The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node specific random effects that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by combining approximate penalized pseudolikelihood estimation for the random effects with maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the AIC to check for node specific heterogeneity.
翻译:在指数随机图模型(ERGM)中存在未观测到的节点具体差异性是一个普遍的关注问题,既涉及模型有效性,也涉及估计不稳定性。因此,我们扩大了ERGM, 纳入了考虑到网络中未观测到的异质性的节点特定随机效应。这导致一种混合模型,包括参数和随机系数,称为混合ERGM。估计是通过将随机效应的近似已受处罚的假象估计与模型剩余参数的最大可能性估计相结合来进行的。这种方法提供了一种稳定的算法,使得即使在大型网络中也能够适应交点异性效应。我们还根据AIC提出了模型选择模式,以检查节点的具体异性。