Exact conditional goodness-of-fit tests for the mixed membership stochastic block model

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.