Statistical Modelling 19 (4) (2019), 386–411

Pǿlya–Aeppli regression model for overdispersed count data

Linda SL Tan
Department of Statistics and Applied Probability,
Faculty of Science,
National University of Singapore,
Singapore.
e-mail: statsll@nus.edu.sg

Maria De Iorio
Department of Statistical Science,
University College London,
London,
UK.


Abstract:

A nonparametric approach to the modelling of social networks using degree-corrected stochastic blockmodels is proposed. The model for static network consists of a stochastic blockmodel using a probit regression formulation, and popularity parameters are incorporated to account for degree heterogeneity. We specify a Dirichlet process prior to detect community structure as well as to induce clustering in the popularity parameters. This approach is flexible yet parsimonious as it allows the appropriate number of communities and popularity clusters to be determined automatically by the data. We further discuss and implement extensions of the static model to dynamic networks. In a Bayesian framework, we perform posterior inference through MCMC algorithms. The models are illustrated using several real-world benchmark social networks.

Keywords:

Community detection; degree correction; Dirichlet process; stochastic blockmodels.

Downloads:

Code and supplementary material in zipped archive. The data used in this article can be downloaded from this link.
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