Dyadic (state-pair) data is completely inappropriate for analyzing multilateral events (such as large alliances and major wars). Scholars, particularly in international relations, often divide the actors in a multilateral event into a series of dyadic relations. Though this practice can dramatically increase the size of data sets, using dyadic data to analyze what are, in reality, k-adic events leads to model misspecification and, inevitably, statistical bias. In short, one cannot recover a k-adic data generating process using dy-adic data. In this paper, I accomplish three tasks. First, I use Monte Carlo simulations to confirm that analyzing k-adic events with dyadic data produces substantial bias. Second, I show that choice-based sampling, as popularized by King and Zeng (2001a, Explaining rare events in international relations. International Organization 55:693–715, and 2001b, Logistic regression in rare events data. Political Analysis 9:137–63), can be used to create feasibly sized k-adic data sets. Finally, I use the study of alliance formation by Gibler and Wolford (2006, Alliances, then democracy: An examination of the relationship between regime type and alliance formation. The Journal of Conflict Resolution 50:1–25) to illustrate how to apply this choice-based sampling solution and explain how to code independent variables in a k-adic context.