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Bayesian model selection for the latent position cluster model for social networks

  • CAITRÍONA RYAN (a1), JASON WYSE (a2) and NIAL FRIEL (a3)
Abstract
Abstract

The latent position cluster model is a popular model for the statistical analysis of network data. This model assumes that there is an underlying latent space in which the actors follow a finite mixture distribution. Moreover, actors which are close in this latent space are more likely to be tied by an edge. This is an appealing approach since it allows the model to cluster actors which consequently provides the practitioner with useful qualitative information. However, exploring the uncertainty in the number of underlying latent components in the mixture distribution is a complex task. The current state-of-the-art is to use an approximate form of BIC for this purpose, where an approximation of the log-likelihood is used instead of the true log-likelihood which is unavailable. The main contribution of this paper is to show that through the use of conjugate prior distributions, it is possible to analytically integrate out almost all of the model parameters, leaving a posterior distribution which depends on the allocation vector of the mixture model. This enables posterior inference over the number of components in the latent mixture distribution without using trans-dimensional MCMC algorithms such as reversible jump MCMC. Our approach is compared with the state-of-the-art latentnet (Krivitsky & Handcock, 2015) and VBLPCM (Salter-Townshend & Murphy, 2013) packages.

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Adamic L. A., Lukose R. M., Puniyani A. R., & Huberman B. A. (2001). Search in power-law networks. Physical Review E, 64 (Sep), 046135.
Faloutsos M., Faloutsos P., & Faloutsos C. (1999). On power-law relationships of the internet topology. Sigcomm Computer Communication Review, 29 (4), 251262.
Fraley C., & Raftery A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97 (458), 611631.
Fraley C., & Raftery A. E. (2003). Enhanced model-based clustering, density estimation, and discriminant analysis software: MCLUST. Journal of Classification, 20 (2), 263286.
Friel N., & Wyse J. (2012). Estimating the evidence—a review. Statistica Neerlandica, 66 (3), 288308.
Handcock M. S., Raftery A. E., & Tantrum J. M. (2007). Model-based clustering for social networks. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170 (2), 301354.
Hoff P. D., Raftery A. E., & Handcock M. S. (2002). Latent space approaches to social network analysis. Journal of the American Statistical Association, 97 (460), 10901098.
Kolaczyk E. D. (2009). Statistical analysis of network data: methods and models. New York: Springer.
Krivitsky P. N., & Handcock M. S. (2008). Fitting latent cluster models for networks with latentnet. Journal of Statistical Software, 24 (5), 123.
Krivitsky P. N., & Handcock M. S. (2015). Latentnet: Latent position and cluster models for statistical networks. The Statnet Project (http://www.statnet.org). R package version 2.7.1.
Lusseau D., Schneider K., Boisseau O. J., Haase P., Slooten E., & Dawson S. M. (2003). The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behavioral Ecology and Sociobiology, 54 (4), 396405.
Michailidis G. (2012). Statistical challenges in biological networks. Journal of Computational and Graphical Statistics, 21 (4), 840855.
Miller W., & Harrison M. T. (2016). Mixture models with a prior on the number of components. Journal of the American Statistical Association. doi:10.1080/01621459.2016.1255636
Nobile A. (2007). Bayesian finite mixtures: A note on prior specification and posterior computation. preprint, arxiv:0711.0458.
Nobile A., & Fearnside A. T. (2007). Bayesian finite mixtures with an unknown number of components: The allocation sampler. Statistics and Computing, 17 (2), 147162.
Nowicki K., & Snijders T. A. B. (2001). Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association, 96 (455), 10771087.
Raftery A. E., Niu X., Hoff P. D., & Yeung K. Y. (2012). Fast inference for the latent space network model using a case-control approximate likelihood. Journal of Computational and Graphical Statistics, 21 (4), 901919.
Richardson S., & Green P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59 (4), 731792.
Robins G., Snijders T., Wang P., Handcock M. S., & Pattison P. (2007). Recent developments in exponential random graph (p*) models for social networks. Social Networks, 29 (2), 192215.
Salter-Townshend M., & Murphy T. B. (2013). Variational Bayesian inference for the latent position cluster model. Computational Statistics and Data Analysis, 57 (1), 661671.
Sampson S. F. (1968). A novitiate in a period of change: An experimental and case study of social relationships. Ph.D. thesis, Cornell University, September.
Schwarz G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6 (2), 461464.
Shortreed S., Handcock M. S., & Hoff P. (2006). Positional estimation within a latent space model for networks. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 2 (1), 2433.
Sibson R. (1979). Studies in the robustness of multidimensional scaling: Perturbational analysis of classical scaling. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 41 (2), 217229.
Wasserman S., & Galaskiewicz J. (1994). Advances in social network analysis: Research in the social and behavioral sciences. Thousand Oaks, California: Sage Publications.
Wasserman S., & Pattison P. (1996). Logit models and logistic regressions for social networks: I. an introduction to markov graphs and p*. Psychometrika, 61 (3), 401425.
Wyse J., & Friel N. (2012). Block clustering with collapsed latent block models. Statistics and Computing, 22 (2), 415428.
Zachary W. W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33 (4), 452473.
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Network Science
  • ISSN: 2050-1242
  • EISSN: 2050-1250
  • URL: /core/journals/network-science
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