Network inference from temporally dependent grouped observations

In social network analysis, the observed data usually reflect certain social behaviors, such as the formation of groups, rather than an explicit network structure. Zhao and Weko proposed a model-based approach called the hub model to infer implicit networks from grouped observations (Zhao and Weko, 2019). The hub model assumes independence between groups, which sometimes is not valid in practice. The hub model is generalized into the case of grouped observations with temporal dependence. As in the hub model, the group at each time point is gathered under one leader in the new model. Unlike in the hub model, the group leaders are not sampled independently but follow a Markov chain, and other members in adjacent groups can also be correlated. An expectation-maximization (EM) algorithm is developed for this model and a polynomial-time algorithm is proposed for the E-step. The performance of the new model is evaluated under different simulation settings. The proposed model is applied to a data set of the Kibale Chimpanzee Project.