IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v69y2017i3d10.1007_s10463-016-0560-2.html
   My bibliography  Save this article

Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs

Author

Listed:
  • Elizabeth Gross

    (San José State University)

  • Sonja Petrović

    (Illinois Institute of Technology)

  • Despina Stasi

    (Illinois Institute of Technology)

Abstract

Social networks and other sparse data sets pose significant challenges for statistical inference, since many standard statistical methods for testing model/data fit are not applicable in such settings. Algebraic statistics offers a theoretically justified approach to goodness-of-fit testing that relies on the theory of Markov bases. Most current practices require the computation of the entire basis, which is infeasible in many practical settings. We present a dynamic approach to explore the fiber of a model, which bypasses this issue, and is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models. We demonstrate the approach on the Holland–Leinhardt $$p_1$$ p 1 model for random directed graphs that allows for reciprocation effects.

Suggested Citation

  • Elizabeth Gross & Sonja Petrović & Despina Stasi, 2017. "Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 673-704, June.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0560-2
    DOI: 10.1007/s10463-016-0560-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-016-0560-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-016-0560-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Satoshi Aoki & Akimichi Takemura, 2003. "Minimal Basis for a Connected Markov Chain over 3 × 3 ×K Contingency Tables with Fixed Two‐Dimensional Marginals," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 229-249, June.
    2. Aleksandra Slavković & Xiaotian Zhu & Sonja Petrović, 2015. "Fibers of multi-way contingency tables given conditionals: relation to marginals, cell bounds and Markov bases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 621-648, August.
    3. Fabio Rapallo & Ruriko Yoshida, 2010. "Markov bases and subbases for bounded contingency tables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 785-805, August.
    4. Hara, Hisayuki & Takemura, Akimichi & Yoshida, Ruriko, 2009. "A Markov basis for conditional test of common diagonal effect in quasi-independence model for square contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1006-1014, February.
    5. Hunter, David R. & Goodreau, Steven M. & Handcock, Mark S., 2008. "Goodness of Fit of Social Network Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 248-258, March.
    6. Mitsunori Ogawa & Hisayuki Hara & Akimichi Takemura, 2013. "Graver basis for an undirected graph and its application to testing the beta model of random graphs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 191-212, February.
    Full references (including those not matched with items on IDEAS)

    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. Abraham Martín del Campo & Sarah Cepeda & Caroline Uhler, 2017. "Exact Goodness-of-Fit Testing for the Ising Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 285-306, June.
    2. Sándor Juhász, 2021. "Spinoffs and tie formation in cluster knowledge networks," Small Business Economics, Springer, vol. 56(4), pages 1385-1404, April.
    3. Kayvan Sadeghi & Alessandro Rinaldo, 2020. "Hierarchical models for independence structures of networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 439-457, August.
    4. John McLevey & Alexander V. Graham & Reid McIlroy-Young & Pierson Browne & Kathryn S. Plaisance, 2018. "Interdisciplinarity and insularity in the diffusion of knowledge: an analysis of disciplinary boundaries between philosophy of science and the sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 117(1), pages 331-349, October.
    5. Tom A. B. Snijders & Christian E. G. Steglich, 2015. "Representing Micro–Macro Linkages by Actor-based Dynamic Network Models," Sociological Methods & Research, , vol. 44(2), pages 222-271, May.
    6. Stefano Ghinoi & Riccardo Vita & Bodo Steiner & Alessandro Sinatra, 2024. "Family firm network strategies in regional clusters: evidence from Italy," Small Business Economics, Springer, vol. 62(1), pages 87-103, January.
    7. Cornelius Fritz & Michael Lebacher & Göran Kauermann, 2020. "Tempus volat, hora fugit: A survey of tie‐oriented dynamic network models in discrete and continuous time," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 275-299, August.
    8. Li, Jing & Yu, Qian & Ma, Ding, 2024. "Does China's high-speed rail network promote inter-city technology transfer? ——A multilevel network analysis based on the electronic information industry," Transport Policy, Elsevier, vol. 145(C), pages 11-24.
    9. Tiandong Wang & Panpan Zhang, 2022. "Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 957-986, October.
    10. Anna‐Maria Kindt & Matthias Geissler & Kilian Bühling, 2022. "Be my (little) partner?!—Universities' role in regional innovation systems when large firms are rare," Journal of Regional Science, Wiley Blackwell, vol. 62(5), pages 1274-1295, November.
    11. Milad Abbasiharofteh & Tom Broekel, 2021. "Still in the shadow of the wall? The case of the Berlin biotechnology cluster," Environment and Planning A, , vol. 53(1), pages 73-94, February.
    12. De Nicola, Giacomo & Fritz, Cornelius & Mehrl, Marius & Kauermann, Göran, 2023. "Dependence matters: Statistical models to identify the drivers of tie formation in economic networks," Journal of Economic Behavior & Organization, Elsevier, vol. 215(C), pages 351-363.
    13. Brennecke, Julia & Rank, Olaf, 2017. "The firm’s knowledge network and the transfer of advice among corporate inventors—A multilevel network study," Research Policy, Elsevier, vol. 46(4), pages 768-783.
    14. Kabirigi, Michel & Abbasiharofteh, Milad & Sun, Zhanli & Hermans, Frans, 2022. "The importance of proximity dimensions in agricultural knowledge and innovation systems: The case of banana disease management in Rwanda," Agricultural Systems, Elsevier, vol. 202(C).
    15. Hara, Hisayuki & Sei, Tomonari & Takemura, Akimichi, 2012. "Hierarchical subspace models for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 19-34, January.
    16. Carter, Nathan & Hadlock, Charles & Haughton, Dominique, 2008. "Generating random networks from a given distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3928-3938, April.
    17. Tom Broekel & Marcel Bednarz, 2018. "Disentangling link formation and dissolution in spatial networks: An Application of a Two-Mode STERGM to a Project-Based R&D Network in the German Biotechnology Industry," Networks and Spatial Economics, Springer, vol. 18(3), pages 677-704, September.
    18. Clark, Duncan A. & Macinko, James & Porfiri, Maurizio, 2022. "What factors drive state firearm law adoption? An application of exponential-family random graph models," Social Science & Medicine, Elsevier, vol. 305(C).
    19. Koenig, Michael & Hsieh, Chih-Sheng & Liu, Xiaodong & Zimmermann, Christian, 2018. "Superstar Economists: Coauthorship networks and research output," CEPR Discussion Papers 13239, C.E.P.R. Discussion Papers.
    20. Martin Rosvall & Carl T Bergstrom, 2010. "Mapping Change in Large Networks," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-7, January.

    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:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0560-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.