Many recent papers in political science and economics use rainfall as a strategy to facilitate causal inference. Rainfall shocks are as-if randomly assigned, but the assignment of rainfall by county is highly correlated across space. Since clustered assignment does not occur within well-defined boundaries, it is challenging to estimate the variance of the effect of rainfall on political outcomes. I propose using randomization inference with historical weather patterns from 73 years as potential randomizations. I replicate the influential work on rainfall and voter turnout in presidential elections in the United States by Gomez, Hansford, and Krause (2007) and compare the estimated average treatment effect (ATE) to a sampling distribution of estimates under the sharp null hypothesis of no effect. The alternate randomizations are random draws from national rainfall patterns on election and would-be election days, which preserve the clustering in treatment assignment and eliminate the need to simulate weather patterns or make assumptions about unit boundaries for clustering. I find that the effect of rainfall on turnout is subject to greater sampling variability than previously estimated using conventional standard errors.

Mixed-methods designs, especially those where cases selected for small-N analysis (SNA) are nested within a large-N analysis (LNA), have become increasingly popular. Yet, since the LNA in this approach assumes that units are independently distributed, such designs are unable to account for spatial dependence, and dependence becomes a threat to inference, rather than an issue for empirical or theoretical investigation. This is unfortunate, since research in political science has recently drawn attention to diffusion and interconnectedness more broadly. In this paper we develop a framework for mixed-methods research with spatially dependent data—a framework we label “geo-nested analysis”—where insights gleaned at each step of the research process set the agenda for the next phase and where case selection for SNA is based on diagnostics of a spatial-econometric analysis. We illustrate our framework using data from a seminal study of homicides in the United States.

How do individuals’ influence in a large social network change? Social scientists have difficulty answering this question because measuring influence requires frequent observations of a population of individuals’ connections to each other, while sampling that social network removes information in a way that can bias inferences. This paper introduces a method to measure influence over time accurately from sampled network data. Ranking individuals by the sum of their connections’ connections—neighbor cumulative indegree centrality—preserves the rank influence ordering that would be achieved in the presence of complete network data, lowering the barrier to measuring influence accurately. The paper then shows how to measure that variable changes each day, making it possible to analyze when and why an individual’s influence in a network changes. This method is demonstrated and validated on 21 Twitter accounts in Bahrain and Egypt from early 2011. The paper then discusses how to use the method in domains such as voter mobilization and marketing.

Parties and social movements play an important role in many theories of political science. Yet, the study of intraparty politics remains underdeveloped as random samples are difficult to conduct among political activists. This paper proposes a novel procedure to sample different parties over time and space by utilizing the advertising option of the social media webpage Facebook. As this method allows for quotas and the collection of large samples at relatively low cost, it becomes possible to improve the representativeness through poststratification and subsample robustness checks. Three examples illustrate these advantages of Facebook sampling: First, a Facebook sample approximated intraparty decisions and the outcome of a leadership contest of the Alternative for Germany. Second, a weighted Facebook sample achieved similar estimates as a representative local leader survey of the Social Democratic Party of Germany. Third, by evaluating subgroups of key demographics for parties with unknown population parameters, two Facebook samples show that the color-coded conflict in Thailand was driven by different concepts of regime type, but not by a left–right divide on economic policy-making. Facebook sampling appears to be the best and cheapest method to conduct time-series cross-sectional studies for political activists.

Methodologists and substantive scholars alike agree that one of process tracing’s foremost contributions to qualitative research is its capacity to adjudicate among competing explanations of a phenomenon. Existing approaches, however, only provide explicit guidance on dealing with mutually exclusive explanations, which are exceedingly rare in social science research. I develop a tripartite solution to this problem. The Relationships among Rivals (RAR) framework (1) introduces a typology of relationships between alternative hypotheses, (2) develops specific guidelines for identifying which relationship is present between two hypotheses, and (3) maps out the varied implications for evidence collection and inference. I then integrate the RAR framework into each of the main process-tracing approaches and demonstrate how it affects the inferential process. Finally, I illustrate the purchase of the RAR framework by reanalyzing a seminal example of process-tracing research: Schultz’s (2001) analysis of the Fashoda Crisis. I show that the same evidence can yield new and sometimes contradictory inferences once scholars approach comparative hypothesis testing with this more nuanced framework.

Bayesian probability holds the potential to serve as an important bridge between qualitative and quantitative methodology. Yet whereas Bayesian statistical techniques have been successfully elaborated for quantitative research, applying Bayesian probability to qualitative research remains an open frontier. This paper advances the burgeoning literature on Bayesian process tracing by drawing on expositions of Bayesian “probability as extended logic” from the physical sciences, where probabilities represent rational degrees of belief in propositions given the inevitably limited information we possess. We provide step-by-step guidelines for explicit Bayesian process tracing, calling attention to technical points that have been overlooked or inadequately addressed, and we illustrate how to apply this approach with the first systematic application to a case study that draws on multiple pieces of detailed evidence. While we caution that efforts to explicitly apply Bayesian learning in qualitative social science will inevitably run up against the difficulty that probabilities cannot be unambiguously specified, we nevertheless envision important roles for explicit Bayesian analysis in pinpointing the locus of contention when scholars disagree on inferences, and in training intuition to follow Bayesian probability more systematically.

This article presents a conceptual clarification of asymmetric hypotheses and a discussion of methodologies available to test them. Despite the existence of a litany of theories that posit asymmetric hypotheses, most empirical studies fail to capture their core insight: boundaries separating zones of data from areas that lack data are substantively interesting. We discuss existing set-theoretic and large-N approaches to the study of asymmetric hypotheses, introduce new ones from the literatures on stochastic frontier and data envelopment analysis, evaluate their relative merits, and give three examples of how asymmetric hypotheses can be studied with this suite of tools.

Political scientists commonly focus on quantities of interest computed from model coefficients rather than on the coefficients themselves. However, the quantities of interest, such as predicted probabilities, first differences, and marginal effects, do not necessarily inherit the small-sample properties of the coefficient estimates. Indeed, unbiased coefficient estimates are neither necessary nor sufficient for unbiased estimates of the quantities of interest. I characterize this transformation-induced bias, calculate an approximation, illustrate its importance with two simulation studies, and discuss its relevance to methodological research.