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.     

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.     

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.     

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.     

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.     

Splitting the Difference? Causal Inference and Theories of Split-party Delegations

Matthew J. Butler Department of Economics, 549 Evans Hall, University of California, Berkeley, CA 94720 e-mail: butler{at}econ.berkeley.edu e-mail: daniel_butler{at}stanford.edu (corresponding author) We provide an introduction to the regression discontinuity design(RDD) and use the technique to evaluate models of sequentialSenate elections predicting that the winning party for one Senateseat will receive fewer votes in the next election for the otherseat. Using data on U.S. Senate elections from 1946 to 2004,we find strong evidence that the outcomes of the elections forthe two Senate seats are independent.     

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.     

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.     

Event Dependence and Heterogeneity in Duration Models: The Conditional Frailty Model

Suzanna De Boef and Kyle A. Joyce Department of Political Science, 219 Pond Laboratory, The Pennsylvania State University, University Park, PA 16802 e-mail: sdeboef{at}psu.edu e-mail: kjoyce{at}psu.edu e-mail: jboxstef+{at}osu.edu (corresponding author) We introduce the conditional frailty model, an event historymodel that separates and accounts for both event dependenceand heterogeneity in repeated events processes. Event dependenceand heterogeneity create within-subject correlation in eventtimes thereby violating the assumptions of standard event historymodels. Simulations show the advantage of the conditional frailtymodel. Specifically they demonstrate the model's ability todisentangle the sources of within-subject correlation as wellas the gains in both efficiency and bias of the model when comparedto the widely used alternatives, which often produce conflictingconclusions. Two substantive political science problems illustratethe usefulness and interpretation of the model: state policyadoption and terrorist attacks. Authors' note: Three anonymous reviewers gave valuable advice.Replication materials and an online appendix are available onthe Political Analysis Web site. Any errors are our own responsibility.     

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.     

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.     

Complex Causal Relations and Case Study Methods: The Example of Path Dependence

Colin Elman Department of Political Science, Arizona State University, Box 873902, Tempe, AZ 85287-3902 e-mail: bennetta{at}georgetown.edu e-mail: colin.elman{at}asu.edu (corresponding author) This article discusses the application of qualitative methodsin analyzing causal complexity. In particular, the essay reviewshow process tracing and systematic case comparisons can addresspath-dependent explanations. The article unpacks the conceptof path dependence and its component elements of causal possibility,contingency, closure of alternatives, and constraints to thecurrent path. The article then reviews four strengths that casestudies bring to the study of path dependence: offering a detailedand holistic analysis of sequences in historical cases, beingsuitable for the study of rare events, facilitating the searchfor omitted variables that might lie behind contingent events,and allowing for the study of interaction effects within oneor a few cases.     

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.     

Issue Attitudes and Survey Continuity across Interview Mode in the 2000 NES

Nathan J. Kelly Department of Political Science, University at Buffalo, The State University of New York, Buffalo, NY 14260-4120 e-mail: nkelly{at}buffalo.edu H. Whitt Kilburn Department of Political Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3265 e-mail: wkilburn{at}email.unc.edu Can researchers draw consistent inferences about the U.S. public'sissue attitudes when studying survey results from both the in-personand telephone interview modes of the 2000 National ElectionStudies (NES) survey? We address this question through an analysiscontrasting the distribution of issue attitudes across modesin the dual sample design of the 2000 NES. We find clear differencesacross mode even when applying a method devised by the NES toimprove comparability by recoding issue attitude scales fromthe in-person mode. We present an alternative method of recodingthese scales, which substantially improves comparability betweenmodes. Through an analysis of the covariance structure of theissues and simple models of vote choice, we discuss the implicationsof the results for the study of issue attitudes in the 2000NES.     

Parties in Elections, Parties in Government, and Partisan Bias

Adam Meirowitz Department of Politics, Princeton University, Princeton, NJ 08544 e-mail: ameirowi{at}princeton.edu Thomas Romer Department of Politics and Woodrow Wilson School of Public and International Affairs, Princeton University, Princeton, NJ 08544 e-mail: romer{at}princeton.edu Political parties are active when citizens choose among candidatesin elections and when winning candidates choose among policyalternatives in government. But the inextricably linked institutions,incentives, and behavior that determine these multistage choicesare substantively complex and analytically unwieldy, particularlyif modeled explicitly and considered in total, from citizenpreferences through government outcomes. To strike a balancebetween complexity and tractability, we modify standard spatialmodels of electoral competition and governmental policy-makingto study how components of partisanship—such as candidateplatform separation in elections, party ID-based voting, nationalpartisan tides, and party-disciplined behavior in the legislature—arerelated to policy outcomes. We define partisan bias as the distancebetween the following two points in a conventional choice space:the ideal point of the median voter in the median legislativedistrict and the policy outcome selected by the elected legislature.The study reveals that none of the party-in-electorate conditionsis capable of producing partisan bias independently. Specifiedcombinations of conditions, however, can significantly increasethe bias and/or the variance of policy outcomes, sometimes insubtle ways.     

UK OC OK? Interpreting Optimal Classification Scores for the U.K. House of Commons

Iain McLean Nuffield College, Oxford University, Oxford OX1 1NF, United Kingdom. e-mail: iain.mclean{at}nuffield.ox.ac.uk e-mail: spln{at}mail.rochester.edu (corresponding author) Poole's (2000, Non-parametric unfolding of binary choice data.Political Analysis 8:211–37) nonparametric Optimal Classificationprocedure for binary data produces misleading rank orderingswhen applied to the modern House of Commons. With simulationsand qualitative evidence, we show that the problem arises fromthe government-versus-opposition nature of British (Westminster)parliamentary politics and the strategic voting that is entailedtherein. We suggest that political scientists think seriouslyabout strategic voting in legislatures when interpreting resultsfrom such techniques.     

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.     

Comparing Experimental and Matching Methods Using a Large-Scale Voter Mobilization Experiment

Alan S. Gerber and Donald P. Green Yale University, Institution for Social and Policy Studies, P.O. Box 208209, 77 Prospect Street, New Haven, CT 06520 e-mail: kevin.arceneaux{at}temple.edu (corresponding author) e-mail: alan.gerber{at}yale.edu e-mail: donald.green{at}yale.edu In the social sciences, randomized experimentation is the optimalresearch design for establishing causation. However, for a numberof practical reasons, researchers are sometimes unable to conductexperiments and must rely on observational data. In an effortto develop estimators that can approximate experimental resultsusing observational data, scholars have given increasing attentionto matching. In this article, we test the performance of matchingby gauging the success with which matching approximates experimentalresults. The voter mobilization experiment presented here comprisesa large number of observations (60,000 randomly assigned tothe treatment group and nearly two million assigned to the controlgroup) and a rich set of covariates. This study is analyzedin two ways. The first method, instrumental variables estimation,takes advantage of random assignment in order to produce consistentestimates. The second method, matching estimation, ignores randomassignment and analyzes the data as though they were nonexperimental.Matching is found to produce biased results in this applicationbecause even a rich set of covariates is insufficient to controlfor preexisting differences between the treatment and controlgroup. Matching, in fact, produces estimates that are no moreaccurate than those generated by ordinary least squares regression.The experimental findings show that brief paid get-out-the-votephone calls do not increase turnout, while matching and regressionshow a large and significant effect.