Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T16:39:39.171Z Has data issue: false hasContentIssue false
  • English
  • Français

Hierarchical Item Response Models for Analyzing Public Opinion

Published online by Cambridge University Press:  12 February 2019

Xiang Zhou
Xiang Zhou*
Affiliation:
Department of Government, Harvard University, 1737 Cambridge Street, Cambridge, MA 02138, USA. Email: [email protected]
*
*Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Opinion surveys often employ multiple items to measure the respondent’s underlying value, belief, or attitude. To analyze such types of data, researchers have often followed a two-step approach by first constructing a composite measure and then using it in subsequent analysis. This paper presents a class of hierarchical item response models that help integrate measurement and analysis. In this approach, individual responses to multiple items stem from a latent preference, of which both the mean and variance may depend on observed covariates. Compared with the two-step approach, the hierarchical approach reduces bias, increases efficiency, and facilitates direct comparison across surveys covering different sets of items. Moreover, it enables us to investigate not only how preferences differ among groups, vary across regions, and evolve over time, but also levels, patterns, and trends of attitude polarization and ideological constraint. An open-source R package, hIRT, is available for fitting the proposed models.

Keywords

item response theorypublic opinionhierarchical modeling
Type
Articles
Information
Political Analysis , Volume 27 , Issue 4 , October 2019 , pp. 481 - 502
Copyright
Copyright © The Author(s) 2019. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Author’s note: The author thanks Ken Bollen, Bryce Corrigan, Max Goplerud, Gary King, Jonathan Kropko, Jie Lv, Barum Park, Yunkyu Sohn, Yu-Sung Su, Dustin Tingley, Yu Xie, Teppei Yamamoto, and two anonymous reviewers for helpful comments on previous versions of this work. Replication data are available in Zhou (2018b).

Contributing Editor: Jeff Gill

References

Abramowitz, A. 2010. The Disappearing Center: Engaged citizens, Polarization, and American Democracy . Yale University Press.Google Scholar
Abramowitz, A. I., and Saunders, K. L.. 2008. “Is Polarization a Myth?.” The Journal of Politics 70(2):542–555.Google Scholar
Agresti, A. 2013. Categorical Data Analysis . Hoboken, NJ: John Wiley & Sons.Google Scholar
Aitkin, M. 1987. “Modelling Variance Heterogeneity in Normal Regression Using Glim.” Applied Statistics 36(3):332–339.Google Scholar
Aldrich, J. H., and McKelvey, R. D.. 1977. “A Method of Scaling with Applications to the 1968 and 1972 Presidential Elections.” American Political Science Review 71(1):111–130.Google Scholar
Andrich, D. 1978. “A Rating Formulation for Ordered Response Categories.” Psychometrika 43(4):561–573.Google Scholar
Ansolabehere, S., Rodden, J., and Snyder, J. M.. 2008. “The Strength of Issues: Using Multiple Measures to Gauge Preference Stability, Ideological Constraint, and Issue Voting.” American Political Science Review 102(2):215–232.Google Scholar
Armstrong, D. A., Bakker, R., Carroll, R., Hare, C., Poole, K. T., and Rosenthal, H.. 2014. Analyzing Spatial Models of Choice and Judgment with R . Boca Raton, FL: Chapman and Hall/CRC.Google Scholar
Bafumi, J., Gelman, A., Park, D. K., and Kaplan, N.. 2005. “Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation.” Political Analysis 13:171–187.Google Scholar
Bafumi, J., and Herron, M. C.. 2010. “Leapfrog Representation and Extremism: A Study of American Voters and their Members in Congress.” American Political Science Review 104(3):519–542.Google Scholar
Bailey, M. 2001. “Ideal Point Estimation with a Small Number of Votes: A Random-effects Approach.” Political Analysis 9(3):192–210.Google Scholar
Bailey, M., and Chang, K. H.. 2001. “Comparing Presidents, Senators, and Justices: Interinstitutional Preference Estimation.” Journal of Law, Economics, and Organization 17(2):477–506.Google Scholar
Bailey, M. A. 2007. “Comparable Preference Estimates Across Time and Institutions for the Court, Congress, and Presidency.” American Journal of Political Science 51(3):433–448.Google Scholar
Baker, F. B., and Kim, S.-H.. 2004. Item Response Theory: Parameter Estimation Techniques . CRC Press.Google Scholar
Baldassarri, D., and Gelman, A.. 2008. “Partisans Without Constraint: Political Polarization and Trends in American Public Opinion.” American Journal of Sociology 114(2):408–446.Google Scholar
Bock, R. D. 1972. “Estimating Item Parameters and Latent Ability When Responses are Scored in Two or More Nominal Categories.” Psychometrika 37(1):29–51.Google Scholar
Bock, R. D., and Aitkin, M.. 1981. “Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm.” Psychometrika 46(4):443–459.Google Scholar
Broockman, D. E., and Butler, D. M.. 2017. “The Causal Effects of Elite Position-Taking on Voter Attitudes: Field Experiments with Elite Communication.” American Journal of Political Science 61(1):208–221.Google Scholar
Carsey, T. M., and Layman, G. C.. 2006. “Changing Sides or Changing Minds? Party Identification and Policy Preferences in the American Electorate.” American Journal of Political Science 50(2):464–477.Google Scholar
Caughey, D., Dunham, J., and Warshaw, C.. 2018. “The Ideological Nationalization of Partisan Subconstituencies in the American States.” Public Choice 176(1):133–151.Google Scholar
Caughey, D., and Warshaw, C.. 2015. “Dynamic Estimation of Latent Opinion Using a Hierarchical Group-Level IRT Model.” Political Analysis 23(2):197–211.Google Scholar
Caughey, D., and Warshaw, C.. 2016. “The Dynamics of State Policy Liberalism, 1936–2014.” American Journal of Political Science 60(4):899–913.Google Scholar
Clinton, J., Jackman, S., and Rivers, D.. 2004. “The Statistical Analysis of Roll Call Data.” American Political Science Review 98(02):355–370.Google Scholar
Converse, P. 1964. “The Nature of Belief Systems in Mass Publics.” In Ideology and Discontent , edited by David, A., 206–261. New York: Free Press.Google Scholar
Cook, R. D., and Weisberg, S.. 1983. “Diagnostics for Heteroscedasticity in Regression.” Biometrika 70(1):1–10.Google Scholar
Delli Carpini, M. X., and Keeter, S.. 1996. What Americans Know about Politics and Why It Matters . New Haven, CT: Yale University Press.Google Scholar
DiMaggio, P., Evans, J., and Bryson, B.. 1996. “Have American’s Social Attitudes Become More Polarized?.” American Journal of Sociology 102(3):690–755.Google Scholar
Evans, J. H. 2003. “Have Americans’ Attitudes Become More Polarized? - An Update.” Social Science Quarterly 84(1):71–90.Google Scholar
Fiorina, M. P., Abrams, S. A., and Pope, J. C.. 2008. “Polarization in the American Public: Misconceptions and Misreadings.” The Journal of Politics 70(2):556–560.Google Scholar
Fiorina, M. P., and Abrams, S. J.. 2012. Disconnect: The Breakdown of Representation in American Politics . Norman, OK: University of Oklahoma Press.Google Scholar
Fiorina, M. P., Abrams, S. J., and Pope, J.. 2006. Culture war?: The Myth of a Polarized America . New York: Longman Publishing Group.Google Scholar
Hare, C., Armstrong, D. A., Bakker, R., Carroll, R., and Poole, K. T.. 2015. “Using Bayesian Aldrich–McKelvey Scaling to Study Citizens’ Ideological Preferences and Perceptions.” American Journal of Political Science 59(3):759–774.Google Scholar
Hill, S. J., and Tausanovitch, C.. 2015. “A Disconnect in Representation? Comparison of Trends in Congressional and Public Polarization.” The Journal of Politics 77(4):1058–1075.Google Scholar
Hoff, P. D., and Niu, X.. 2012. “A Covariance Regression Model.” Statistica Sinica 22:729–753.Google Scholar
Hurwitz, J., and Peffley, M.. 1987. “How are Foreign Policy Attitudes Structured? A Hierarchical Model.” American Political Science Review 81(4):1099–1120.Google Scholar
Imai, K., Lo, J., and Olmsted, J.. 2016. “Fast Estimation of Ideal Points with Massive Data.” American Political Science Review 110(4):631–656.Google Scholar
Inglehart, R., and Welzel, C.. 2005. Modernization, Cultural change, and Democracy: The Human Development Sequence . New York: Cambridge University Press.Google Scholar
Jackson, J. E. 1983. “The Systematic Beliefs of the Mass Public: Estimating Policy Preferences with Survey Data.” The Journal of Politics 45(4):840–865.Google Scholar
Jacoby, W. G. 2006. “Value Choices and American Public Opinion.” American Journal of Political Science 50(3):706–723.Google Scholar
Jessee, S. 2016. “How Can We Estimate the Ideology of Citizens and Political Elites on the Same Scale?.” American Journal of Political Science 60(4):1108–1124.Google Scholar
Jessee, S. A. 2009. “Spatial Voting in the 2004 Presidential Election.” American Political Science Review 103(1):59–81.Google Scholar
Jöreskog, K. G., and Goldberger, A. S.. 1975. “Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable.” Journal of the American Statistical Association 70(351a):631–639.Google Scholar
Judd, C. M., and Milburn, M. A.. 1980. “The Structure of Attitude Systems in the General Public: Comparisons of a Structural Equation Model.” American Sociological Review 45(4):627–643.Google Scholar
King, G., Murray, C. J., Salomon, J. A., and Tandon, A.. 2004. “Enhancing the Validity and Cross-cultural Comparability of Measurement in Survey Research.” American Political Science Review 98(1):191–207.Google Scholar
Lauderdale, B. E. 2010. “Unpredictable Voters in Ideal Point Estimation.” Political Analysis 18(2):151–171.Google Scholar
Layman, G. C., and Carsey, T. M.. 2002. “Party Polarization and “Conflict Extension” in the American Electorate.” American Journal of Political Science 46(4):786–802.Google Scholar
Layman, G. C., Carsey, T. M., and Horowitz, J. M.. 2006. “Party Polarization in American Politics: Characteristics, Causes, and Consequences.” Annual Review of Political Science 9:83–110.Google Scholar
Lewis, J. B. 2001. “Estimating Voter Preference Distributions from Individual-level Voting Data.” Political Analysis 9(3):275–297.Google Scholar
Londregan, J. 2000. “Estimating Legislator’s Preferred Points.” Political Analysis 8(1):35–56.Google Scholar
Lord, F. M., Novick, M. R., and Birnbaum, A.. 1968. Statistical Theories of Mental Test Scores . Boston, MA: Addison-Wesley.Google Scholar
Martin, A. D., and Quinn, K. M.. 2002. “Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the U.S. Supreme Court, 1953–1999.” Political Analysis 10(2):134–153.Google Scholar
Martin, A. D., Quinn, K. M., and Park, J. H.. 2011. “Mcmcpack: Markov Chain Monte Carlo in R.” Journal of Statistical Software 42(9):1–21.Google Scholar
Masters, G. N. 1982. “A Rasch Model for Partial Credit Scoring.” Psychometrika 47(2):149–174.Google Scholar
McCarty, N., Poole, K. T., and Rosenthal, H.. 2016. Polarized America: The Dance of Ideology and Unequal Riches . Cambridge, MA: MIT Press.Google Scholar
Mendelberg, T., McCabe, K. T., and Thal, A.. 2017. “College Socialization and the Economic Views of Affluent Americans.” American Journal of Political Science 61(3):606–623.Google Scholar
Mislevy, R. J. 1987. “Exploiting Auxiliary Infornlation about Examinees in the Estimation of Item Parameters.” Applied Psychological Measurement 11(1):81–91.Google Scholar
Mouw, T., and Sobel, M. E.. 2001. “Culture Wars and Opinion Polarization: The Case of Abortion.” American Journal of Sociology 106(4):913–943.Google Scholar
Muraki, E. 1992. “A Generalized Partial Credit Model: Application of an EM Algorithm.” Applied Psychological Measurement 16(2):159–176.Google Scholar
Muthén, B. 1984. “A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators.” Psychometrika 49(1):115–132.Google Scholar
Norpoth, H., and Lodge, M.. 1985. “The Difference Between Attitudes and Nonattitudes in the Mass Public: Just Measurements.” American Journal of Political Science 29(2):291–307.Google Scholar
Park, D. K., Gelman, A., and Bafumi, J.. 2004. “Bayesian Multilevel Estimation with Poststratification: State-level Estimates from National Polls.” Political Analysis 12(4):375–385.Google Scholar
Peterson, B., and Harrell, F. E.. 1990. “Partial Proportional Odds Models for Ordinal Response Variables.” Applied statistics 39(2):205–217.Google Scholar
Poole, K. T., and Rosenthal, H.. 1991. “Patterns of Congressional Voting.” American Journal of Political Science 35(1):228–278.Google Scholar
Rasch, G. 1960. Probabilistic Models for Some Intelligence and Achievement Tests . Copenhagen: Danish Institute for Educational Research.Google Scholar
Rasch, G. 1961. “On General Laws and the Meaning of Measurement in Psychology.” In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4 , 321–333. University of California Press Berkeley.Google Scholar
Rueda, D., and Stegmueller, D.. 2016. “The Externalities of Inequality: Fear of Crime and Preferences for Redistribution in Western Europe.” American Journal of Political Science 60(2):472–489.Google Scholar
Samejima, F.1969. “Estimation of Latent Ability Using a Response Pattern of Graded Scores” (Psychometric Monograph No. 17). Richmond, VA: Psychometric Society. Retrieved from http://www.psychometrika.org/journal/online/MN17.pdf.Google Scholar
Tausanovitch, C., and Warshaw, C.. 2013. “Measuring Constituent Policy Preferences in Congress, State Legislatures, and Cities.” The Journal of Politics 75(2):330–342.Google Scholar
Treier, S., and Hillygus, D. S.. 2009. “The Nature of Political Ideology in the Contemporary Electorate.” Public Opinion Quarterly 73(4):679–703.Google Scholar
Treier, S., and Jackman, S.. 2008. “Democracy as a Latent Variable.” American Journal of Political Science 52(1):201–217.Google Scholar
Verbyla, A. P. 1993. “Modelling Variance Heterogeneity: Residual Maximum Likelihood and Diagnostics.” Journal of the Royal Statistical Society. Series B (Methodological) 55(2):493–508.Google Scholar
Western, B., and Bloome, D.. 2009. “Variance Function Regressions for Studying Inequality.” Sociological Methodology 39(1):293–326.Google Scholar
Zaller, J. 1992. The Nature and Origins of Mass Opinion . New York: Cambridge University Press.Google Scholar
Zhou, X. 2014. “Increasing Returns to Education, Changing Labor Force Structure, and the Rise of Earnings Inequality in Urban China, 1996–2010.” Social Forces 93(2):429–455.Google Scholar
Zhou, X.2018a. hIRT: Hierarchical Item Response Theory Models. R package version 0.1.3, available at the Comprehensive R Archive Network (CRAN).Google Scholar
Zhou, X.2018b. “Replication Data for: Hierarchical Item Response Models for Analyzing Public Opinion.” https://doi.org/10.7910/DVN/HCSQBD, Harvard Dataverse, V1.Google Scholar
Supplementary material: File

Zhou supplementary material

Zhou supplementary material 1

Download Zhou supplementary material(File)
File 286.9 KB