Multiplicative latent factor models for description and prediction of social networks

  • Peter D. Hoff


We discuss a statistical model of social network data derived from matrix representations and symmetry considerations. The model can include known predictor information in the form of a regression term, and can represent additional structure via sender-specific and receiver-specific latent factors. This approach allows for the graphical description of a social network via the latent factors of the nodes, and provides a framework for the prediction of missing links in network data.


Eigenvalue decomposition Exchangeability Prediction Singular value decomposition Social network Visualization 


  1. Aldous DJ (1981) Representations for partially exchangeable arrays of random variables. J Multivar Anal 11:581–598 CrossRefGoogle Scholar
  2. Aldous DJ (1985) Exchangeability and related topics. In: École d’été de probabilités de Saint-Flour, XIII—1983. Lecture notes in math, vol 1117. Springer, Berlin, pp 1–198 CrossRefGoogle Scholar
  3. Handcock MS (2003) Assessing degeneracy in statistical models of social networks. Working paper no. 39. Center for Statistics and the Social Sciences, University of Washington, Seattle Google Scholar
  4. Hoff PD (2005) Bilinear mixed-effects models for dyadic data. J Am Stat Assoc 100:286–295 CrossRefGoogle Scholar
  5. Hoff PD, Raftery AE, Handcock MS (2002) Latent space approaches to social network analysis. J Am Stat Assoc 97:1090–1098 CrossRefGoogle Scholar
  6. McCullagh P, Nelder JA (1983) Generalized linear models. Monographs on statistics and applied probability. Chapman & Hall, London Google Scholar
  7. Nowicki K, Snijders TAB (2001) Estimation and prediction for stochastic blockstructures. J Am Stat Assoc 96:1077–1087 CrossRefGoogle Scholar
  8. Snijders TAB (2002) Markov chain Monte Carlo estimation of exponential random graph models. J Soc Struct 3 Google Scholar
  9. Tierney L (1994) Markov chains for exploring posterior distributions. Ann Stat 22:1701–1762 (with discussion and a rejoinder by the author.) CrossRefGoogle Scholar
  10. Ward MD, Hoff PD (2005) Persistent patterns of international commerce. Working paper no. 45. Center for Statistics and the Social Sciences, University of Washington, Seattle Google Scholar
  11. Warner R, Kenny DA, Stoto M (1979) A new round robin analysis of variance for social interaction data. J Personal Soc Psychol 37:1742–1757 CrossRefGoogle Scholar
  12. Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge Google Scholar
  13. Wasserman S, Pattison P (1996) Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika 61:401–425 CrossRefGoogle Scholar
  14. Wong GY (1982) Round robin analysis of variance via maximum likelihood. J Am Stat Assoc 77:714–724 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Departments of Statistics, Biostatistics and the Center for Statistics and the Social SciencesUniversity of WashingtonSeattleUSA

Personalised recommendations