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.

翻译：针对有向混合成员度随机块模型，我们提出了精确条件拟合优度检验。给定个体对层面的发送方和接收方角色，块配对边总数对块概率矩阵是充分的；以这些总数为条件，可在有限纤维上获得无干扰的均匀分布律。这为残余的发送方与接收方异质性、互惠性及有向传递闭包提供了有限样本随机化检验。该方法采用独立纤维采样器与蒙特卡洛秩 \(p\) 值，可在从后验分布中抽取潜在块配对分配后进行应用。模拟实验及萨姆森修道院网络表明，该检验在原假设下具有校准性，并对有向模型误诊具有诊断价值。