Analysing the mediating role of a network: a Bayesian latent space approach

The use of network analysis for the investigation of social structures has recently seen a rise, due both to the high availability of data and to the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different point of view, by considering the whole network as a random variable conveying the effect of an exposure on a response.This point of view represents a classical mediation setting, where the interest lies in the estimation of the indirect effect, that is, the effect propagated through the mediating variable.We introduce a latent space model mapping the network into a space of smaller dimension by considering the hidden positions of the units in the network. Furthermore, the mediation analysis is extended by using generalised linear models. A Bayesian approach allows to obtain the entire distribution of the indirect effect,generally unknown, and to compute highest density intervals, which give accurate and interpretable bounds for the mediated effect. Finally, an application to social interactions among a group of adolescents and their attitude toward smoking is presented.