Inferring Network Structure From Partially Observed Graphs

Abstract

Collecting social network data is notoriously difficult, meaning that indirectly observed or missing observations are very common. In this dissertation, We address two of such scenarios: inference on network measures without any direct network observations, and inference of regression coefficients when actors in the network have latent block memberships. Direct network data is expensive to collect because it requires soliciting connections between all members of the population. Collecting aggregate relational data (ARD) is much more cost effective. In the first two methodological chapters, we show that we can use ARD to estimate individual and global network properties. We connect ARD to a network formation model, which allows us to obtain draws from the posterior distribution over graphs given the ARD response vector. We can then compute network statistics based on these posterior samples. We demonstrate our method using evidence from simulation and replicating results from cases where the complete graph was observed. In the last methodological chapter, we discuss how we make inference on coefficients where the outcome of a linear regression is the interaction between an ordered pair of actors. We propose block-exchangeable errors and algorithms for estimating standard errors. We show that the block-exchangeable estimator is preferable to the exchangeable estimator when latent blocks and observed covariates are dependent.