A Bayesian Multilevel Modeling Approach to Time-Series Cross-Sectional Data

Joseph Bafumi Department of Government, Dartmouth College,6108 Silsby HallHanover, NH 03755 e-mail: joseph.bafumi{at}dartmouth.edu Luke Keele Department of Political Science, Ohio State University,2137 Derby Hall, 154 N Oval Mall, Columbus, OH 43210 e-mail: keele.4{at}polisci.osu.edu David Park Department of Political Science, George Washington University,1922 F Street, N.W. 414C, Washington, DC 20052 e-mail: dkp{at}gwu.edu e-mail: bshor{at}uchicago.edu (corresponding author) The analysis of time-series cross-sectional (TSCS) data hasbecome increasingly popular in political science. Meanwhile,political scientists are also becoming more interested in theuse of multilevel models (MLM). However, little work existsto understand the benefits of multilevel modeling when appliedto TSCS data. We employ Monte Carlo simulations to benchmarkthe performance of a Bayesian multilevel model for TSCS data.We find that the MLM performs as well or better than other commonestimators for such data. Most importantly, the MLM is moregeneral and offers researchers additional advantages. Authors' note: A previous version of this article was presentedat the 2005 Midwest Political Science Meeting. We would liketo thank the following for comments and advice in writing thispaper: Andrew Gelman, Nathaniel Beck, Greg Wawro, Sam Cooke,John Londregan, David Brandt. Any errors are our own.     

Understanding Interaction Models: Improving Empirical Analyses

William Roberts Clark University of Michigan, Center for Political Studies, ISR 4202 Box 1248, 426 Thompson Street, Ann Arbor, MI 48106-1248 Matt Golder Florida State University, Department of Political Science, 531 Bellamy Building, Tallahassee, FL 32306-2230 e-mail: thomas.brambor{at}nyu.edu e-mail: wrclark{at}umich.edu e-mail: matt.golder{at}nyu.edu (corresponding author) Multiplicative interaction models are common in the quantitativepolitical science literature. This is so for good reason. Institutionalarguments frequently imply that the relationship between politicalinputs and outcomes varies depending on the institutional context.Models of strategic interaction typically produce conditionalhypotheses as well. Although conditional hypotheses are ubiquitousin political science and multiplicative interaction models havebeen found to capture their intuition quite well, a survey ofthe top three political science journals from 1998 to 2002 suggeststhat the execution of these models is often flawed and inferentialerrors are common. We believe that considerable progress inour understanding of the political world can occur if scholarsfollow the simple checklist of dos and don'ts for using multiplicativeinteraction models presented in this article. Only 10% of thearticles in our survey followed the checklist.     

Specification Issues in Proximity Models of Candidate Evaluation (with Issue Importance)

Bryce E. Corrigan Department of Political Science, University of Michigan, 5700 Haven Hall, 505 S. State Street, Ann Arbor, MI 48109-1045 e-mail: becorrig{at}umich.edu e-mail: grynaviski{at}uchicago.edu (corresponding author) The use of the proximity model to represent the relationshipbetween citizens' policy attitudes and the positions of candidateson the issues of the day has considerable appeal because itoffers a bridge between theoretical models of political behaviorand empirical work. However, there is little consensus amongapplied researchers about the appropriate representation ofvoter behavior with respect to the measurement of issue distance,candidate location, or whether to allow heterogeneity in theweight that each individual places on particular issues. Eachof these choices suggests a different, and reasonably complicated,nonlinear relationship between voter utility and candidate andvoter issue positions which may have a meaningful influenceon the substantive conclusions drawn by the researcher. Yet,little attention has been given to the best way to representthe proximity model in applied work. The purpose of this paperis to identify which forms of the proximity model work best,with particular consideration given to the identification offunctional forms that are invariant to the choice of scale forthe independent variables.     

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.     

Revisiting the Influence of Campaign Tone on Turnout in Senate Elections

Jason C. Sides Reubin O'D. Askew School of Public Administration and Policy, Florida State University, Tallahassee, FL 32306 e-mail: rjackson{at}garnet.acns.fsu.edu (corresponding author) e-mail: jcs6605{at}garnet.acns.fsu.edu Examining the influence of campaign tone on individual turnoutin the 1990 U.S. Senate elections, this note revisits Kahn andKenney's conclusion that the political profile of citizens (asbased on partisanship, level of political interest, and levelof political expertise) conditions their responsiveness. Implementingan appropriate modeling strategy for making group comparisons,our analyses do not provide statistical support for the conditionaleffects that they highlight. More generally, our results doreinforce Kahn and Kenney's finding that negativity in toneof news coverage mobilizes citizens, but they do not revealsignificant turnout influence for television advertising tone.     

The Logic of the Survey Experiment Reexamined

Paul J. Quirk Department of Political Science, University of British Columbia, 2329 West Mall, Vancouver, British Columbia, Canada, V6T 1Z4 e-mail: quirk{at}politics.ubc.ca e-mail: bjgaines{at}uiuc.edu (corresponding author) e-mail: kuklinsk{at}ad.uiuc.edu Scholars of political behavior increasingly embed experimentaldesigns in opinion surveys by randomly assigning respondentsalternative versions of questionnaire items. Such experimentshave major advantages: they are simple to implement and theydodge some of the difficulties of making inferences from conventionalsurvey data. But survey experiments are no panacea. We identifyproblems of inference associated with typical uses of surveyexperiments in political science and highlight a range of difficulties,some of which have straightforward solutions within the survey-experimentalapproach and some of which can be dealt with only by exercisinggreater caution in interpreting findings and bringing to bearalternative strategies of research.     

Does Mode Matter For Modeling Political Choice? Evidence From the 2005 British Election Study

Harold D. Clarke and Marianne C. Stewart School of Economic, Political and Policy Sciences, University of Texas at Dallas, Richardson, TX 75083 e-mail: hclarke{at}utdallas.edu e-mail: mstewart{at}utdallas.edu Paul Whiteley Department of Government, University of Essex, Colchester, England CO4 3SQ e-mail: whiteley{at}essex.ac.uk e-mail: sanders{at}essex.ac.uk (Corresponding author) Although political scientists have begun to investigate theproperties of Internet surveys, much remains to be learned aboutthe utility of the Internet mode for conducting major surveyresearch projects such as national election studies. This paperaddresses this topic by presenting the results of an extensivesurvey comparison experiment conducted as part of the 2005 BritishElection Study. Analyses show statistically significant, butgenerally small, differences in distributions of key explanatoryvariables in models of turnout and party choice. Estimatingmodel parameters reveals that there are few statistically significantdifferences between coefficients generated using the in-personand Internet data, and the relative explanatory power of rivalmodels is virtually identical for the two types of data. Ingeneral, the in-person and Internet data tell very similar storiesabout what matters for turnout and party preference in Britain.Determining if similar findings obtain in other countries shouldhave high priority on the research agenda for national electionstudies. Authors' note: We thank the U.K. Economics and Social ResearchCouncil (ESRC) and Gary Williams, Senior Science Manager atthe ESRC, for their generous support of, and interest in, thisproject. We also thank the editor and anonymous reviewers forhelpful comments and suggestions.     

Dynamic Models for Dynamic Theories: The Ins and Outs of Lagged Dependent Variables

Nathan J. Kelly Department of Political Science, University of Tennessee, 1001 McClung Tower, Knoxville, TN 37996-0410 e-mail: luke.keele{at}mail.polisci.ohio-state.edu (corresponding author) e-mail: nathan.j.kelly{at}gmail.com A lagged dependent variable in an OLS regression is often usedas a means of capturing dynamic effects in political processesand as a method for ridding the model of autocorrelation. Butrecent work contends that the lagged dependent variable specificationis too problematic for use in most situations. More specifically,if residual autocorrelation is present, the lagged dependentvariable causes the coefficients for explanatory variables tobe biased downward. We use a Monte Carlo analysis to assessempirically how much bias is present when a lagged dependentvariable is used under a wide variety of circumstances. In ouranalysis, we compare the performance of the lagged dependentvariable model to several other time series models. We showthat while the lagged dependent variable is inappropriate insome circumstances, it remains an appropriate model for thedynamic theories often tested by applied analysts. From theanalysis, we develop several practical suggestions on when andhow to use lagged dependent variables on the right-hand sideof a model.     

Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference

Kosuke Imai Department of Politics, Princeton University, Princeton, NJ 08544 e-mail: kimai{at}princeton.edu Gary King Department of Government, Harvard University, 1737 Cambridge Street, Cambridge, MA 02138 Elizabeth A. Stuart Departments of Mental Health and Biostatistics, Johns Hopkins Bloomberg School of Public Health, 624 North Broadway, Room 804, Baltimore, MD 21205 e-mail: estuart{at}jhsph.edu e-mail: king{at}harvard.edu (corresponding author) Although published works rarely include causal estimates frommore than a few model specifications, authors usually choosethe presented estimates from numerous trial runs readers neversee. Given the often large variation in estimates across choicesof control variables, functional forms, and other modeling assumptions,how can researchers ensure that the few estimates presentedare accurate or representative? How do readers know that publicationsare not merely demonstrations that it is possible to find aspecification that fits the author's favorite hypothesis? Andhow do we evaluate or even define statistical properties likeunbiasedness or mean squared error when no unique model or estimatoreven exists? Matching methods, which offer the promise of causalinference with fewer assumptions, constitute one possible wayforward, but crucial results in this fast-growing methodologicalliterature are often grossly misinterpreted. We explain howto avoid these misinterpretations and propose a unified approachthat makes it possible for researchers to preprocess data withmatching (such as with the easy-to-use software we offer) andthen to apply the best parametric techniques they would haveused anyway. This procedure makes parametric models producemore accurate and considerably less model-dependent causal inferences. Authors' note: Our thanks to Dan Carpenter and Jeff Koch fordata; Alberto Abadie, Neal Beck, Sam Cook, Alexis Diamond, BenHansen, Guido Imbens, Olivia Lau, Gabe Lenz, Paul Rosenbaum,Don Rubin, and Jas Sekhon for many helpful comments; and theNational Institutes of Aging (P01 AG17625-01), the NationalInstitute of Mental Health (MH066247), the National ScienceFoundation (SES-0318275, IIS-9874747, SES-0550873), and thePrinceton University Committee on Research in the Humanitiesand Social Sciences for research support. Software to implementthe methods in this paper is available at http://GKing.Harvard.edu/matchitand a replication data file is available as Ho et al. (2006).     

The Introduction of Voter Registration and Its Effect on Turnout

David M. Konisky Department of Political Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room E53-386, Cambridge, MA 02139 e-mail: sda{at}mit.edu e-mail: konisky{at}mit.edu (corresponding author) Studies of voter turnout across states find that those withmore facilitative registration laws have higher turnout rates.Eliminating registration barriers altogether is estimated toraise voter participation rates by up to 10%. This article presentspanel estimates of the effects of introducing registration thatexploits changes in registration laws and turnout within states.New York and Ohio imposed registration requirements on all oftheir counties in 1965 and 1977, respectively. We find thatthe introduction of registration to counties that did not previouslyrequire registration decreased participation over the long termby three to five percentage points. Though significant, thisis lower than estimates of the effects of registration fromcross-sectional studies and suggests that expectations aboutthe effects of registration reforms on turnout may be overstated.     

Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation

Andrew Gelman Department of Statistics and Department of Political Science, Columbia University, New York, NY e-mail: gelman{at}stat.columbia.edu, www.stat.columbia.edu/~gelman/ David K. Park Department of Political Science, Washington University, St. Louis, MO e-mail: dpark{at}artsci.wustl.edu Noah Kaplan Department of Political Science, University of Houston, Houston, TX e-mail: nkaplan{at}uh.edu Logistic regression models have been used in political sciencefor estimating ideal points of legislators and Supreme Courtjustices. These models present estimation and identifiabilitychallenges, such as improper variance estimates, scale and translationinvariance, reflection invariance, and issues with outliers.We address these issues using Bayesian hierarchical modeling,linear transformations, informative regression predictors, andexplicit modeling for outliers. In addition, we explore newways to usefully display inferences and check model fit.     

Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis

John R. Freeman Department of Political Science, University of Minnesota, 267 19th Avenue, Minneapolis, MN 55455 e-mail: pbrandt{at}utdallas.edu (corresponding author) e-mail: freeman{at}polisci.umn.edu Bayesian approaches to the study of politics are increasinglypopular. But Bayesian approaches to modeling multiple time serieshave not been critically evaluated. This is in spite of thepotential value of these models in international relations,political economy, and other fields of our discipline. We reviewrecent developments in Bayesian multi-equation time series modelingin theory testing, forecasting, and policy analysis. Methodsfor constructing Bayesian measures of uncertainty of impulseresponses (Bayesian shape error bands) are explained. A referenceprior for these models that has proven useful in short- andmedium-term forecasting in macroeconomics is described. Oncemodified to incorporate our experience analyzing political dataand our theories, this prior can enhance our ability to forecastover the short and medium terms complex political dynamics likethose exhibited by certain international conflicts. In addition,we explain how contingent Bayesian forecasts can be constructed,contingent Bayesian forecasts that embody policy counterfactuals.The value of these new Bayesian methods is illustrated in areanalysis of the Israeli-Palestinian conflict of the 1980s.     

Shirking in the Contemporary Congress: A Reappraisal

Michael H. Crespin Department of Political Science, Michigan State University, 303 S. Kedzie Hall, East Lansing, MI 48824 e-mail: e-mail: crespinm{at}msu.edu Jeffery A. Jenkins Department of Political Science, Northwestern University, 601 University Place, Evanston, IL 60208 e-mail: e-mail: j-jenkins3{at}northwestern.edu Ryan J. Vander Wielen Department of Political Science, Washington University in St. Louis, Campus Box 1027, One Brookings Drive, St. Louis, MO 63130 e-mail: e-mail: rjvander{at}artsci.wustl.edu This paper replicates the findings that appeared in the article"Severing the Electoral Connection: Shirking in the ContemporaryCongress," published in the American Journal of Political Science(44:316–325), in which Lawrence Rothenberg and MitchellSanders incorporated a new research design and, contrary toall previous studies, found evidence of ideological shirkingin the U.S. House of Representatives. We investigate the robustnessof their results by reestimating their model with Congress-specificfixed effects and find that their results no longer hold.     

A Simple Multivariate Test for Asymmetric Hypotheses

Michael J. Gilligan Department of Politics, New York University, 7th Floor, 726 Broadway, New York, NY 10003 Matt Golder Department of Political Science, Florida State University, 531 Bellamy Building, Tallahassee, FL 32306-2230 e-mail: wrclark{at}umich.edu (corresponding author) e-mail: michael.gilligan{at}nyu.edu e-mail: mgolder{at}fsu.edu In this paper, we argue that claims of necessity and sufficiencyinvolve a type of asymmetric causal claim that is useful inmany social scientific contexts. Contrary to some qualitativeresearchers, we maintain that there is nothing about such asymmetriesthat should lead scholars to depart from standard social sciencepractice. We take as given that deterministic and monocausaltests are inappropriate in the social world and demonstratethat standard multiplicative interaction models are up to thetask of handling asymmetric causal claims in a multivariate,probabilistic manner. We illustrate our argument with examplesfrom the empirical literature linking electoral institutionsand party system size.     

Simulating Models of Issue Voting

Ola Listhaug Department of Sociology and Political Science, Norwegian University of Science and Technology, N-7491 Trondheim, Norway e-mail: olal{at}svt.ntnu.no e-mail: rabinowitz{at}unc.edu (corresponding author) How should one analyze data when the underlying models beingtested are statistically intractable? In this article, we offera simulation approach that involves creating sets of artificialdata with fully known generating models that can be meaningfullycompared to real data. The strategy depends on constructingsimulations that are well matched to the data against whichthey will be compared. Our particular concern is to considerconcurrently how voters place parties on issue scales and howthey evaluate parties based on issues. We reconsider the Lewisand King (2000) analysis of issue voting in Norway. The simulationfindings resolve the ambiguity that Lewis and King report, asvoters appear to assimilate and contrast party placements andto evaluate parties directionally. The simulations also providea strong caveat against the use of individually perceived partyplacements in analyses of issue voting.     

Network Analysis and the Law: Measuring the Legal Importance of Precedents at the U.S. Supreme Court

Timothy R. Johnson Department of Political Science, University of Minnesota, Twin Cities, 1414 Social Sciences Building, 267 19th Ave. South, Minneapolis, MN 55455 e-mail: trj{at}umn.edu James F. Spriggs, II Department of Political Science, Washington University in St. Louis, Campus Box 1063, One Brookings Drive, St Louis, MO 63130 e-mail: jspriggs{at}artsci.wustl.edu Sangick Jeon Department of Political Science, Stanford University, 616 Serra Street, Encina Hall West, Room 100, Stanford, CA 94305-6044 e-mail: sjeon{at}stanford.edu Paul J. Wahlbeck Department of Political Science, George Washington University, 1922 F Street, N.W. Suite 401, Washington, DC 20052 e-mail: wahlbeck{at}gwu.edu e-mail: jhfowler{at}ucsd.edu (corresponding author) We construct the complete network of 26,681 majority opinionswritten by the U.S. Supreme Court and the cases that cite themfrom 1791 to 2005. We describe a method for using the patternsin citations within and across cases to create importance scoresthat identify the most legally relevant precedents in the networkof Supreme Court law at any given point in time. Our measuresare superior to existing network-based alternatives and, forexample, offer information regarding case importance not evidentin simple citation counts. We also demonstrate the validityof our measures by showing that they are strongly correlatedwith the future citation behavior of state courts, the U.S.Courts of Appeals, and the U.S. Supreme Court. In so doing,we show that network analysis is a viable way of measuring howcentral a case is to law at the Court and suggest that it canbe used to measure other legal concepts. Authors' note: We appreciate the suggestions of Randy Calvert,Frank Cross, Pauline Kim, Andrew Martin, Richard Pacelle, JimRogers, Margo Schlanger, Amy Steigerwalt, and participants inthe Workshop on Empirical Research in the Law at WashingtonUniversity in St Louis School of Law. We presented former versionsof this article at the 2006 meeting of the Midwest PoliticalScience Association, Chicago, April 20–23; the 2006 meetingof the Southern Political Science Association, Atlanta, GA,January 5–7; and the 2006 Empirical Legal Studies Conference,Austin, TX, October 27–28.     

Dynamic Tempered Transitions for Exploring Multimodal Posterior Distributions

George Casella Department of Statistics, University of Florida, Griffin-Floyd Hall, P.O. Box 118545, Gainesville, FL 32611 e-mail: casella{at}stat.ufl.edu Multimodal, high-dimension posterior distributions are wellknown to cause mixing problems for standard Markov chain MonteCarlo (MCMC) procedures; unfortunately such functional formsreadily occur in empirical political science. This is a particularlyimportant problem in applied Bayesian work because inferencesare made from finite intervals of the Markov chain path. Toaddress this issue, we develop and apply a new MCMC algorithmbased on tempered transitions of simulated annealing, addinga dynamic element that allows the chain to self-tune its annealingschedule in response to current posterior features. This importantfeature prevents the Markov chain from getting trapped in minormodal areas for long periods of time. The algorithm is appliedto a probabilistic spatial model of voting in which the objectivefunction of interest is the candidate's expected return. Wefirst show that such models can lead to complex target formsand then demonstrate that the dynamic algorithm easily handleseven large problems of this kind.     

Statistical Backwards Induction: A Simple Method for Estimating Recursive Strategic Models

Curtis S. Signorino 303 Harkness Hall, Department of Political Science, University of Rochester, Rochester, NY 14627 e-mail: curt.signorino{at}rochester.edu Robert W. Walker Department of Political Science, Center for Applied Statistics, Washington University in Saint Louis, Campus Box 1063, One Brookings Drive, St. Louis, MO 63130 e-mail: rww{at}wustl.edu e-mail: mbas{at}gov.harvard.edu (corresponding author) We present a simple method for estimating regressions basedon recursive extensive-form games. Our procedure, which canbe implemented in most standard statistical packages, involvessequentially estimating standard logits (or probits) in a manneranalogous to backwards induction. We demonstrate that the techniqueproduces consistent parameter estimates and show how to calculateconsistent standard errors. To illustrate the method, we replicateLeblang's (2003) study of speculative attacks by financial marketsand government responses to these attacks. Authors' note: Our thanks to Kevin Clarke, John Londregan, JeffRitter, Ahmer Tarar, and Kuzey Yilmaz for helpful discussionsconcerning this paper. A previous version was presented at the2002 Political Methodology Summer Meeting.     

The Constrained Instability of Majority Rule: Experiments on the Robustness of the Uncovered Set

Michael S. Lynch Department of Political Science, University of Kansas, 504 Blake Hall, Lawrence, KS 66044 e-mail: mlynch{at}ku.edu Gary J. Miller and Itai Sened Department of Political Science, Washington University in St. Louis, Campus Box 1063, One Brooking Drive, St. Louis, MO 63130 e-mail: gjmiller{at}wustl.edu e-mail: sened{at}wustl.edu (corresponding author) The uncovered set has frequently been proposed as a solutionconcept for majority rule settings. This paper tests this propositionusing a new technique for estimating uncovered sets and a seriesof experiments, including five-player computer-mediated experimentsand 35-player paper-format experiments. The results supportthe theoretic appeal of the uncovered set. Outcomes overwhelminglylie in or near the uncovered set. Furthermore, when preferencesshift, outcomes track the uncovered set. Although outcomes tendto occur within the uncovered set, they are not necessarilystable; majority dominance relationships still produce instability,albeit constrained by the uncovered set. Authors' note: We thank Matthew M. Schneider for research assistance.We thank James Holloway, Tse-Min Lin, Jim Granato, Randall L.Calvert, Rick K. Wilson, faculty and students of the Juan MarchInstitute, and reviewers of Political Analysis for their veryhelpful comments and suggestions.     

Analyzing the 2000 National Election Study

Nancy Burns Center for Political Studies 4246 ISR, University of Michigan, Ann Arbor, Michigan 48106-1248 e-mail: nburns{at}umich.edu (corresponding author) Michael J. Ensley Department of Political Science, 210 Woodburn Hall, Indiana University, Bloomington, IN 47405 e-mail: ensley{at}indiana.edu Donald R. Kinder Center for Political Studies 4258 ISR, University of Michigan, Ann Arbor, Michigan 48106-1248 e-mail: drkinder{at}umich.edu In an earlier report, two of us (Bowers and Ensley, 2003, NationalElection Studies Technical Report, www.umich.edu/nes) provideda general framework for understanding the particular strategyoutlined by Fogarty et al. (in this issue). Fogarty et al.'sstrategy is to make the face-to-face variables more like therandom digit dial (RDD) telephone variables by trimming theends in order to reduce the variance of the face-to-face (FTF)variables. Perhaps some scholars will want the FTF variablesto look like the RDD variables, but that would be a fix fora specific research question. Given the significant differencesin the representativeness of the samples, the processes of surveynonresponse, and the quality and character of the responsesbetween data taken from a National Area Probability sample inperson and data taken from an RDD telephone sample, researchquestions involving comparisons with other years in the 50-yeartime series will require different remedies.