Consistently estimating network statistics using Aggregated Relational Data
. Collecting complete network data is expensive, time-consuming, and often infeasible. Aggregated Relational Data (ARD), which capture information about a social network by asking a respondent questions of the form “How many people with characteris-tic X do you know?” provide a low-cost option when collecting complete network data is not possible. Rather than asking about connections between each pair of individuals directly, ARD collects the number of contacts the respondent knows with a given trait. Despite widespread use and a growing literature on ARD methodology, there is still no systematic understanding of when and why ARD should accurately recover features of the unobserved network. This paper provides such a characterization. Our ﬁrst contribution is to observe that ARD allows for consistent estimation of any model where cross-group link probabilities for a collection of (possibly unobserved) groups identiﬁes the model parameters. This covers a broad range of models, with rich unobserved heterogeneity, such as the Beta-model with node-speciﬁc unobserved eﬀects, the stochastic block model with unobserved community structure, and latent geometric space models with unobserved latent locations. Then, given consistent estimates of network model parameters, it is possible to simulate graphs from the ﬁtted distribution and analyze the distribution of network statistics. Our second contribution is to characterize conditions on a given network statistic, such as the degree of a node or its eigenvector centrality, under which simulated network statistics based on ARD will accurately estimate the network statistics of the unobserved graph.