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Exact conditional goodness-of-fit tests for the mixed mem...
[Submitted on 19 Jul 2025 (v1), last revised 1 Jun 2026 (this ve · 2026-06-02 · via stat updates on arXiv.org

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Abstract:We propose exact conditional goodness-of-fit tests for directed mixed membership stochastic block models. Given dyad-level sender and receiver roles, the block-pair edge totals are sufficient for the block probability matrix; conditioning on these totals gives a nuisance-free uniform law on a finite fiber. This yields finite-sample randomization tests for residual sender and receiver heterogeneity, reciprocity, and directed transitive closure. The procedure uses an independent fiber sampler, Monte Carlo rank \(p\)-values, and can be applied after drawing latent block-pair assignments from the posterior distribution. Simulations and the Sampson monastery network show that the tests are calibrated under the null and diagnostically useful for directed model misspecification.

Submission history

From: Sourav Majumdar [view email]
[v1] Sat, 19 Jul 2025 03:45:42 UTC (44 KB)
[v2] Mon, 1 Jun 2026 04:35:00 UTC (322 KB)