Interpersonal interaction over short time scales is frequently understood in terms of actions, which can be thought of as discrete events in which one individual emits a behavior directed at one or more other entities in his or her environment (possibly including him or herself). Here, we introduce a highly flexible framework for modeling actions within social settings, which permits likelihood-based inference for behavioral mechanisms with complex dependence. The utility of the framework is illustrated via an application to dynamic modeling of responder radio communications during the early hours of the World Trade Center disaster.

Exponential family models for random graphs (ERGs, also known as p∗ models) are an increasingly popular tool for the analysis of social networks. ERGs allow for the parameterization of complex dependence among edges within a likelihood-based framework, and are often used to model local influences on global structure. This paper introduces a family of cycle statistics, which allow for the modeling of long-range dependence within ERGs. These statistics are shown to arise from a family of partial conditional dependence assumptions based on an extended form of reciprocity, here called reciprocal path dependence. Algorithms for computing cycle statistic changescores and the cycle census are provided, as are analytical expressions for the first and approximate second moments of the cycle census under a Bernoulli null model. An illustrative application of ERG modeling using cycle statistics is also provided.

Although it is well-known that there is a relationship between socio-physical dis- tance and edge probability in interpersonal networks, the predictive power of such distances for total network structure has not been established. Here, it is shown that upper bounds on the marginal edge probabilities for farflung dyads can be used to place a lower bound on the predictive power of distance, and one such bound is de- rived. Application of this bound to the special case of uniformly placed vertices on the plane suggests that only modest constraints are required for distance effects to dominate at large physical scales.

Statistical network models have been shown to be of particular relevance for understanding various phenomena; one of the richest areas for research is understanding the spread of sexually transmitted infections such as HIV. With the advent of new epidemiological protocols designed to prevent spread and foundational work analyzing the impact of network structure on diffusion of contagion, network analysis is poised to tackle various questions relating to the spread of HIV amongst vulnerable populations. Chapter 1 presents a methodological development integrating Goffman's conception of stigma within the exponential random graph modeling framework. Various properties are explored under simulation and as a test case, this is used to quantify the level of behavioral stigma in an adolescent friendship network based on gender. Chapter 2 utilizes the development from Chapter 1 to quantify the level of HIV stigma in informal social networks of young black men who have sex with men (from a structural perspective). This is then linked to a framework for understanding the consequences of network perturbations in the resultant network structure (i.e. the impacts of "coming out HIV positive" on the network) and its subsequent effects on HIV diffusion. Chapter 3 focuses on issues of data collection in informal social networks, specifically resolving conflicting self-reports on relationships within the context of informant accuracy and network inference. The tools developed in this dissertation are far-reaching and can provide insight to the study of populations at risk or other social environments beyond HIV.

This dissertation investigates coordination as a key component of social systems, from a network of international environmental governance to a localized response to disaster. Chapter 2 is a study of international environmental agreement (IEA) co-ratification. I focus specifically on mixing effects and how these demonstrate a shift in the global configuration of cooperative behavior within this context. Chapter 3 dives deeper into this network, looking more closely at the structural factors influencing ratification of IEAs, including factors at the agreement level. The goal of this chapter was to better understand the formation of new ratification ties over time, while making several methodological contributions as well. Finally, Chapter 4 is a study of dynamic communication patterns across 17 localized first responder networks in the midst of a disaster. We utilized a recently developed tool for relational event model simulation to study the resilience of these networks as they reorganized in the face of varied disruption. This dissertation pushes for the view of social systems as interconnected and specifically demonstrates the advantages of studying coordination from this perspective. I hope it spurs future research on these topics, especially in the realm of environmental degradation as it is ever more often encompassing both regulation and disaster response.

Networks (graphs) are broadly used to represent relations between entities in a wide range of scientific fields. Exponential-family random graph models (ERGMs) provide a highly general way of specifying distributions on graphs, allowing the complex dependence structure of edges in a network to be specified in terms of local structural properties. This thesis addresses problems related to three lines of inquiry for ERGMs: faster Bayesian inference algorithms; comparison of newly proposed and traditional model selection techniques; and methodological innovation for modeling ensembles of networks.

In Chapter 2 of this dissertation, we present a highly parallel algorithm that enables fast Bayesian inference on ERGMs. The impetus for this work comes from the facts that conducting Bayesian inference for ERGMs is challenging because of the intractability of both the likelihood and posterior normalizing factor and auxiliary-variable based Markov Chain Monte Carlo (MCMC) methods for this problem are asymptotically exact but computationally demanding. We propose a kernel-based approximate Bayesian computation algorithm for fitting ERGMs, which is easily parallelizable. Through empirical comparisons against the state-of-the-art approximate exchange algorithm, we show that the proposed algorithm yields comparable accuracy to the state-of-the-art MCMC approach, the approximate exchange algorithm (Caimo and Friel, 2011), while cutting the wallclock runtime by half with 5 cores, and by 80\% with 30 cores.

In Chapter 3 of this dissertation, we carry out simulation studies to compare newly proposed and traditional model selection techniques. This work is driven by the importance of understanding the strengths and weaknesses of those model selection techniques for ERGMs that are currently available, including Akaike information criterion (Akaike, 1973), Bayesian information criterion (Schwarz, 1978), Held-Out Predictive Evaluation (HOPE) (Yin et al., 2019), Bayes factors (Raftery, 1995) and graphical goodness of fit (Hunter et al., 2008). In particular, we focus on the first three techniques, as the calculation of Bayes factor for ERGMs relies on reversible jump Markov chain Monte Carlo algorithm extension of the approximate exchange algorithm (Caimo and Friel, 2013), which is hard to implement and tune; the graphical goodness of fit is more suitable for checking whether a model is adequate rather than comparing competing models. The simulation studies are carried out under two scenarios, closed-M (under which the true model is among the set of candidate models) and open-M (under which the true model is not among the set of candidate models), and we evaluate the performance of model selection techniques from various aspects covering the model selection accuracy, predictive deviance and prediction accuracy of edge variables.

In Chapter 4 of this dissertation, we propose a novel methodology that can be used for modeling the generative processes of ensembles of networks. The motivation of this work is that ensembles of networks arise in many scientific fields, but there are few statistical tools for inferring their generative processes, particularly in the presence of both dyadic dependence and cross-graph heterogeneity. To fill in this gap, we propose characterizing network ensembles via finite mixtures of exponential family random graph models, a framework for parametric statistical modeling of graphs that has been successful in explicitly modeling the complex stochastic processes that govern the structure of edges in a network. Our proposed methodology can also be used for applications such as model-based clustering of ensembles of networks and density estimation for complex graph distributions. We develop a Metropolis-within-Gibbs algorithm to conduct fully Bayesian inference and adapt a version of deviance information criterion for missing data models to choose the number of latent heterogeneous generative mechanisms. Simulation studies show that the proposed procedure can recover the true number of latent heterogeneous generative processes and corresponding parameters. We demonstrate the utility of the proposed approach using an ensemble of political co-voting networks among U.S. Senators and an ensemble of advice-seeking networks among school teachers.