Although a growing number of political scientists are conducting randomized experiments, many of them only report the average treatment effects and do not systematically explore the variation in treatment effects across subpopulations. This is unfortunate from a scientific point of view because heterogeneous treatment effects can provide additional substantive insights. This current state of affairs is also problematic from a policy makers' perspective since such studies do not identify subgroups for which treatments are effective. In this paper, we propose a formal two-step framework that first identifies heterogeneous treatment effects from a randomized experiment and then uses this information to derive an optimal policy about which treatment should be given to whom. Our proposed method avoids the risk of false discoveries that are likely in post hoc subgroup analysis routinely conducted in the discipline. We discuss our methodology in the context of get-out-the-vote randomized field experiments and show how the proposed two-step framework can be applied in real-world settings.

Ordinal variables—categorical variables with a defined order to the categories, but without equal spacing between them—are frequently used in social science applications. Although a good deal of research exists on the proper modeling of ordinal response variables, there is not a clear directive as to how to model ordinal treatment variables. The usual approaches found in the literature for using ordinal treatment variables are either to use fully unconstrained, though additive, ordinal group indicators or to use a numeric predictor constrained to be continuous. Generalized additive models are a useful exception to these assumptions. In contrast to the generalized additive modeling approach, we propose the use of a Bayesian shrinkage estimator to model ordinal treatment variables. The estimator we discuss in this paper allows the model to contain both individual group—level indicators and a continuous predictor. In contrast to traditionally used shrinkage models that pull the data toward a common mean, we use a linear model as the basis. Thus, each individual effect can be arbitrary, but the model “shrinks” the estimates toward a linear ordinal framework according to the data. We demonstrate the estimator on two political science examples: the impact of voter identification requirements on turnout and the impact of the frequency of religious service attendance on the liberality of abortion attitudes.

Markov chain Monte Carlo (MCMC) methods have facilitated an explosion of interest in Bayesian methods. MCMC is an incredibly useful and important tool but can face difficulties when used to estimate complex posteriors or models applied to large data sets. In this paper, we show how a recently developed tool in computer science for fitting Bayesian models, variational approximations, can be used to facilitate the application of Bayesian models to political science data. Variational approximations are often much faster than MCMC for fully Bayesian inference and in some instances facilitate the estimation of models that would be otherwise impossible to estimate. As a deterministic posterior approximation method, variational approximations are guaranteed to converge and convergence is easily assessed. But variational approximations do have some limitations, which we detail below. Therefore, variational approximations are best suited to problems when fully Bayesian inference would otherwise be impossible. Through a series of examples, we demonstrate how variational approximations are useful for a variety of political science research. This includes models to describe legislative voting blocs and statistical models for political texts. The code that implements the models in this paper is available in the supplementary material.

Many studies in economics and political science include the concept of ethnic diversity as a key independent variable in empirical studies. To date, however, only single-dimensional measures of ethnic diversity, such as ethnic fractionalization, have been available. In this paper, I define and measure three multidimensional characteristics of social structure—cross-cuttingness, cross-fractionalization, and subgroup fractionalization—and present a new cross-national data set comprised of indices along combinations of five cleavages: race, language, religion, region, and income. After addressing important definitional and measurement issues, I discuss the data and show how their inclusion in economic growth regressions reopens the theoretical debate regarding the influence of ethnic diversity, indicating the potential for these new indices to shed light on the role of ethnic diversity (and social structure more generally) with regards to a number of phenomena of concern to political scientists. The data set is publicly available from the Inter-University Consortium for Political and Social Research data archives and the Institute for Quantitative Social Science Dataverse Network.

Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in recent years. However, methods for statistical inference with network data remain fledgling by comparison. We introduce and evaluate a general model for inference with network data, the Exponential Random Graph Model (ERGM) and several of its recent extensions. The ERGM simultaneously allows both inference on covariates and for arbitrarily complex network structures to be modeled. Our contributions are three-fold: beyond introducing the ERGM and discussing its limitations, we discuss extensions to the model that allow for the analysis of non-binary and longitudinally observed networks and show through applications that network-based inference can improve our understanding of political phenomena.

This paper analyzes the use of ideal point estimates for testing pivot theories of lawmaking such as Krehbiel's (1998, Pivotal politics: A theory of U.S. lawmaking. Chicago, IL: University of Chicago) pivotal politics and Cox and McCubbins's (2005, Setting the Agenda: Responsible Party Government in the U.S. House of Representations. New York: Cambridge University Press) party cartel model. Among the prediction of pivot theories is that all pivotal legislators will vote identically on all successful legislation. Clinton (2007, Lawmaking and roll calls. Journal of Politics 69:455–67) argues that the estimated ideal points of the pivotal legislators are therefore predicted to be statistically indistinguishable and false when estimated from the set of successful final passage roll call votes, which implies that ideal point estimates cannot logically be used to test pivot theories. I show using Monte Carlo simulation that when pivot theories are augmented with probabilistic voting, Clinton's prediction only holds in small samples when voting is near perfect. I furthermore show that the predicted bias is unlikely to be consequential with U.S. Congressional voting data. My analysis suggests that the methodology of estimating ideal points to compute theoretically relevant quantities for empirical tests is not inherently flawed in the case of pivot theories.

Political scientists have increasingly focused on causal processes that operate not solely on mean differences but on other stochastic characteristics of the distribution of a dependent variable. This paper surveys important statistical tools used to assess data in situations where the entire distribution of values is of interest. We first outline three broad conditions under which stochastic process methods are applicable and show that these conditions cover many domains of social inquiry. We discuss a variety of visual and analytical techniques, including distributional analysis, direct parameter estimates of probability density functions, and quantile regression. We illustrate the utility of these statistical tools with an application to budgetary data because strong theoretical expectations at the micro- and macrolevel exist about the distributional characteristics for such data. The expository analysis concentrates on three budget series (total, domestic, and defense outlays) of the U.S. government for 1800–2004.