Date of Original Version

6-2011

Type

Article

Rights Management

This is an electronic version of an article published by Oxford University Press. The version of record is available online at http://dx.doi.org/10.1093/biomet/asr053

Abstract or Description

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising self-reported school friendships, resulting in block estimates that reveal residual structure.

DOI

10.1093/biomet/asr053

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Published In

Biometrika, 99, 2, 273-284.