IDEAS home Printed from https://ideas.repec.org/p/net/wpaper/1316.html
   My bibliography  Save this paper

Approximate variational inference for a model of social interactions

Author

Listed:
  • Angelo Mele

    (Johns Hopkins University - Carey Business School)

Abstract

This paper proposes approximate variational inference methods for estimation of a strategic model of social interactions. Players interact in an exogenous network and sequentially choose a binary action. The utility of an action is a function of the choices of neighbors in the network. I prove that the interaction process can be represented as a potential game and it converges to a unique stationary equilibrium distribution. However, exact inference for this model is infeasible because of a computationally intractable likelihood, which cannot be evaluated even when there are few players. To overcome this problem, I propose variational approximations for the likelihood that allow approximate inference. This technique can be applied to any discrete exponential family, and therefore it is a general tool for inference in models with a large number of players. The methodology is illustrated with several simulated datasets and compared with MCMC methods.

Suggested Citation

  • Angelo Mele, 2013. "Approximate variational inference for a model of social interactions," Working Papers 13-16, NET Institute.
    • Handle: RePEc:net:wpaper:1316
    as

    Download full text from publisher

    File URL: http://www.netinst.org/Mele_13-16.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Ryo Nakajima, 2007. "Measuring Peer Effects on Youth Smoking Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 897-935.
    3. Angelo Mele, 2010. "A structural model of segregation in social networks," CeMMAP working papers CWP32/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Braun, Michael & McAuliffe, Jon, 2010. "Variational Inference for Large-Scale Models of Discrete Choice," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 324-335.
    5. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    6. Grimmer, Justin, 2011. "An Introduction to Bayesian Inference via Variational Approximations," Political Analysis, Cambridge University Press, vol. 19(1), pages 32-47, January.
    7. Anton Badev, 2014. "Discrete Games in Endogenous Networks: Theory and Policy," 2014 Meeting Papers 901, Society for Economic Dynamics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gibbons, Steve & Overman, Henry G. & Patacchini, Eleonora, 2015. "Spatial Methods," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 115-168, Elsevier.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers CWP52/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    3. Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
    4. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    5. Asim Ansari & Yang Li & Jonathan Z. Zhang, 2018. "Probabilistic Topic Model for Hybrid Recommender Systems: A Stochastic Variational Bayesian Approach," Marketing Science, INFORMS, vol. 37(6), pages 987-1008, November.
    6. Yann Algan & Quoc-Anh Do & Nicolò Dalvit & Alexis Le Chapelain & Yves Zenou, 2015. "How Social Networks Shape Our Beliefs: A Natural Experiment among Future French Politicians," Working Papers hal-03459820, HAL.
    7. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    8. Gaonkar, Shweta & Mele, Angelo, 2023. "A model of inter-organizational network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 82-104.
    9. Chih‐Sheng Hsieh & Lung‐Fei Lee & Vincent Boucher, 2020. "Specification and estimation of network formation and network interaction models with the exponential probability distribution," Quantitative Economics, Econometric Society, vol. 11(4), pages 1349-1390, November.
    10. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    11. repec:hal:spmain:info:hdl:2441/78vacv4udu92eq3fec89svm9uv is not listed on IDEAS
    12. Bansal, Prateek & Krueger, Rico & Graham, Daniel J., 2021. "Fast Bayesian estimation of spatial count data models," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    13. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference for the DINA Model," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 569-597, October.
    14. Timothy Conley & Nirav Mehta & Ralph Stinebrickner & Todd Stinebrickner, 2015. "Social Interactions, Mechanisms, and Equilibrium: Evidence from a Model of Study Time and Academic Achievement," NBER Working Papers 21418, National Bureau of Economic Research, Inc.
    15. Áureo de Paula & Seth Richards-Shubik & Elie Tamer, 2015. "Identification of preferences in network formation games," CeMMAP working papers 29/15, Institute for Fiscal Studies.
    16. Matthew O. Jackson & Brian W. Rogers & Yves Zenou, 2017. "The Economic Consequences of Social-Network Structure," Journal of Economic Literature, American Economic Association, vol. 55(1), pages 49-95, March.
    17. Daziano, Ricardo A., 2022. "Willingness to delay charging of electric vehicles," Research in Transportation Economics, Elsevier, vol. 94(C).
    18. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    19. Hulya Eraslan & Xun Tang, 2018. "Identification and Estimation of Large Network Games with Private Link Information," Koç University-TUSIAD Economic Research Forum Working Papers 1809, Koc University-TUSIAD Economic Research Forum.
    20. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    21. Matthew O. Jackson, 2014. "Networks in the Understanding of Economic Behaviors," Journal of Economic Perspectives, American Economic Association, vol. 28(4), pages 3-22, Fall.

    More about this item

    Keywords

    Variational approximations; Bayesian Estimation; Social Interactions;
    All these keywords.

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:net:wpaper:1316. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nicholas Economides (email available below). General contact details of provider: http://www.NETinst.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.