Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels
| Autor: | Karwa, Vishesh, Pati, Debdeep, Petrović, Sonja, Solus, Liam, Alexeev, Nikita, Raič, Mateja, Wilburne, Dane, Williams, Robert, Yan, Bowei |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 86, Issue 1, February 2024, Pages 90-121 |
| Druh dokumentu: | Working Paper |
| Popis: | We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the \emph{latent} block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel, and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behavior. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models. Comment: substantial revision from v3, updated simulations and theoretical discussions |
| Databáze: | arXiv |
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