The promise of digital trace data for sociological research is still partly unfulfilled due to the complexities of trace data. Such data are behavioral byproducts rather than collected to directly answer sociological questions. In this dissertation, I address two fundamental challenges to working with networked digital trace data: the opacity problem and the demographic prediction problem. The opacity problem presents a fundamental and unrecognized limitation to our ability to understand the dynamics of social contagion using behavioral data. I examine the problems it creates and demonstrate that careful statistical methodology can reduce error and provide meaningful insight into contagion dynamics. Then, I address the well-known demographic prediction problem in the context of networks. Network-correlated errors present a formidable challenge for our ability to use any method with measurement error (such as predictions or recall of alter group) to quantify intergroup contact. I formalize the problem and present a solution, employing the methodology I develop to derive estimates of interaction within and between groups on Twitter. These estimates are compared to the General Social Survey, indicating that homophily by race and gender are somewhat less than is present in offline discussion networks. Finally, I employ evolutionary game theory to examine conditions under which homophily can facilitate or inhibit cooperation in pairwise games.