Regression of network data: dealing with dependence - Marrs, Frank W., author; Fosdick, Bailey K., advisor; Breidt, F. Jay, committee member; Zhou, Wen, committee member; Wilson, James B., committee member (Colorado State University. Libraries, 2019)
Network data, which consist of measured relations between pairs of actors, characterize some of the most pressing problems of our time, from environmental treaty legislation to human migration flows. A canonical problem in analyzing network data is to estimate the effects of exogenous covariates on a response that forms a network. Unlike typical regression scenarios, network data often naturally engender excess statistical dependence -- beyond that represented by covariates -- due to relations that share an actor. For analyzing bipartite network data observed over time, we propose a new model that accounts for excess network dependence directly, as this dependence is of scientific interest. In an example of international state interactions, we are able to infer the networks of influence among the states, such as which states' military actions are likely to incite other states' military actions. In the remainder of the dissertation, we focus on situations where inference on effects of exogenous covariates on the network is the primary goal of the analysis, and thus, the excess network dependence is a nuisance effect. In this setting, we leverage an exchangeability assumption to propose novel parsimonious estimators of regression coefficients for both binary and continuous network data, and new estimators for coefficient standard errors for continuous network data. The exchangeability assumption we rely upon is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression of network data. Although the estimators we propose are aligned with many network models in the literature, our estimators are derived from the assumption of exchangeability rather than proposing a particular parametric model for representing excess network dependence in the data.
Keywords: bipartite network; maximum likelihood; temporal network; dependent data; autoregression; regression