Estimating Personal Network Size with Non-random Mixing via Latent Kernels

Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)


A major problem in the study of social networks is estimating the number of people an individual knows. However, there is no general method to account for barrier effects, a major source of bias in common estimation procedures. The literature describes approaches that model barrier effects, or non-random mixing, but they suffer from unstable estimates and fail to give results that agree with specialists’ knowledge. In this paper we introduce a model that builds off existing methods, imposes more structure, requires significantly fewer parameters, and yet allows for greater interpretability. We apply our model on responses gathered from a survey we designed and show that our conclusions better match what sociologists find in practice. We expect that this approach will provide more accurate estimates of personal network sizes and hence remove a significant hurtle in sociological research.


Personal network size estimation Non-random mixing Barrier effects Kernel-based models 



This research is supported by NSF grant SES 1023176.


  1. 1.
    De Boor, C.: A Practical Guide to Splines, vol. 27. Springer, New York (1978)Google Scholar
  2. 2.
    Gelman, A., Stern, H.S., Carlin, J.B., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC (2013)Google Scholar
  3. 3.
    Killworth, P.D., Johnsen, E.C., McCarty, C., Shelley, G.A., Bernard, H.R.: A social network approach to estimating seroprevalence in the United States. Soc. Netw. 20(1), 23–50 (1998)Google Scholar
  4. 4.
    McCarty, C., Killworth, P.D., Bernard, H.R., Johnsen, E.C., Shelley, G.A.: Comparing two methods for estimating network size. Hum. Organ. 60(1), 28–39 (2001)Google Scholar
  5. 5.
    McCormick, T.H., Salganik, M.J., Zheng, T.: How many people do you know? Efficiently estimating personal network size. J. Am. Stat. Assoc. 105(489), 59–70 (2010)Google Scholar
  6. 6.
    McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Ann. Rev. Sociol. 27(1), 415–444 (2001)Google Scholar
  7. 7.
    Stan Development Team: Stan modeling language: User’s guide and reference manual (2016). Version 2.14.0.
  8. 8.
    Zheng, T., Salganik, M.J., Gelman, A.: How many people do you know in prison? Using overdispersion in count data to estimate social structure in networks. J. Am. Stat. Assoc. 101(474), 409–423 (2006)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MangolyticsSan FranciscoUSA
  2. 2.Department of StatisticsColumbia UniversityNew YorkUSA
  3. 3.Sociology DepartmentNew York UniversityNew YorkUSA

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