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Substance and Change in Congressional Ideology: NOMINATE and Its Alternatives

Published online by Cambridge University Press:  05 July 2016

Devin Caughey*
Massachusetts Institute of Technology
Eric Schickler
University of California–Berkeley


Poole and Rosenthal's NOMINATE scores have been a boon to the study of Congress, but they are not without limitations. We focus on two limitations that are especially important in historical applications. First, the dimensions uncovered by NOMINATE do not necessarily have a consistent ideological meaning over time. Our case study of the 1920s highlights the challenge of interpreting NOMINATE scores in periods when party lines do not map well onto the main contours of ideological debate in political life. Second, the commonly used DW-NOMINATE variant of these scores makes assumptions that are not well suited to dealing with rapid or non-monotonic ideological change. A case study of Southern Democrats in the New Deal era suggests that a more flexible dynamic item-response model provides a better fit for this important period. These applications illustrate the feasibility and value of tailoring one's model and data to one's research goals rather than relying on off-the-shelf NOMINATE scores.

Research Article
Copyright © Cambridge University Press 2016 

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1. For a recent overview of the NOMINATE project, see Keith T. Poole and Howard Rosenthal, Ideology and Congress (New Brunswick, NJ: Transaction, 2007).

2. See, e.g., Schickler, Eric, “Institutional Change in the House of Representatives, 1867–1998: A Test of Partisan and Ideological Power Balance Models,American Political Science Review 94, no. 2 (2000): 269–88CrossRefGoogle Scholar; John H. Aldrich, Mark M. Berger, and David W. Rohde, “The Historical Variability in Conditional Party Government, 1877–1994,” in Party, Process, and Political Change in Congress: New Perspectives on the History of Congress, ed. David Brady and Mathew D. Mc-Cubbins (Stanford, CA: Stanford University Press, 2002), 23–51; Gary W. Cox and Matthew D. McCubbins, Setting the Agenda: Responsible Party Government in the U.S. House of Representatives (New York: Cambridge University Press, 2005); Han, Hahrie and Brady, David W., “A Delayed Return to Historical Norms: Congressional Party Polarization after the Second World War,British Journal of Political Science 37, no. 3 (2007): 505 CrossRefGoogle Scholar; Lebo, Matthew J., McGlynn, Adam J., and Koger, Gregory, “Strategic Party Government: Party Influence in Congress, 1789–2000,American Journal of Political Science 51, no. 3 (2007): 464–81CrossRefGoogle Scholar.

3. By ideology we mean something more robust than simply a set of political positions that tend empirically to “go together”—what Poole and Rosenthal, following Philip Converse, call “constraint”; Poole and Rosenthal, Ideology and Congress, 12; Philip E. Converse, “The Nature of Belief Systems in Mass Publics,” in Ideology and Discontent, ed. David E. Apter (London: Free Press, 1964), 206–61. Rather, we think of ideology as a relatively coherent, if not perfectly consistent, set of general ideas and beliefs from which specific political positions can be derived. On conceptualizing ideology, see John Gerring, Party Ideologies in America, 1828–1996 (New York: Cambridge University Press, 1998).

4. Keith T. Poole and Howard Rosenthal, Congress: A Political-Economic History of Roll Call Voting (New York: Oxford University Press, 1997).

5. Snyder, James M. Jr., “Artificial Extremism in Interest Group Ratings,Legislative Studies Quarterly 17, no. 3 (1992): 319–45Google Scholar.

6. Poole and Rosenthal, Ideology and Congress, 42.

7. Ibid., 61.

8. Beginning in 1925 and continuing for a decade, the two parties in the Senate divided along both the first and second NOMINATE dimension. As a result, the cutting lines for party-line votes was not perpendicular to the first dimension, but rather ran at a –45 degree angle to it; ibid., 57.

9. Rodgers, Daniel T., “In Search of Progressivism,Reviews in American History 10, no. 4 (1983): 114 Google Scholar.

10. Filene, Peter G., “An Obituary for ‘The Progressive Movement,’American Quarterly 22, no. 1 (1970): 2034 Google Scholar.

11. Hans Noel, Political Ideologies and Political Parties in America (New York: Cambridge University Press, 2014), 87–89.

12. In his New American Nation Series history of the 1920s, John Hicks argues that Davis and Coolidge were quite similar in outlook. More generally, Hicks highlights the similarity between Democrats and Republicans in the mid-1920s; John D. Hicks, Republican Ascendancy: 1921–1933 (New York: Harper and Brothers, 1960).

13. Robert K. Murray, The Politics of Normalcy: Governmental Theory and Practice in the Harding-Coolidge Era (New York: W.W. Norton, 1973), 43–44.

14. See also Bradley, Phillips, “The Farm Bloc,Social Forces 3, no. 4 (1925): 714–18Google Scholar; John Mark Hansen, Gaining Access: Congress and the Farm Lobby, 1919–1981 (Chicago: University of Chicago Press, 1991), 37; Donald L. Winters, Henry Cantwell Wallace as Secretary of Agriculture, 1921–1924 (Urbana: University of Illinois, 1970), 90.

15. Black, John D., “The McNary-Haugen Movement,American Economic Review 18 (1928): 405 Google Scholar.

16. Rogers, Lindsay, “First and Second Sessions of the Sixty-Eighth Congress,American Political Science Review 19 (1925): 762 Google Scholar, 766; Roy G. Blakey and Gladys C. Blakey, The Federal Income Tax (New York: Longmans, Green, 1940), 223–46; Murray, Politics of Normalcy, 132–33.

17. Hicks, Republican Ascendancy, 92; Murray, Politics of Normalcy, 137.

18. Erik Newland Olssen, “Dissent from Normalcy: Progressives in Congress, 1918–1925” (PhD diss., Duke University, 1970); see also Erik N. Olssen, “Southern Senators and Reform Issues in the 1920s: A Paradox Unravelled,” in The South Is Another Land: Essays on the Twentieth-Century South, ed. Bruce Clayton and John A. Salmond (Westport, CT: Greenwood Press, 1987), 49–66.

19. This is not to say that political actors' perceptions of the relevant cleavage necessarily trump other potential conceptualizations (see the concluding section for a discussion of this complicated question).

20. Olssen, “Dissent from Normalcy,” 361–68, lists the specific votes used by the three organizations. Elsewhere in this work Olssen compares senators' scores on indices derived from the key votes and also uses cluster bloc analysis to examine the frequency with which pairs of senators voted together. Based on our reading of this work, it is less clear that the Farm Bloc used the votes to evaluate senators than is the case for the AFL and CPPA. As such, we recommend treating the Farm Bloc votes with greater caution.

21. Ibid., 69–71.

22. Ibid.

23. Progressives in both houses put forward a detailed a program for the 68th Congress that indicates the range of their policy goals: tightened railroad regulation, campaign finance restrictions, a Child Labor Constitutional amendment, opposition to reduced taxes on the wealthy, restoration of the excess profits tax, increased inheritance taxes, payment of the Veterans' Bonus, abolition of the Railroad Labor group, and limitations on the use of injunctions; Olssen, “Dissent from Normalcy”; see also “Progressives Call for Radical Laws; House Faces Tie-Up,” New York Times, Dec. 1, 1923, 1

24. Olssen, “Dissent from Normalcy,” 220–25. Cummins had alienated Progressives due to his sponsorship of the Transportation Act of 1920, which was seen as, on balance, pro-railroad.

25. We use IRT to scale the CPPA votes mainly for the sake of convenience. Though they differ in certain respects, NOMINATE and IRT typically yield very similar ideal-point estimates; Carroll, Royce et al. , “Comparing NOMINATE and IDEAL: Points of Difference and Monte Carlo Tests,Legislative Studies Quarterly 34, no. 4 (2009): 555–91Google Scholar; Clinton, Joshua D. and Jackman, Simon, “To Simulate or NOMINATE?Legislative Studies Quarterly 34, no. 4 (2009): 593621 Google Scholar. We estimate the IRT models using the R package MCMCpack, but similar functionality is provided by wnominate, which implements NOMINATE in R, as well as by the package plsc; Martin, Andrew D., Quinn, Kevin M., and Park, Jong Hee, “MCMCpack: Markov Chain Monte Carlo in R,Journal of Statistical Software 42, no. 9 (2011): 121 Google Scholar; Poole, Keith et al. , “Scaling Roll Call Votes with wnominate in R,Journal of Statistical Software 42, no. 14 (2011): 121 Google Scholar,; Simon Jackman, pscl: Classes and Methods for R Developed in the Political Science Computational Laboratory, Stanford University, Department of Political Science, Stanford University. Stanford, California. R package version 1.4.9 (2015),

26. See Clinton, Joshua, Jackman, Simon, and Rivers, Douglas, “The Statistical Analysis of Roll Call Data,American Political Science Review 98, no. 2 (2004): 355–70Google Scholar.

27. With only seventy-five roll calls, we pooled the CPPA bills across the three Congresses' votes rather than attempting to estimate separate CPPA scores for each Congress. The mean DW-NOMINATE scores correlate at 0.99 with the DW-NOMINATE score in each Congress.

28. Olssen, “Dissent from Normalcy,” 84–92.

29. Arthur Sears Henning, “Democrats Face Battle Royal in Convention Ring,” Chicago Tribune, Jan. 20, 1924, 3; “Bryan Scores Underwood,” New York Times, Feb. 27, 1924, 2; Harry N. Price, “Selection of West Virginian is Made Unanimous on 103D Ballot,” Washington Post, July 10, 1924, 1–2; “Underwood Favors Cut in Surtaxes,” Los Angeles Times, June 10, 1925, 1.

30. These descriptions of Underwood are quoted in George Brown Tindall, The Emergence of the New South, 1913–1945 (Baton Rouge: Louisiana State University Press, 1967), 242.

31. “Underwood Favors Cut in Surtaxes.”

32. Glass favored a surtax on high incomes of no greater than 25 percent, which was Mellon's position; “Underwood's Plea Stirs Democrats,” New York Times, June 14, 1925, 1; see also Olssen, “Dissent from Normalcy,” 252. Though not in the Senate, leading Democrat and future Speaker John Nance Garner also “did not agree with the progressives” on taxation, standing “well to the right of the progressive Democrats” (ibid., 213). Indeed, Garner had backed Mellon's 1921 tax plan and favored less aggressive changes than the progressives in 1924 (ibid., 227–34). Yet Garner's NOMINATE score placed him well to the left of the Democratic median in the House; indeed, his DW-NOMINATE score in the mid-1920s was at the far end of the Democratic spectrum, placing Garner to the left of such well-known liberals as Adolph Sabath, the Chicago Democrat who in the late 1930s and 1940s fought against Garner's conservative Democratic allies on the House Rules Committee.

33. Donald R. McCoy, The Quiet President (New York: Macmillan, 1967), 274; James T. Patterson, Congressional Conservatism and the New Deal: The Growth of the Conservative Coalition in Congress, 1933–1939 (Lexington: University of Kentucky Press, 1967), 64. Underwood worked out a deal with Secretary of War John Weeks to promote private development in 1925. Conservative Democrats generally backed the Underwood plan while progressive Democrats supported Norris's public power alternative (Olssen, “Dissent from Normalcy,” 268–73). Southern Democrats split nearly evenly in what Olssen characterizes as a “revolt of the conservative Democrats, led by [William] Bruce [of Maryland] and Underwood” (ibid., 273).

34. A regression of CPPA scores on both first- and second-dimension NOMINATE scores explains 76 percent of the variance in CPPA scores, compared to 64 percent for the first dimension alone. Running the former regression within each party explains 69 percent of Republicans' variance but only 36 percent of Democrats’.

35. Underwood, whose second-dimension score of −0.96 was among the lowest in Senate, was an outspoken opponent of the Ku Klux Klan, which in the 1920s South was associated not only with racial and religious bigotry but also with a variety of progressive reforms favored by its constituency of middle- and lower-class whites; see, e.g., Thornton, J. Mills III, “Hugo Black and the Golden Age,Alabama Law Review 36, no. 3 (1985): 899913 Google Scholar.

36. These figures were calculated by comparing each member's score in a given Congress to the party medians in that Congress. For CPPA scores, each member's score was constant across Congresses but the party medians did shift a bit due to member turnover.

37. Olssen, who found the AFL roll calls in the papers of Senator Henrik Shipstead (FL-MN), enumerates them in “Dissent from Normalcy,” 367–68.

38. The CIO sided with immigration advocates and against nativists when the industrial union rose to prominence in the late 1930s. Progressives were generally split on immigration restriction, with most Progressive Democrats, along with George Norris, Lynn Frazier, and Edwin Ladd, favoring restrictions, while others, such as David Walsh, Royal Copeland, Henrik Shipstead, and Smith Brookhart, opposed drastic restrictions; Olssen, “Dissent from Normalcy,” 240.

39. The AFL scores correlate with party at 0.61.

40. The AFL scores' correlation with second-dimension NOMINATE scores for Democrats is a stronger 0.53.

41. Olssen describes these votes as “common knowledge” and for details refers the reader to the secondary literature; see Olssen, “Southern Senators,” 63. For the full list of roll calls, see ibid., 365–67. Although the votes do reflect the position favored by the bloc and its leaders, it is not altogether clear that the bloc itself compiled this list of votes. As such, treating it as a “scorecard” is more problematic than is the case for the CPPA and AFL votes. Still, the votes can be considered a measure of support for the programs advocated by the Farm Bloc.

42. The AFL and Farm Bloc ideal points suggest even greater party overlap than the CPPA scores.

43. James L. Sundquist, Dynamics of the Party System: Alignment and Realignment of Political Parties in the United States, rev. ed. (Washington, DC: The Brookings Institution, 1983).

44. The epithet “schizophrenic” is from Anthony J. Badger, The New Deal: The Depression Years, 1933–1940 (Chicago: Ivan R. Dee, 2002), 271. On one-party Democratic politics as a central prop of the South's exclusionary racial and political system, see V. O. Key Jr., Southern Politics in State and Nation (New York: Knopf, 1949); Robert W. Mickey, Paths Out of Dixie: The Democratization of Authoritarian Enclaves in America's Deep South (Princeton, NJ: Princeton University Press, 2015).

45. Patterson, Congressional Conservatism; Katznelson, Ira, Geiger, Kim, and Kryder, Daniel, “Limiting Liberalism: The Southern Veto in Congress, 1933–1950,Political Science Quarterly 108, no. 2 (1993): 283306 Google Scholar; Schickler, Eric and Pearson, Kathryn, “Agenda Control, Majority Party Power, and the House Committee on Rules, 1937–52,Legislative Studies Quarterly 34, no. 4 (2009):455–91Google Scholar.

46. See, e.g., pages 42–62 and 135–42 in Poole and Rosenthal, Ideology and Congress.

47. See, e.g., Shor, Boris, Berry, Christopher, and McCarty, Nolan, “A Bridge to Somewhere: Mapping State and Congressional Ideology on a Cross-Institutional Common Space,Legislative Studies Quarterly 35, no. 3 (January 2010): 417–48Google Scholar.

48. See, e.g., Bailey, Michael A., “Comparable Preference Estimates across Time and Institutions for the Court, Congress, and Presidency,American Journal of Political Science 51, no. 3 (2007): 433–48CrossRefGoogle Scholar; and Jessee, Stephen A., “Spatial Voting in the 2004 Presidential Election,American Political Science Review 103, no. 1 (2009): 5981 Google Scholar. More technically, the bridging assumption is that the item characteristic curve that maps observed dichotomous (yes/no) responses to the latent ideal-point space is invariant across contexts.

49. For efforts to bridge over time using votes repeated across congresses, see Asmussen, Nicole and Jo, Jinhee, “Anchors Away: A New Approach for Estimating Ideal Points Comparable across Time and Chambers.Political Analysis 24, No. 2 (2016): 172–88CrossRefGoogle Scholar. David A. Bateman, Joshua Clinton, and John Lapinski, “A House Divided? Roll Calls, Polarization, and Policy Differences in the U.S. House, 1877–2011” (unpublished manuscript, Sept. 1, 2015),

50. Ideal points are constrained to be constant within congresses. In addition, the ideal points of members who serve in only a few congresses are constrained to be constant over time. For details on DW-NOMINATE, see Carroll, Royce et al. , “Measuring Bias and Uncertainty in DW-NOMINATE Ideal Point Estimates via the Parametric Bootstrap,Political Analysis 17, no. 3 (2009): 261–75Google Scholar.

51. Poole and Rosenthal, Ideology and Congress, acknowledge this, and also note that the years 1931–37 were a period of unusual temporal instability in the Senate.

52. Martin and Quinn use this approach to estimate a dynamic model of Supreme Court justices' ideal points; Martin, Andrew D. and Quinn, Kevin M., “Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the U.S. Supreme Court, 1953–1999,Political Analysis 10, no. 2 (2002): 134–53CrossRefGoogle Scholar.

53. This is called a “local level” or “random walk” prior; see Simon Jackman, Bayesian Analysis for the Social Sciences (Hoboken, NJ: Wiley, 2009), 471–72.

54. In Bayesian terminology, the posterior distribution of the ideal point parameter is proportional to its prior distribution (from term t − 1) times its likelihood (in term t). Priors can be thought of as adding “pseudo-observations” to the data actually observed. These pseudo-observations may derived from subjective beliefs, but in this application they are derived from each legislator's actual votes in adjacent terms. The number of pseudo-observations is inversely proportional to the user-specified variance of the random-walk prior.

55. Like DW-NOMINATE, the dynamic IRT model does not account for aggregate spatial movement in Congress as a whole. If no legislators retired between periods and all moved a constant amount to the right, the model would not detect any ideological change among legislators. More subtly, if a large bloc of legislators became more conservative while all others remained constant, the estimated movement of the bloc would be biased toward zero and that of the constant legislators biased away from zero.

56. The assumption that the organizations' positions reflect a broad ideology is most plausible for the CPPA and least applicable to the Farm Bloc.

57. This was especially true of labor issues in the years 1937–45; Poole and Rosenthal, Ideology and Congress, 137–38.

58. Roll calls where voting patterns are weakly correlated with other roll calls will be estimated to have low discrimination parameters (β j , in Equation 1), and thus a legislator's position on this bill will have little impact on their estimated ideal point. This interpretation also presumes that no “liberal” votes are coded as “conservative,” which appears to be a safe assumption in the roll calls we consider.

59. Anthony J. Badger, “How Did the New Deal Change the South?” chap. 2 in New Deal/New South (Fayetteville: University of Arkansas Press, 2007), 31–44; Wright, Gavin, “The New Deal and the Modernization of the South,Federal History 2 (2010): 5873 Google Scholar.

60. Patterson, James T., “A Conservative Coalition Forms in Congress, 1933–1939,Journal of American History 52, no. 4 (March 1966): 757–72Google Scholar.

61. Anthony J. Badger, “Whatever Happened to Roosevelt's New Generation of Southerners?” chap. 4 in New Deal/New South (Fayetteville: University of Arkansas Press, 2007), 58–71.

62. Robert A. Garson, The Democratic Party and the Politics of Sectionalism, 1941–1948 (Baton Rouge: Louisiana State University Press, 1974); Schickler, Eric and Caughey, Devin, “Public Opinion, Organized Labor, and the Limits of New Deal Liberalism, 1936–1945,Studies in American Political Development 25, no. 2 (2011): 128 CrossRefGoogle Scholar.

63. Patterson, Congressional Conservatism, 329–30.

64. Garson, Politics of Sectionalism; Katznelson et al., “Limiting Liberalism”; Reiter, Howard L., “The Building of a Bifactional Structure: The Democrats in the 1940s,Political Science Quarterly 116, no. 1 (April 2001): 107–29Google Scholar; Schickler and Pearson, “Agenda Control.”

65. Clinton, Katznelson, and Lapinski have engaged in a similar exploration of voting patterns in this time period, with a focus on partisan polarization, which they argue is poorly captured by DW-NOMINATE scores in this era; see Joshua D. Clinton, Ira Katznelson, and John S. Lapinski, “Where Measures Meet History: Party Polarization During the New Deal and Fair Deal,” chap. 8 in Governing in a Polarized Age: Elections, Parties, and Representation in America, ed. Alan S. Gerber and Eric Schickler (New York: Cambridge University Press, forthcoming). As an alternative, they compute recentered and rescaled W-NOMINATE scores using the method suggested by Groseclose, Tim, Levitt, Stephen D., and Snyder, James M. Jr., “Comparing Interest Group Scores across Time and Chambers: Adjusted ADA Scores for the U.S. Congress,American Political Science Review 93, no. 1 (1999): 3350 Google Scholar. The adjusted W-NOMINATE scores are comparable over time under the assumption that a member's estimated ideal point in a given congress is a function of their long-run average ideal point, “shift” and “stretch” parameters specific to that congress, and an i.i.d. random shock. The shift and stretch adjust for changes in the agenda across periods. (Note, however, that Poole and Rosenthal claim that NOMINATE is quite robust to agenda differences.) See Groseclose et al., “Comparing Interest Group Scores,” 45–49, for an insightful discussion of the assumptions of this model and its relationship to NOMINATE. The random shock allows ideal points to deviate randomly in each congress, creating an effect similar to the random walk prior in Martin and Quinn's dynamic IRT model. The primary difference between the two models is that the former treats ideal points in each congress as deviations from legislators' average over their entire career, whereas the latter treats them as deviations from their ideal point in the previous congress.

66. R Core Team, R: A Language and Environment for Statistical Computing (Vienna, Austria: R Foundation for Statistical Computing, 2013),; Martin and Quinn, “Dynamic Ideal Point Estimation”; Martin et al., “MCMCpack: Markov Chain Monte Carlo in R.”

67. Billy R. Weeks, “The Pledge ‘To Plow a Straight Furrow’: The 1947 Senatorial Campaign of John C. Stennis” (master's thesis, Mississippi State University, 1974); Keith M. Finley, Delaying the Dream: Southern Senators and the Fight against Civil Rights, 1938–1965 (Baton Rouge: Louisiana State University Press, 2008).

68. Chester M. Morgan, Redneck Liberal: Theodore G. Bilbo and the New Deal (London: Louisiana State University Press, 1985).

69. Ibid., 3–4.

70. Ibid., 247–50.

71. For details on the estimation of these standard errors, see Carroll et al., “Bias and Uncertainty.” The greater uncertainty of the DW-NOMINATE estimates is probably due to the linear model's poor fit to Bilbo's trajectory over time.

72. Because the IRT model is Bayesian, its “standard errors” are actually posterior standard deviations, which we derived from the distribution of ideal points across Markov chain Monte Carlo draws.

73. Though Southern Democrats who entered the Senate in the 78th and 79th Congresses were a little more conservative on average than those they replaced, Southerners' rightward turn in these congresses is mostly attributable to the adaptation of continuing members; see Devin Caughey, “Congress, Public Opinion, and Representation in the One-Party South, 1930s–1960s” (PhD diss., University of California, Berkeley, 2012), chapter 2.4. This contrasts with Poole and Rosenthal's finding that in general replacement dominates adaptation in the U.S. Congress (see Poole and Rosenthal, Ideology and Congress, 72).

74. See, e.g., Poole and Rosenthal, Ideology and Congress; Carroll et al., “Comparing NOMINATE and IDEAL”; Clinton and Jackman, “To Simulate or NOMINATE?”; Nolan McCarty, Measuring Legislative Preferences,” in The Oxford Handbook of the American Congress, ed. Eric Schickler and Frances Lee (New York: Oxford University Press, 2011), 66–94.

75. As Groseclose et al., “Comparing Interest Group Scores,” 46–47, note, the linearity restriction means that hypotheses positing rapid ideological change—such as final-term shirking or responses to redistricting—cannot be tested using DW-NOMINATE.

76. Nokken, Timothy P. and Poole, Keith T., “Congressional Party Defection in American History,Legislative Studies Quarterly 29, no. 4 (2004): 545–68Google Scholar. As of this writing, uncertainty estimates for Nokken-Poole NOMINATE scores are not publicly available.

77. An additional reason to use a dynamic measure is that pooling information across time can result in more accurate estimates of legislator locations in any given congress.

78. This is true unless information available to bridge the choices available to legislators in different time periods; see Bailey, “Comparable Preference Estimates.”

79. Controlling for a variable that is affected by the cause or “treatment” of interest leads to “post-treatment bias” in the estimated causal effect; see Rosenbaum, Paul R., “The Consequences of Adjustment for a Concomitant Variable That Has Been Affected by the Treatment,Journal of the Royal Statistical Society: Series A (General) 147, no. 5 (1984): 656–66CrossRefGoogle Scholar.

80. The uncertainty of auxiliary quantities such as the median can, however, be estimated via bootstrap simulation; see Carroll et al., “Bias and Uncertainty.”

81. Other options include those provided by the R packages wnominate and pscl; see Poole et al., “Scaling Roll Call Votes” and Jackman, pscl.

82. Another cost of a dynamic IRT model is the lack of a software program for estimating more than one spatial dimension. Though we are not aware of any existing implementation, a two-dimensional dynamic IRT model could in theory be estimated using a Bayesian simulation program such as Stan.

83. Estimating the dynamic version of the model is much more computationally intensive than estimating a static version for each congress. The simulations required for the progressivism case study in Section 2 took less than an hour.

84. See, e.g., Frances E. Lee, Beyond Ideology: Politics, Principles and Partisanship in the U.S. Senate (Chicago: University of Chicago Press, 2009); Aldrich, John H., Montgomery, Jacob M., and Sparks, David B., “Polarization and Ideology: Partisan Sources of Low Dimensionality in Scaled Roll Call Analyses,Political Analysis 22, no. 4 (Autumn, 2014): 435–56Google Scholar, doi: 10.1093/pan/mpt048; Noel, Political Ideologies and Political Parties in America.

85. See, e.g., Gerring, Party Ideologies in America; Bawn, Kathleen et al. , “A Theory of Political Parties: Groups, Policy Demands and Nominations in American Politics,Perspectives on Politics 10, no. 3 (2012): 571–97CrossRefGoogle Scholar.

86. Noel, Political Ideologies and Political Parties in America.

87. Olssen, “Dissent from Normalcy,” 267.