International relations theorists tend to think in terms of continuous processes. Yet we observe only discrete events, such as wars or alliances, and summarize them in terms of the frequency of occurrence. As such, most empirical analyses in international relations are based on event count variables. Unfortunately, analysts have generally relied on statistical techniques that were designed for continuous data. This mismatch between theory and method has caused bias, inefficiency, and numerous inconsistencies in both theoretical arguments and empirical findings throughout the literature. This article develops a much more powerful approach to modeling and statistical analysis based explicity on estimating continuous processes from observed event counts. To demonstrate this class of models, I present several new statistical techniques developed for and applied to different areas of international relations. These include the influence of international alliances on the outbreak of war, the contagious process of multilateral economic sanctions, and reciprocity in superpower conflict. I also show how one can extract considerably more information from existing data and relate substantive theory to empirical analyses more explicitly with this approach.
This paper builds a stochastic model of the processes that give rise to observed patterns of representation and bias in congressional and state legislative elections. The analysis demonstrates that partisan swing and incumbency voting, concepts from the congressional elections literature, have determinate effects on representation and bias, concepts from the redistricting literature. The model shows precisely how incumbency and increased variability of partisan swing reduce the responsiveness of the electoral system and how partisan swing affects whether the system is biased toward one party or the other. Incumbency, and other causes of unresponsive representation, also reduce the effect of partisan swing on current levels of partisan bias. By relaxing the restrictive portions of the widely applied "uniform partisan swing" assumption, the theoretical analysis leads directly to an empirical model enabling one more reliably to estimate responsiveness and bias from a single year of electoral data. Applying this to data from seven elections in each of six states, the paper demonstrates that redistricting has effects in predicted directions in the short run: partisan gerrymandering biases the system in favor of the party in control and, by freeing up seats held by opposition party incumbents, increases the system’s responsiveness. Bipartisan-controlled redistricting appears to reduce bias somewhat and dramatically to reduce responsiveness. Nonpartisan redistricting processes substantially increase responsiveness but do not have as clear an effect on bias. However, after only two elections, prima facie evidence for redistricting effects evaporate in most states. Finally, across every state and type of redistricting process, responsiveness declined significantly over the course of the decade. This is clear evidence that the phenomenon of "vanishing marginals," recognized first in the U.S. Congress literature, also applies to these different types of state legislative assemblies. It also strongly suggests that redistricting could not account for this pattern.
This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.
This paper discusses the problem of variance specification in models for event count data. Event counts are dependent variables that can take on only nonnegative integer values, such as the number of wars or coups d’etat in a year. I discuss several generalizations of the Poisson regression model, presented in King (1988), to allow for substantively interesting stochastic processes that do not fit into the Poisson framework. Individual models that cope with, and help analyze, heterogeneity, contagion, and negative contagion are each shown to lead to specific statistical models for event count data. In addition, I derive a new generalized event count (GEC) model that enables researchers to extract significant amounts of new information from existing data by estimating features of these unobserved substantive processes. Applications of this model to congressional challenges of presidential vetoes and superpower conflict demonstrate the dramatic advantages of this approach.
This paper presents analytical, Monte Carlo, and empirical evidence on models for event count data. Event counts are dependent variables that measure the number of times some event occurs. Counts of international events are probably the most common, but numerous examples exist in every empirical field of the discipline. The results of the analysis below strongly suggest that the way event counts have been analyzed in hundreds of important political science studies have produced statistically and substantively unreliable results. Misspecification, inefficiency, bias, inconsistency, insufficiency, and other problems result from the unknowing application of two common methods that are without theoretical justification or empirical unity in this type of data. I show that the exponential Poisson regression (EPR) model provides analytically, in large samples, and empirically, in small, finite samples, a far superior model and optimal estimator. I also demonstrate the advantage of this methodology in an application to nineteenth-century party switching in the U.S. Congress. Its use by political scientists is strongly encouraged.
The translation of citizen votes into legislative seats is of central importance in democratic electoral systems. It has been a longstanding concern among scholars in political science and in numerous other disciplines. Through this literature, two fundamental tenets of democratic theory, partisan bias and democratic representation, have often been confused. We develop a general statistical model of the relationship between votes and seats and separate these two important concepts theoretically and empirically. In so doing, we also solve several methodological problems with the study of seats, votes and the cube law. An application to U.S. congressional districts provides estimates of bias and representation for each state and deomonstrates the model’s utility. Results of this application show distinct types of representation coexisting in U.S. states. Although most states have small partisan biases, there are some with a substantial degree of bias.
Three articles, published in the leading journals of three disciplines over the last five decades, have each used the Poisson probability distribution to help describe the frequency with which presidents were able to appoint United States Supreme Court Justices. This work challenges these previous findings with a new model of Court appointments. The analysis demonstrates that the number of appointments a president can expect to make in a given year is a function of existing measurable variables.
The Davis v. Bandemer case focused much attention on the problem of using statistical evidence to demonstrate the existence of political gerrymandering. In this paper, we evaluate the uses and limitations of measures of the seat-votes relationship in the Bandemer case. We outline a statistical method we have developed that can be used to estimate bias and the form of representation in legislative redistricting. We apply this method to Indiana State House and Senate elections for the period 1972 to 1984 and demonstrate a maximum bias 6.2% toward the Republicans in the House and a 2.8% bias in the Senate.
An analysis of panel data reveals the unique importance of early learning to the development of political activism among Americans. A combination of two learning models– the frequently used crystallization model and the rarely analyzed sensitization model– is advanced as most appropriate for understanding political socialization and the development of political activism. The findings contribute to research on elite behavior and on the process of political socialization.
This article identifies a set of serious theoretical mistakes appearing with troublingly high frequency throughout the quantitative political science literature. These mistakes are all based on faulty statistical theory or on erroneous statistical analysis. Through algebraic and interpretive proofs, some of the most commonly made mistakes are explicated and illustrated. The theoretical problem underlying each is highlighted, and suggested solutions are provided throughout. It is argued that closer attention to these problems and solutions will result in more reliable quantitative analyses and more useful theoretical contributions.
This article introduces the theory and approach of structural anthropology and applies it to a problem in American political science. Through this approach, the "bipartisan foreign policy hypothesis" and that "two presidencies hypothesis" are reformulated and reconsidered. Until now participants in the debate over each have only rarely built on, or even cited, the other’s research. An additional problem is that the widespread conventional wisdom in support of the two hypotheses is inconsistent with systematic scholarly analyses. This paper demonstrates that the two hypotheses are drawn from the same underlying structure. Each hypothesis and the theoretical model it implies is conceptually and empirically extended to take into account the differences between congressional leaders and members. Then, historical examples and statistical analyses of House roll call data are used to demonstrate that the hypotheses, while sometimes supported for the congressional members, are far more applicable to leadership decision making. Conclusions suggest that conventional wisdom be revised to take these differences into account.
In the long history of legislative roll call analyses, there continues to exist a particularly troubling problem: There is no satisfactory method for measuring the relative importance or significance of individual roll calls. A measure of roll call significance would be interesting in and of itself, but many have realized that it could also substantially improve empirical research. The consequence of this situation is that hundreds of researchers risk heteroskedastic disturbances (resulting in inefficient estimates and biased standard errors and test statistics), are unable to appropriately choose the roll calls most suited to their theory (resulting in analyses that may not correctly test their theory), and often use methods that create more problems than they solve (resulting in selection bias, unrealistic weighting schemes, or relatively subjective measures). This article introduces a new method designed to meet these problems. Based on an application of Box-Tiao intervention analysis, the method extracts from observed voting participation scores the "revealed preferences" of legislators as a measure of roll call significance. Applying this method to roll calls from the U.S. Senate demonstrates the success of the method and suggests its utility in applied research.