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Respondent-driven sampling (RDS) is a network sampling methodology used worldwide to sample key populations at high risk for HIV/AIDS who often practice stigmatized/illegal behaviors and are not typically reachable by conventional sampling techniques. In RDS, study participants recruit their peers to enroll, resulting in a sampling mechanism that is unknown to researchers. Current estimators for RDS data require many assumptions about the sampling process, including that recruiters choose people from their network uniformly at random to participate in the study. However, this is likely not true in practice. We believe that people recruit based on observable covariates, such as age, frequency of interaction, geography, socioeconomic status, or social capital.To model preferential recruitment, I develop a sequential two-sided rational-choice framework, referred to as the RCPR model. At each wave of recruitment, each recruiter has a utility for selecting each peer, and symmetrically each peer has a utility for being recruited by each recruiter. Each person also has utilities for selecting themself (not recruiting or not participating). People in the network behave in a way that maximizes their utility given the constraints of the network and the restrictions on recruitment. Although a person's utility is not observed, it can be modeled as a linear combination of observable nodal or dyadic covariates plus unobserved pair-specific heterogeneities. This framework allows generative probabilistic network models to be created for the RDS recruitment process. The models can incorporate observable characteristics of the population and have interpretable parameters. It greatly increases the sophistication of the modeling of the RDS sampling mechanism. Inference can be made about the preference coefficients by maximizing the likelihood of the observed recruitment chain given the observed covariates. As the likelihood is computationally intractable, I develop a Bayesian framework where inference is made feasible by approximating the posterior distribution of the preference coefficients via a Markov chain Monte Carlo algorithm. Each update step samples new values of the preference coefficients and utilities via Metropolis-Hastings, subject to constraints. New prevalence estimates can be calculated be generating many recruitment chains from the population using the RCPR coefficients, then directly obtaining the first-order and second-order inclusion probabilities. This framework allows the incorporation of covariates we think effect recruitment into the sample weights.

Networks have been widely used to represent and analyze a system of connected elements. Online social media networks, as a result of the expansion of the Internet and increased need of communication, have become an increasingly important part of people's lives. This thesis focuses on the statistical analysis of network data motivated by problems in online social media. It discusses problems arising from both explicit network data and implicit network data. Explicit network data are data where network structures are observable, implicit network data are those that do not have a network structure but occur under the influence of an underlying network. For the explicit network data analysis, we develop a novel method of recovering a fundamental characteristic -- network degree distributions -- under sampling. We formulate the problem of estimating degree distribution as an inverse problem. We show that this problem is ill-conditioned for many sampling methods in practice, and accordingly propose a constrained, penalized weighted least-squares approach to solve this problem. We demonstrate the ability of our method to accurately reconstruct the degree distributions from simulated network data and real world social network data. We also propose practical usage of the estimates relevant to marketing and advertising. For the implicit network data analysis, we look at review data from the popular review websites. Motivated by articles from the popular press and the research community which publicized that the average rating for top review sites is above 4 out of 5 stars, we study the phenomena of review rating trends and convergence using restaurant review data from TripAdvisor. We analyze the trend on different levels -- a rough analysis of the characteristics of the ratings, and a subtler statistical modeling with ordinal logistic regressions. Taking into account the implicit network underlying the review data, we suggest the upward trend observed in restaurant review ratings may be explained by social influence on an individual's perception of qualities. We use the intensity of review postings as an indicator of how popular a restaurant is and to test to what extent the increase in review intensity explains increases in average rating. After that, we consider a more nuanced approach to the joint modeling of ratings and review intensity which would allow for interaction between the two, rather than intensity serving only as an explanatory variable to ratings. Specifically, a state-space model is used to test the interaction between review intensity and review ratings.