Modeling three-way social network data: A cross-nested random effects model for gossip in the workplace

Social networks are usually collected as dyadic data: the relations between pairs of actors are recorded, directed or undirected, complete or personal networks. The actors act either as sender or receiver of a tie. Three-way social network data are rare and occur when relations are recorded involving three actors. An example that will be analyzed in this paper is gossip: In a closed group setting it is recorded, by means of selfreport, who gossips with whom about whom. In three-way data, actors have three roles: as sender, receiver, and as object (of gossip). A random effects model for binary three-way social network data is developed relating the probability of a gossip tie to individual properties and roles of the actors, network relations that may exist between any pair of them, possibly available three-way characteristics of them as a triplet. The random effects are used to account for the dependence between the observations, caused by each actor having multiple roles, and caused by each actor being involved in multiple ties (within and across roles). The resulting model, a combination of a logistic regression model with a trivariate normal distribution, is estimated using MCMC, as implemented in WinBUGS