What Ordered Optimal Classification reveals about ideological structure, cleavages, and polarization in the American mass public

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper develops an extension of Poole’s (Polit Anal 8(3):211–237, 2000) Optimal Classification (OC) scaling procedure to the analysis of polytomous or ordered choice data. This type of data is regularly encountered in public opinion and expert surveys, legislative and judicial bodies where abstention is relevant, and measures of policy that are coded along ordinal scales. OC is nonparametric and requires only minimal assumptions about voters’ utility functions and the error term. As such, Ordered Optimal Classification (OOC) provides a flexible modeling strategy to estimate latent ideological spaces from ordinal choice data. OOC is also easily estimated in multidimensional space without identifying restrictions. After describing the OOC procedure, we perform a series of Monte Carlo experiments and apply the method to analyze survey data from the 2015 Cooperative Congressional Election Study. We then conclude with a discussion of how scholars can utilize OOC in future work involving multidimensional spatial models of choice.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Notes

  1. 1.

    This includes, for instance, the Chapel Hill Expert Survey (Bakker et al. 2015), the Congressional Election Study (Stone and Simas 2010), the Convention Delegate Study (Layman et al. 2010), the United Nations (Bailey et al. 2017), the IMF (Thacker 1999), human rights policies (Fariss and Schnakenberg 2014), and legal systems (Rosenthal and Voeten 2007).

  2. 2.

    OOC can also be used to analyze the strategic and sincere components of roll call voting on a series of related dichotomous votes (particularly amendment voting) by coding legislators’ voting patterns (e.g., YY, NY, NN) categorically (Silberman and Durden 1976; Nunez and Rosenthal 2004; Ladha 1991). As discussed in the next section, OOC uses a constrained normal vector to model the dichotomous components of a single ordinal scale. This means that all of the votes that comprise a given voting pattern will have an identical orientation in the recovered ideological space. We thank Howard Rosenthal for raising this point.

  3. 3.

    However, an underappreciated aspect of measuring mass ideology concerns the researcher’s reliance on which issues and policy alternatives are and are not included in public opinion surveys. This is a subtle—though still consequential—form of agenda control. We thank Bob Erickson for this observation.

  4. 4.

    Although OC is not guaranteed to find the global maximum, it regularly does so or gets very close to it. Poole (2000) reports the results of extensive Monte Carlo tests in one to ten dimensions which show that, at worst, only about 43 misclassifications per 50,000 total choices occur. Such a figure indicates that OC is very closely approximating the global classification maximum.

  5. 5.

    The starting values for the ideal points are obtained from an eigenvalue–eigenvector decomposition of the double-centered voter agreement score matrix.

  6. 6.

    As Adam Bonica has pointed out, OC and SVMs are closely related in their pursuit of a separation hyperplane that optimally divides two classes of data. The major differences between the two methods concerns their loss functions (OC uses overall correct classification rates while SVMs assess classification performance using both the correct classification rate and the robustness of the derived hyperplane), constraints on the separating hyperplane (SVMs allow for nonlinear separating hyperplanes, while OC uses strictly linear separating hyperplanes), and their treatment of the predictor variables X (standard SVMs requires the predictor variables to be observed, while in OC the predictor variables [i.e., the ideal point coordinates of the observations] are treated as latent variables to be estimated) (Hastie et al. 2009; Bonica 2018).

  7. 7.

    The cost parameter C controls the width of the margin—i.e., the number of observations that are allowed to violate the margin and constitute the support vectors.

  8. 8.

    We use a linear kernel to simplify analysis, although one of the attractive properties of SVMs is that alternative kernel functions can be used to estimate nonlinear decision boundaries and prediction functions. We note that the adaptation of such kernels provides one possible avenue for future development of the OOC procedure.

  9. 9.

    Implemented in the krls package in R (Ferwerda et al. 2017).

  10. 10.

    We follow Hainmueller and Hazlett (2014) and use the Gaussian kernel function.

  11. 11.

    We have found that support vector regression (SVR) tends to slightly outperform its competitors in terms of classification performance, and does so with reasonable computation efficiency. Hence, we set SVR as the default method for the normal vector routine and use it in the analyses presented in this paper.

References

  1. Abramowitz, A. (2010). The disappearing center: Engaged citizens, polarization, and American democracy. New Haven: Yale University Press.

    Google Scholar 

  2. Aldrich, J. H., & 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.

    Article  Google Scholar 

  3. Alvarez, R. M. (1997). Information and elections. Ann Arbor: University of Michigan Press.

    Google Scholar 

  4. Alvarez, R. M., & Brehm, J. (1995). American ambivalence towards abortion policy: Development of a heteroskedastic probit model of competing values. American Journal of Political Science, 39(4), 1055–1082.

    Article  Google Scholar 

  5. Ansolabehere, S., Rodden, J., & Snyder, J. M, Jr. (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.

    Article  Google Scholar 

  6. Bafumi, J., & Shapiro, R. Y. (2009). A new partisan voter. Journal of Politics, 71(1), 1–24.

    Article  Google Scholar 

  7. Bailey, M. A., Strezhnev, A., & Voeten, E. (2017). Estimating dynamic state preferences from United Nations voting data. Journal of Conflict Resolution, 61(2), 430–456.

    Article  Google Scholar 

  8. Bakker, R., Vries, Cd, Edwards, E., Hooghe, L., Jolly, S., Marks, G., et al. (2015). Measuring party positions in Europe: The Chapel Hill Expert Survey trend file, 1999–2010. Party Politics, 21(1), 143–152.

    Article  Google Scholar 

  9. Berinsky, A. J., & Lewis, J. B. (2007). An estimate of risk aversion in the U.S. electorate. Quarterly Journal of Political Science, 2(2), 139–154.

    Article  Google Scholar 

  10. Bonica, A. (2013). Ideology and interests in the political marketplace. American Journal of Political Science, 57(2), 294–311.

    Article  Google Scholar 

  11. Bonica, A. (2014). The punctuated origins of Senate polarization. Legislative Studies Quarterly, 39(1), 5–26.

    Article  Google Scholar 

  12. Bonica, A. (2018). Inferring roll call scores from campaign contributions using supervised machine learning. American Journal of Political Science. https://doi.org/10.2139/ssrn.2732913.

    Google Scholar 

  13. Brady, H. E. (2011). The art of political science: Spatial diagrams as iconic and revelatory. Perspectives on Politics, 9(2), 311–331.

    Article  Google Scholar 

  14. Brady, H. E., & Ansolabehere, S. (1989). The nature of utility functions in mass publics. American Political Science Review, 83(1), 143–163.

    Article  Google Scholar 

  15. Brazill, T. J., & Grofman, B. (2002). Factor analysis versus multi-dimensional scaling: Binary choice roll-call voting and the US Supreme Court. Social Networks, 24(3), 201–229.

    Article  Google Scholar 

  16. Brewer, P. R. (2003). The shifting foundations of public opinion about gay rights. Journal of Politics, 65(4), 1208–1220.

    Article  Google Scholar 

  17. Bullock, J. G., Gerber, A. S., Hill, S. J., & Huber, G. A. (2015). Partisan bias in factual beliefs about politics. Quarterly Journal of Political Science, 10(4), 519–578.

    Article  Google Scholar 

  18. Carroll, R., Lewis, J. B., Lo, J., Poole, K. T., & Rosenthal, H. (2013). The structure of utility in spatial models of voting. American Journal of Political Science, 57(4), 1008–1028.

    Google Scholar 

  19. Clinton, J. D., & Jackman, S. (2009). To simulate or NOMINATE? Legislative Studies Quarterly, 34(4), 593–621.

    Article  Google Scholar 

  20. Clinton, J., Jackman, S., & Rivers, D. (2004). The statistical analysis of roll call data. American Political Science Review, 98(2), 355–370.

    Article  Google Scholar 

  21. Converse, P. E. (1964). The nature of belief systems in mass publics. In D. E. Apter (Ed.), Ideology and discontent (pp. 206–261). New York: Free Press.

    Google Scholar 

  22. Coombs, C., & Kao, R. (1960). On a connection between factor analysis and multidimensional unfolding. Psychometrika, 25(3), 219–231.

    Article  Google Scholar 

  23. Croft, W., & Poole, K. T. (2008). Inferring universals from grammatical variation: Multidimensional scaling for typological analysis. Theoretical Linguistics, 34(1), 1–37.

    Article  Google Scholar 

  24. Enelow, J. M., & Hinich, M. J. (1984). The spatial theory of voting: An introduction. New York: Cambridge University Press.

    Google Scholar 

  25. Fariss, C. J., & Schnakenberg, K. (2014). Measuring mutual dependence between state repressive actions. Journal of Conflict Resolution, 58(6), 1003–1032.

    Article  Google Scholar 

  26. Feldman, S. (1988). Structure and consistency in public opinion: The role of core beliefs and values. American Journal of Political Science, 32(2), 416–440.

    Article  Google Scholar 

  27. Ferwerda, J., Hainmueller, J., & Hazlett, C. J. (2017). Kernel-based regularized least squares in R (KRLS) and Stata (krls). Journal of Statistical Software, 79(3), 1–26.

    Article  Google Scholar 

  28. Gibson, T., & Hare, C. (2016). Moral epistemology and ideological conflict in American political behavior. Social Science Quarterly, 97(5), 1157–1173.

    Article  Google Scholar 

  29. Goren, P. (2008). The two faces of government spending. Political Research Quarterly, 61(1), 147–157.

    Article  Google Scholar 

  30. Groseclose, T. (2001). A model of candidate location when one candidate has a valence advantage. American Journal of Political Science, 45(4), 862–886.

    Article  Google Scholar 

  31. Hainmueller, J., & Hazlett, C. (2014). Kernel regularized least squares: Reducing misspecification bias with a flexible and interpretable machine learning approach. Political Analysis, 22(2), 143–168.

    Article  Google Scholar 

  32. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). New York: Springer.

    Google Scholar 

  33. Hetherington, M. J., & Weiler, J. D. (2009). Authoritarianism and polarization in American politics. Cambridge: Cambridge University Press.

    Google Scholar 

  34. Hinich, M. J., & Munger, M. C. (1994). Ideology and the theory of political choice. Ann Arbor: University of Michigan Press.

    Google Scholar 

  35. Hinich, M. J., & Munger, M. C. (1997). Analytical politics. Cambridge: Cambridge University Press.

    Google Scholar 

  36. Hix, S., Noury, A., & Roland, G. (2006). Dimensions of politics in the European Parliament. American Journal of Political Science, 50(2), 494–511.

    Article  Google Scholar 

  37. Jacoby, W. G. (1985). Inconsistent preferences and the multidimensional unfolding model. Political Methodology, 11(3/4), 201–220.

    Google Scholar 

  38. Jacoby, W. G. (1994). Public attitudes toward government spending. American Journal of Political Science, 38(2), 336–361.

    Article  Google Scholar 

  39. Jacoby, W. G. (2002). Core values and political attitudes. In B. Norrander & C. Wilcox (Eds.), Understanding public opinion (2nd ed., pp. 177–201). Washington, DC: CQ Press.

    Google Scholar 

  40. Jacoby, W. G. (2006). Value choices and American public opinion. American Journal of Political Science, 50(3), 706–723.

    Article  Google Scholar 

  41. Jacoby, W. G. (2008). Comment: The dimensionality of public attitudes toward government spending. Political Research Quarterly, 61(1), 158–161.

    Article  Google Scholar 

  42. Jacoby, W. G. (2014). Is there a culture war? Conflicting value structures in American public opinion. American Political Science Review, 108(4), 754–771.

    Article  Google Scholar 

  43. Jessee, S. A. (2009). Spatial voting in the 2004 presidential election. American Political Science Review, 103(1), 59–81.

    Article  Google Scholar 

  44. Jessee, S. A. (2012). Ideology and spatial voting in American elections. Cambridge: Cambridge University Press.

    Google Scholar 

  45. Keele, L., & Wolak, J. (2006). Value conflict and volatility in party identification. British Journal of Political Science, 36(4), 671–690.

    Article  Google Scholar 

  46. Kellstedt, P. M., Ramirez, M. D., Vedlitz, A., & Zahran, S. (2017). Does political sophistication minimize value conflict? Evidence from a Heteroskedastic graded IRT model of opinions toward climate change. British Journal of Political Science. https://doi.org/10.1017/S0007123417000369

    Google Scholar 

  47. Klar, S. (2014). A multidimensional study of ideological preferences and priorities among the American public. Public Opinion Quarterly, 78(S1), 344–359.

    Article  Google Scholar 

  48. Ladha, K. K. (1991). A spatial model of legislative voting with perceptual error. Public Choice, 68(1–3), 151–174.

    Google Scholar 

  49. Lane, R. (1959). The fear of equality. American Political Science Review, 53(1), 35–51.

    Article  Google Scholar 

  50. Lauderdale, B. E. (2010). Unpredictable voters in ideal point estimation. Political Analysis, 18(2), 151–171.

    Article  Google Scholar 

  51. Layman, G. C., & Carsey, T. M. (2002). Party polarization and “conflict extension” in the American electorate. American Journal of Political Science, 46(4), 786–802.

    Article  Google Scholar 

  52. Layman, G. C., Carsey, T. M., Green, J. C., Herrera, R., & Cooperman, R. (2010). Activists and conflict extension in American party politics. American Political Science Review, 104(2), 324–346.

    Article  Google Scholar 

  53. Layman, G. C., & Green, J. C. (2006). Wars and rumours of wars: The contexts of cultural conflict in American political behaviour. British Journal of Political Science, 36(1), 61–89.

    Article  Google Scholar 

  54. Lewis, J. B. (2001). Estimating voter preference distributions from individual-level voting data. Political Analysis, 9(3), 275–297.

    Article  Google Scholar 

  55. Lupton, R. N., Myers, W. M., & Thornton, J. R. (2015). Political sophistication and the dimensionality of elite and mass attitudes, 1980–2004. Journal of Politics, 77(2), 368–380.

    Article  Google Scholar 

  56. Lupton, R. N., Smallpage, S. M., & Enders, A. M. (2017). Values and political predispositions in the age of polarization: Examining the relationship between partisanship and ideology in the United States, 1988–2012. British Journal of Political Science. https://doi.org/10.1017/S0007123417000370

    Google Scholar 

  57. Martin, A. D., & 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.

    Article  Google Scholar 

  58. McClosky, H., & Zaller, J. (1984). The American ethos: Public attitudes toward capitalism and democracy. Cambridge, MA: Harvard University Press.

    Google Scholar 

  59. McFadden, D. L. (1976). Quantal choice analaysis: A survey. Annals of Economic and Social Measurement, 5(4), 363–390.

    Google Scholar 

  60. Nunez, S., & Rosenthal, H. (2004). Bankruptcy “reform” in Congress: Creditors, committees, ideology, and floor voting in the legislative process. Journal of Law, Economics, and Organization, 20(2), 527–557.

    Article  Google Scholar 

  61. Palfrey, T. R., & Poole, K. T. (1987). The relationship between information, ideology, and voting behavior. American Journal of Political Science, 31(3), 511–530.

    Article  Google Scholar 

  62. Poole, K. T. (1998). Recovering a basic space from a set of issue scales. American Journal of Political Science, 42(3), 954–993.

    Article  Google Scholar 

  63. Poole, K. T. (2000). Nonparametric unfolding of binary choice data. Political Analysis, 8(3), 211–237.

    Article  Google Scholar 

  64. Poole, K. T. (2005). Spatial models of parliamentary voting. New York: Cambridge University Press.

    Google Scholar 

  65. Poole, K. T. (2017). The scientific status of geometric models of choice and similarities judgment. Public Choice, 171(3/4), 245–256.

    Article  Google Scholar 

  66. Poole, K. T., & Rosenthal, H. (1984). U.S. presidential elections 1968–80: A spatial analysis. American Journal of Political Science, 28(2), 282–312.

    Article  Google Scholar 

  67. Poole, K. T., & Rosenthal, H. (1997). Congress: A political-economic history of roll call voting. New York: Oxford University Press.

    Google Scholar 

  68. Poole, K. T., & Rosenthal, H. (2007). Ideology and Congress. New Brunswick, NJ: Transaction.

    Google Scholar 

  69. Rathbun, B. C., Kertzer, J. D., Reifler, J., Goren, P., & Scotto, T. J. (2016). Taking foreign policy personally: Personal values and foreign policy attitudes. International Studies Quarterly, 60(1), 124–137.

    Article  Google Scholar 

  70. Rivers, D. (2003). Identification of multidimensional spatial voting models. Working paper.

  71. Rosenthal, H., & Voeten, E. (2004). Analyzing roll calls with perfect spatial voting: France 1946–1958. American Journal of Political Science, 48(3), 620–632.

    Article  Google Scholar 

  72. Rosenthal, H., & Voeten, E. (2007). Measuring legal systems. Journal of Comparative Economics, 35(4), 711–728.

    Article  Google Scholar 

  73. Shepsle, K. A. (1972). The strategy of ambiguity: Uncertainty and electoral competition. American Political Science Review, 66(2), 555–568.

    Article  Google Scholar 

  74. Silberman, J. I., & Durden, G. C. (1976). Determining legislative preferences on the minimum wage: An economic approach. Journal of Political Economy, 84(2), 317–329.

    Article  Google Scholar 

  75. Smidt, C. D. (2017). Polarization and the decline of the American floating voter. American Journal of Political Science, 61(2), 365–381.

    Article  Google Scholar 

  76. Sniderman, P. M., & Bullock, J. (2004). A consistency theory of public opinion and political choice: The hypothesis of menu dependence. In W. E. Saris & P. M. Sniderman (Eds.), Studies in public opinion: Attitudes, nonattitudes, measurement error, and change (pp. 337–357). Princeton, NJ: Princeton University Press.

    Google Scholar 

  77. Sohn, Y. (2017). Identification and estimation for multidimensional item response theory: An analysis of roll call votes in the United States Congress. Presented at the 2017 Annual Meeting of the Annual Political Science Association, San Francisco, CA.

  78. Stimson, J. A. (2004). Tides of consent: How public opinion shapes American politics. Cambridge: Cambridge University Press.

    Google Scholar 

  79. Stokes, D. E. (1963). Spatial models of party competition. American Political Science Review, 57(2), 368–377.

    Article  Google Scholar 

  80. Stone, W. J., & Simas, E. N. (2010). Candidate valence and ideological positions in U.S. House elections. American Journal of Political Science, 54(2), 371–388.

    Article  Google Scholar 

  81. Tahk, A. (2018). Nonparametric ideal-point estimation and inference. Political Analysis. https://doi.org/10.1017/pan.2017.38.

    Google Scholar 

  82. Thacker, S. C. (1999). The high politics of IMF lending. World Politics, 52(1), 38–75.

    Article  Google Scholar 

  83. Treier, S., & Hillygus, D. S. (2009). The nature of political ideology in the contemporary electorate. Public Opinion Quarterly, 73(4), 679–703.

    Article  Google Scholar 

  84. van Schuur, W. H. (2011). Ordinal item response theory: Mokken Scale analysis. Thousand Oaks, CA: Sage.

    Google Scholar 

  85. van Schuur, W. H., & Kiers, H. A. (1994). Why factor analysis often is the incorrect model for analyzing bipolar concepts, and what model to use instead. Applied Psychological Measurement, 18(2), 97–110.

    Article  Google Scholar 

  86. Weisberg, H. F. (1974). Dimensionland: An excursion into spaces. American Journal of Political Science, 18(4), 743–776.

    Article  Google Scholar 

  87. Weisberg, H. F. (2005). The structure and effects of moral predispositions in contemporary American politics. Journal of Politics, 67(3), 646–668.

    Article  Google Scholar 

  88. Weisberg, H. F., & Rusk, J. G. (1970). Dimensions of candidate evaluation. American Political Science Review, 64(4), 1167–1185.

    Article  Google Scholar 

  89. Zaller, J., & Feldman, S. (1992). A simple theory of the survey response: Answering questions versus revealing preferences. American Journal of Political Science, 36(3), 579–616.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Christopher Hare.

Additional information

An earlier version of this paper was presented at the Keith T. Poole Career Retrospective Conference, May 2017, Athens, GA. Thanks to Keith Poole for his patient and invaluable guidance throughout this project and to Bob Erickson, Howard Rosenthal, and an anonymous review for their insightful comments and suggestions for improvement. Thanks also to the University of Georgia, the Albert B. Saye Fund, and the School of Public and International Affairs for their generous financial support for conference travel. An R package and accompanying code to estimate Ordered Optimal Classification is available at http://github.com/tzuliu/ooc.

Appendix

Appendix

Below we perform two additional sets of Monte Carlo experiments on the statistical properties of the Ordered Optimal Classification estimator. The first assesses OOC’s recovery of the true ideal points of ideologically moderate and ideologically extreme respondents. The second provides an informal test of the consistency of the OOC estimator, replicating the analysis in the main text (specifically, Figs. 3, 4) across an increasing number (25, 50, and 100) of issue questions.

Figure 7 shows the correlations between the true and recovered ideal points separately for ideologically moderate and extreme respondents in two dimensions. Ideologically moderate respondents are defined as those with ideal points in the interquartile range on both dimensions, while ideologically extreme respondents are those with ideal points outside of the interquartile range on both dimensions. OOC clearly performs better in its recovery of extremists’ ideal points, though some of this is an artifact of the wider (more polarized) range of ideal point values for ideologically extreme respondents relative to moderate respondents.

Fig. 7
figure7

Monte Carlo tests of Ordered Optimal Classification recovery of ideologically moderate and extreme respondents’ ideal points

Figures 8 and 9 replicate the analaysis in Figs. 3 and 4 while increasing the number of simulated issue scales from 25 to 50 to 100. If OOC is a consistent estimator, the correlations between true and estimated parameters should increase alongside the number of issues for a given level of error and dimensionality. This is precisely what we observe, with the improvements most apparent in the three-dimensional case in Fig. 9.

Fig. 8
figure8

Monte Carlo tests of Ordered Optimal Classification performance in two dimensions with 25, 50, and 100 issues

Fig. 9
figure9

Monte Carlo tests of Ordered Optimal Classification performance in three dimensions with 25, 50, and 100 issues

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hare, C., Liu, T. & Lupton, R.N. What Ordered Optimal Classification reveals about ideological structure, cleavages, and polarization in the American mass public. Public Choice 176, 57–78 (2018). https://doi.org/10.1007/s11127-018-0540-6

Download citation

Keywords

  • Ideal point estimation
  • Ideology
  • Public opinion
  • Optimal Classification