Bayesian analysis of erg models for multilevel, multiplex, and multilayered networks with sampled or missing data

Social network analysis has typically concerned analysis of one type of tie connecting nodes of the same type. It has however been recognised that people are connected through multiple types of ties and that people in addition are affiliated with multiple types of non-people nodes. Exponential random graph models (ERGM) is a family of statistical models for social networks that at this point allows for a number of different types of network data, including one-mode networks, bipartite networks, multiplex data, as well as multilevel network data. Multilevel networks have been proposed as a joint representation of associations between multiple types of entities or nodes, such as people and organization, where two types of nodes gives rise to three distinct types of ties. The typical roster data collection method may be impractical or infeasible when the node sets are hard to detect or define or because of the cognitive demands on respondents. Multilevel multilayered networks allow us to consider a multitude of different sources of data and to sample on different types of nodes and relations. We consider modelling multilevel multilayered networks using exponential random graph models and extend a recently developed Bayesian data-augmentation scheme to allow for partially missing data. We illustrate the proposed inference procedures for the case of multilevel snowball sampling and sampling with error based on the Noordin Top network.