Latent Variable Models for Imprecisely or Indirectly Measured Networks
In the social sciences, social networks are important structures which represent the relationships and interactions between actors in a population of study. In these fields, the most common method for measuring networks is to directly survey study participants about who their connections are. However, directly measuring the network of interest can be challenging. Participants do not always provide accurate accounts of their connections, which can result in mismeasurement of the network. Furthermore, it may be challenging to solicit connections corresponding to the exact network of interest, for which, depending on the context, links may represent past behavior, social and geographic distance, or the potential for contact given certain sets of circumstances. In this talk, we address examples of two common issues: the influence of mismeasurement on inference and recovering the network of interest when it is indirectly observed.
First, we consider the impact of missing links in the context of experiments of networks. In these experiments, individuals are not only influenced by their own treatment assignments, but also by those of their peers. These treatment spillovers are often of direct scientific interest. Through simulations, we show that missing links can induce bias for these estimates of spillover. We develop a mixture model that provides consistent estimators in this setting and use this model to study information dissemination among garment-making firms in Ghana. In the second part of this talk, we consider an alternative to using survey-based methods: constructing networks by collecting interaction activity between pairs of individuals. Directly logging social interaction data is becoming increasingly feasible due to the spread of mobile technology. However, while potentially cheaper to collect and more reliable than their survey counterparts, social interactions do not directly quantify relationships between individuals. We propose a point-process model for inferring a network of social relations that conceptualizes interaction data as the manifestation of underlying network structure while preserving the data’s continuous-time nature. We explore networks inferred by our method in the contexts of college students and barn swallows.