the National Academy of Sciences, 2009, 106 (50): 21068–21073. doi: 10.1073/pnas.0907096106
    [27]
    Zhao Y, Levina E, Zhu J. Consistency of community detection in networks under degree-corrected stochastic block models. Annals of Statistics, 2012, 40: 2266–2292. doi: 10.1214/12-AOS1036
    [28]
    Kasahara H, Shimotsu K. Sequential estimation of structural models with a fixed point constraint. Econometrica, 2012, 80 (5): 2303–2319. doi: 10.3982/ECTA8291
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