Spatial process models for social network analysis

There has been a recent increase in the use of network models for representing interactions and structure in many complex systems. In this thesis we introduce the use of spatial process models for the statistical analysis of networks, emphasizing applications to social networks. The first methodology we propose is the latent socio-spatial process model. In the spirit of a random effects model, pairwise connections are assumed to be conditionally independent given a latent spatial process evaluated at observed points in a covariate space. This smooths the relationship between connections and covariates in a sample network using relatively few parameters, so the probabilities of connection for a population can be inferred. The second model that is proposed is the meta-distance model. Here, a random function is used to represent the logistic relationship between covariates and binary relations. A spatial covariance structure is assumed for the random function, where the points in space are distances between attribute pairs. A Bayesian framework is used for estimation and prediction. While spatial process models can be very flexible and provide reasonable fit and predictions in many contexts, interpretation of these models can be complicated. To aid in the identification of important covariates, we propose a reference distribution variable selection procedure. An inert variable is appended to the data for analysis, and the posterior distribution of an ``activity'' parameter associated with the covariate is used as a reference distribution against which the true variables can be assessed. The approach is Bayesian, but the variable selection has a frequentist flavor. Finally, we illustrate one important application of the proposed methodology. Local network topology can have a significant impact on contact-based processes, such as epidemics. This is demonstrated by looking at susceptible-infected-susceptible and susceptible-infected-removed epidemic models. We explore how using a predictive network model, such as the latent socio-spatial process model, can help in predicting how a disease might spread in a population.