Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?

Political scientists presenting binary dependent variable (BDV) models often hypothesize that variables interact to influence the probability of an event, Pr( Y ). The current typical approach to testing such hypotheses is (1) estimate a logit or probit model with a product term, (2) test the hypothesis by determining whether the coefficient for this term is statistically significant, and (3) characterize the nature of any interaction detected by describing how the estimated effect of one variable on Pr( Y ) varies with the value of another. This approach makes a statistically significant product term necessary to support the interaction hypothesis. We show that a statistically significant product term is neither necessary nor sufficient for variables to interact meaningfully in influencing Pr( Y ). Indeed, even when a logit or probit model contains no product term, the effect of one variable on Pr( Y ) may be strongly related to the value of another. We present a strategy for testing for interaction in a BDV model, including guidance on when to include a product term.     

The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models

We present a visual method for assessing the predictive power of models with binary outcomes. This technique allows the analyst to evaluate model fit based upon the models’ ability to consistently match high‐probability predictions to actual occurrences of the event of interest, and low‐probability predictions to nonoccurrences of the event of interest. Unlike existing methods for assessing predictive power for logit and probit models such as Percent Correctly Predicted statistics, Brier scores, and the ROC plot, our “separation plot” has the advantage of producing a visual display that is informative and easy to explain to a general audience, while also remaining insensitive to the often arbitrary probability thresholds that are used to distinguish between predicted events and nonevents. We demonstrate the effectiveness of this technique in building predictive models in a number of different areas of political research.     

A multinominal logit analysis of the influence of policy variables and board experience on FOMC voting behavior

Previous studies have used probit or logit models to analyze two states of monetary policy (tighter or looser). In this paper we employ multinominal logit to permit Federal Reserve monetary policy to assume one of three alternative states (tighter, looser, or no change) as a function of three independent economic variables (unemployment, real growth, and inflation) and the amount of experience of the Board of Governors. The results indicate that the Federal Reserve reacted differently under Burns, Miller and Volcker and between Volcker's two operating procedures in the formulation of monetary policy.     

Modeling the interaction of parties, activists and voters: Why is the political center so empty?

Abstract.  The formal stochastic model of voting should be the theoretical benchmark against which empirical models can be gauged. A standard result in the formal model is the 'mean voter theorem' stating that parties converge to the electoral center. Empirical analysis based on the vote-maximizing premise, however, invalidates this convergence result. We consider both empirical and formal models that incorporate exogeneous valence terms for the parties. Valence can be regarded as an electorally perceived attribute of each party leader that is independent of the policy position of the party. We show that the mean voter theorem is valid for empirical multinomial logit and probit models of a number of elections in the Netherlands and Britain. To account for the non-centrist policy positions of parties, we consider a more general formal model where valence is also affected by the behavior of party activists. The results suggest that non-convergent policy choice by party leaders can be understood as rational, vote-maximizing calculation by leaders in response to electoral and activist motivations.     

Mass Administrative Reorganization,Media Attention,and the Paradox of Information

How does media attention influence government decisions about whether to terminate independent administrative agencies? The authors argue that an agency's salience with partisan audiences has a direct effect, but a high media profile can disrupt normal government monitoring processes and obfuscate termination decisions. This argument is evaluated in the context of a recent mass administrative reorganization by the British coalition government using probit and heteroscedastic probit regression models. The evidence suggests that termination is less likely for agencies salient in newspapers popular with the government's core supporters but not those read by its minority coalition partner. We also find that agencies with greater overall newspaper salience as well as younger agencies have a higher error variance.     

Causal Complexity and the Study of Politics

Theories that posit complex causation, or multiple causal paths,pervade the study of politics but have yet to find accuratestatistical expression. To remedy this situation I derive neweconometric procedures, Boolean probit and logit, based on thelogic of complexity. The solution provides an answer to a puzzlein the rational deterrence literature: the divergence betweentheory and case-study findings, on the one hand, and the findingsof quantitative studies, on the other, on the issue of the roleof capabilities and willingness in the initiation of disputes.It also makes the case that different methodological traditions,rather than settling into "separate but equal" status, can insteadinform and enrich one another.     

When Pivotal Politics Meets Partisan Politics

Recent years have witnessed many efforts to understand legislative productivity and gridlock. However, despite theoretical and empirical contributions to how preferences and institutions shape political gridlock's level (e.g., Krehbiel 1996, 1998 ) and empirical evidence about how parties may affect political gridlock (e.g., Binder 1999 ; Coleman 1999 ), we lack a comprehensive perspective theoretically and empirically examining preferences, institutions, and parties. We overcome this deficiency by modeling conditions for gridlock as a function of preferences and institutions—incorporating bicameralism and presidential influence—and of parties. By generating equilibrium gridlock intervals for empirical testing using Poole's (1998) common space scores, and showing that gridlock intervals associated with models in which parties have no effect or an agenda-setting role do not explain policy gridlock but that those linked to models with party-unity effects and strong presidential leadership do, we demonstrate the importance of accounting for party and leadership roles in explaining legislative choices.     

Foreign Aid Shocks as a Cause of Violent Armed Conflict

In this study we resolve part of the confusion over how foreign aid affects armed conflict. We argue that aid shocks—severe decreases in aid revenues—inadvertently shift the domestic balance of power and potentially induce violence. During aid shocks, potential rebels gain bargaining strength vis‐à‐vis the government. To appease the rebels, the government must promise future resource transfers, but the government has no incentive to continue its promised transfers if the aid shock proves to be temporary. With the government unable to credibly commit to future resource transfers, violence breaks out. Using AidData's comprehensive dataset of bilateral and multilateral aid from 1981 to 2005, we evaluate the effects of foreign aid on violent armed conflict. In addition to rare‐event logit analysis, we employ matching methods to account for the possibility that aid donors anticipate conflict. The results show that negative aid shocks significantly increase the probability of armed conflict onset.     

Strategic Interaction and Candidate Competition in U.S. House Elections: Empirical Applications of Probit and Strategic Probit Models

In recent work, Signorino (American Political Science Review93:279–297, 1999; International Interactions 28:93–115,2002) has sought to test statistical models derived from extensive-formgames in the context of international relations research focusingon conflict and interstate bargaining. When two or more actorsinteract with one another under conditions of uncertainty, Signorinodemonstrates that it is necessary to incorporate such strategicinteraction into the underlying model to avoid potential threatsto statistical inference. Outside the realm of internationalrelations research, however, there have been limited applicationsof Signorino's strategic probit model in understanding strategicinteraction. In this article, I present an empirical comparisonof probit and strategic probit models in the context of candidatecompetition in House elections during the 1990s. I show thatincumbent spending deters challenger entry and factors suchas minority party affiliation and redistricting significantlyaffect incumbent career decisions, findings that run counterto those reported in the nonstrategic model. Overall, the resultsillustrate that failing to account for strategic interactioncan lead to biased and inaccurate estimates related to challengerand incumbent entry decisions.     

Assessing the validity of the logit method for ecological inference

Abstract. The logit method for ecological inference, presented by Thomsen in 1987, estimates individual level voting behaviour from aggregate election results. Making comparisons with survey results, this article tests the validity of ecological estimates of voter mobility between parties at three Danish, five Swedish and three Finnish election periods. For all three countries, the ecological estimates are rather close to survey results, but in the cases of Denmark and Sweden the validity of the ecological estimates seems lower than the validity of the survey results. However, for both countries, the differences between the ecological estimates and the survey results show a stable pattern which can be interpreted within the framework of a general logit theory.     

Overcoming the Barriers to Cooperation: Intergovernmental Service Agreements

Interlocal cooperation through service‐sharing agreements has a long history, but its use has increased in popularity during the last 20 years. The decisions of local government units to collaborate through intergovernmental service agreements are best understood as a two‐stage process. The first stage, in which communities decide whether to consider interlocal cooperation, involves the nature of the immediate problem faced plus specific demands for performance and efficiency gains that can result from service cooperation. In the second stage, communities confront a question of institutional supply, and hence must overcome inherent bargaining and collective action issues in order to forge interlocal agreements. Heckman probit estimates of such complex relationships using data drawn from a 2003 ICMA survey suggest strong support for this model. The authors conclude by discussing the role of network relationships among local actors for reducing transaction costs and facilitating intergovernmental collaboration.     

Mixed Logit Models for Multiparty Elections

Mixed logit (MXL) is a general discrete choice model thus farunexamined in the study of multicandidate and multiparty elections.Mixed logit assumes that the unobserved portions of utilityare a mixture of an IID extreme value term and another multivariatedistribution selected by the researcher. This general specificationallows MXL to avoid imposing the independence of irrelevantalternatives (IIA) property on the choice probabilities. Further,MXL is a flexible tool for examining heterogeneity in voterbehavior through random-coefficients specifications. MXL isa more general discrete choice model than multinomial probit(MNP) in several respects, and can be applied to a wider varietyof questions about voting behavior than MNP. An empirical exampleusing data from the 1987 British General Election demonstratesthe utility of MXL in the study of multicandidate and multipartyelections.     

The dynamic properties of individual-level party identification in the United States

Central to traditionalist and revisionist perspectives of individual-level party identification is a debate about the stability of party identification. We revisit the debate about the dynamic properties and processes underlying party identification. We present a conceptual framework that defines heterogeneity and state dependence as endpoints of a continuum underlying partisan stability, which is important in understanding an individual’s capacity for updating partisanship. Using panel data from the 1992-1996 National Election Study, we estimate dynamic, random effects multinomial logit models of party identification that distinguish between heterogeneity and “true state dependence.” In accord with traditionalist perspectives, our evidence suggests that in general, minimal state dependence underlies party identification; party identification is strongly stationary. However, we find that age enhances the magnitude of state dependence, which provides some support for revisionist theories. Overall, our work showcases how explaining individual-level dynamics expands our knowledge of partisan stability.     

In Defense of Comparative Statics: Specifying Empirical Tests of Models of Strategic Interaction

Christopher Zorn Department of Political Science, University of South Carolina, Columbia, SC 29208 e-mail: zorn{at}sc.edu e-mail: ccarrub{at}emory.edu (corresponding author) Beginning in 1999, Curtis Signorino challenged the use of traditionallogits and probits analysis for testing discrete-choice, strategicmodels. Signorino argues that the complex parametric relationshipsgenerated by even the simplest strategic models can lead towildly inaccurate inferences if one applies these traditionalapproaches. In their stead, Signorino proposes generating stochasticformal models, from which one can directly derive a maximumlikelihood estimator. We propose a simpler, alternative methodologyfor theoretically and empirically accounting for strategic behavior.In particular, we propose carefully and correctly deriving one'scomparative statics from one's formal model, whether it is stochasticor deterministic does not particularly matter, and using standardlogit or probit estimation techniques to test the predictions.We demonstrate that this approach performs almost identicallyto Signorino's more complex suggestion. Authors' note: We would like to thank Randy Calvert, Mark Hallerberg,Andrew Martin, Eric Reinhardt, Chris Stanton, and Craig Voldenfor their valuable feedback on this project. All remaining errorsare our own. Replication materials are available at the PoliticalAnalysis Web site.     

Confronting Political--Economic Theories of Voting with Evidence

This paper illustrates one strategy for testing a theory ofeconomic influences on voting. We use a competitive equilibriummodel of the economy to determine the impact of an individual'seconomic position on his or her economic interests and, ultimately,political interests. We then test whether this impact is observedin voting behavior, addressing the resulting specification andestimation problems in the context of U.S. presidential electiondata. Our empirical results suggest that, despite these formidableproblems, we can usefully connect political—economic modelsand discrete-choice (probit) models of voting.     

Public Opinion Polls,Voter Turnout,and Welfare: An Experimental Study

We experimentally study the impact of public opinion poll releases on voter turnout and welfare in a participation game. We find higher overall turnout rates when polls inform the electorate about the levels of support for the candidates than when polls are prohibited. Distinguishing between allied and floating voters, our data show that this increase in turnout is entirely due to floating voters. When polls indicate equal levels of support for the candidates, turnout is high and welfare is low (compared to the situation without polls). In contrast, when polls reveal more unequal levels of support, turnout is lower with than without this information, while the effect of polls on welfare is nonnegative. Finally, many of our results are well predicted by quantal response (logit) equilibrium.     

Under Which Conditions Do Parties Attract Voters’ Reactions to Issues? Party-Varying Issue Voting in German Elections 1987–2009

Are voters’ choices influenced by parties’ position-taking and communication efforts on issues during a campaign? And if so, do voters’ reactions to issues differ across parties? This article outlines a research design for the statistical identification of party-varying issue reactions within the established paradigm of the Spatial Theory of Voting. Using a special feature of conditional logit and probit models – i.e. the estimation of alternative-specific coefficients instead of fixed ‘generic’ issue distance effects – it is possible to detect asymmetrically attached issue saliencies at the level of the voters, and hence at the demand-side of politics. This strategy opens a new way to systematically combine insights obtained by saliency approaches with the Spatial Theory of Voting. An application to the German parliamentary elections from 1987 to 2009 demonstrates that it is predominantly parties taking polar positions – and, more specifically, niche parties taking polar positions – that induce such asymmetric issue voting.     

Interest group–party linkage in the twenty‐first century: Evidence from Denmark,the Netherlands and the United Kingdom

This article systematically investigates interest group–party interactions in the Netherlands, Denmark and the United Kingdom based on cross‐national surveys with responses from 1,225 interest groups. The findings show that interest groups and parties still interact in the beginning of the twenty‐first century, but that the vast majority of their interaction involves a low degree of institutionalisation. Using fractional logit analysis, it is demonstrated that the strength of interest group–party linkage is primarily affected by systematic differences in state–society structures and organisational group characteristics. Moreover, differences are found in what conditions different types of interaction. Whereas historical legacies and partisan origin influence an interest group's structural party links, group resources make interactions of a less institutionalised, ad hoc nature more likely.     

Who “Wins”? Determining the Party of the Prime Minister

The prime ministership is the preeminent political post in parliamentary democracies. Yet few studies examine PM party choice, perhaps under the assumption that the choice is a simple function of party size. In this article, we argue that key strategic actors and the context in which government negotiations take place can play a critical role in PM party choice. We test our hypotheses using a mixed logit with random coefficients on an original data set comprising PM selection opportunities in 28 European countries. Our methodological approach allows us to incorporate qualitative concerns about heterogeneity and causal complexity into our analysis. Contrary to conventional wisdom, we find that the largest party is often disadvantaged when it comes to PM party choice, that some presidents play an influential role in choosing the PM, and that the value of being the incumbent depends on one’s performance in office and how the previous government ended.