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Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the 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 behaviour. 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.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad084","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T17:09:45Z","timestamp":1694797785000},"page":"90-121","source":"Crossref","is-referenced-by-count":9,"title":["Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels"],"prefix":"10.1093","volume":"86","author":[{"given":"Vishesh","family":"Karwa","sequence":"first","affiliation":[{"name":"Department of Statistics, Operations and Data Science,Temple University , Philadelphia , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debdeep","family":"Pati","sequence":"additional","affiliation":[{"name":"Department of Statistics, Texas A & M University , College Station , 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