UC Irvine

Physical space and geography have a significant effect on social structures. This dissertation discusses social networks, which describe the relational structure of a group of entities. In addition, I examine nested spatial data hierarchies. I lead the following research, along with collaborators, to examine three different ways in which social networks and other social systems that are embedded in the world are affected by geography and distance. Chapter 2 of the dissertation examines the mechanisms through which geographic variability affects the spread of COVID-19. We simulate large scale social contact networks for the city of San Francisco and simulate the spread of COVID-19 across these networks, using mortality and case data from early in the pandemic. We find that local social cohesion is a hidden risk factor for the spread of COVID-19 in urban environments. For wild-type COVID-19, individual degree (i.e. the number of social contacts one has), was not as important in explaining the spread of the disease as local cohesion (i.e. how connected your neighbors are to each other). This research also highlights the spatial heterogeneities in COVID spread, where many parts of the city did not experience significant COVID related health outcomes until well after the disease began to spread as a result of the clustered nature of the social networks underlying disease spread. In Chapter 3 of the dissertation, we implement and validate a marginal preserving imputation algorithm to impute three-way crosstab data that is embedded in spatial hierarchies. Spatial data hierarchies, such as the U.S. Census or Google S2 Geometry systems, contain nested sets of areal units. Each level of the spatial hierarchy is composed of aggregated areal units at a lower level of geography. For example, census tracts are composed on a set of census blocks. These data are valuable, as they often are collected at large scales and a variety of degrees of spatial resolution. Despite that, for data collection issues or other reasons, some levels of geography may be missing or unavailable at the three-way level. Given a set of known two way marginals at the target level of imputation, and a full set of three-way data at a higher level of geography, we implement a marginal preserving imputation algorithm that maintains all known two-way marginals at the target level, while preserving higher order correlations between cells in the three-way array with data from the higher level of geography. This imputation algorithm uses MCMC and simulated annealing to optimize the state of a three-way array to the distribution observed at the higher level of geography. We impute the three-way arrays for the distribution of population by race, ethnicity, and gender in census tracts across the US, and census blocks across California. We validate the imputed data quality by comparing imputed three-way arrays for census tracts with their observed counterparts. A case study shows that downstream analyses using imputed arrays is not likely to significantly impact conclusions. Chapter 4 of the dissertation develops an extension of the ERGM framework. Exponential Family Random graph Models (ERGM) model edge probabilities in a network as a function of a set of sufficient statistics. When modeling dynamic social networks, most researchers hold the vertex set, or the people/organizations participating in the social network, constant. We integrate Generalized Location Systems (GLS) into the ERGM framework, which allows for the separable parameterization of vertex and edge processes. This new model framework allows us to model endogenous patterns in network participation in addition to the endogenous edge processes that the ERGM framework can currently model. We develop a quorum of model terms to describe the movement of nodes in and out of the social network. These terms allows for the parameterization of effects for covariates, endogenous participation, and other network effects into the vertex dynamics model. Using the Freeman Windsurfer data, we parameterize and fit several models. We use standard model adequacy techniques (one-step model prediction) to validate the quality of these models. This modeling framework provides new opportunities to model complex network systems in which the process of nodes entering and exiting the network is of interest. These networks include voluntary organizations, social movements, and endogenous groups.