Using Bayesian Aldrich-McKelvey Scaling to Study Citizens’ Ideological Preferences and Perceptions

The forthcoming article, “Using Bayesian Aldrich-McKelvey Scaling to Study Citizens’ Ideological Preferences and Perceptions” by Christopher Hare, David A. Armstrong, Ryan Bakker, Royce Carroll, and Keith T. Poole is currently available on Early View and is summarized here: 

Issue scales (such as the familiar seven-point liberal-conservative scale) have proven to be some of the most useful gauges of citizens’ policy preferences. In the study of contemporary political polarization, for instance, scholars have used survey respondents’ liberal-conservative self-placements to demonstrate that the American public has remained moderate in the face of elite polarization. Respondents are often asked to place political parties and figures (such as presidential candidates) on the same scales, providing estimates of citizens’ ideological perceptions of political stimuli.

However, there are problems with accepting respondents’ issue scale placements at face value. Respondents interpret and use issue scales differently – a problem known as differential-item functioning (DIF). More specifically, respondents have a tendency to understate their own extremism and the extremism of candidates and parties they prefer as well as overstate the extremism of opposing stimuli. For example, in 2012, nearly a third of respondents to the American National Election Study who voted for Obama rated him and themselves as “moderate” or “slightly liberal,” while about 60% of Romney voters placed Obama at the left-most (“extremely liberal”) position.

The problem of DIF contaminates our estimates of respondents’ policy preferences and perceptions that are based on issue scale data. But, there are methods that diagnose and correct for DIF in issue scale usage. One of the most prominent of these methods (and the one we focus on in this paper) is known as Aldrich-McKelvey scaling (for the political scientists John Aldrich and Richard McKelvey, who developed the model). Aldrich-McKelvey scaling directly estimates the ways that individual respondents distort their issue scale placements. The method then corrects for those distortions, producing DIF-corrected estimates of both respondent and stimuli positions on the issue dimension. In this paper we develop a Bayesian implementation of the Aldrich-McKelvey scaling procedures that offers some improvements (namely, the ability to produce uncertainty estimates and handle missing data), but leaves the basic model intact.

Substantively, our use of Bayesian Aldrich-McKelvey (or BAM) scaling to analyze data from the 2012 American National Election Study and the 2010 Cooperative Congressional Election Study reveals that raw liberal-conservative self-placement data masks the true level of polarization in the American electorate. Once we adjust for DIF, there is less ideological overlap between Democrats and Republicans and between Obama and Romney voters than if we rely on respondents’ raw self-placements.

In addition, we exploit the fact that adjusting for DIF also provides cross-comparable estimates of citizens’ ideological perceptions of state political figures. This allows us to place Senators and Senate candidates on a common metric and compare them to external measures of ideology such as DW-NOMINATE scores and Adam Bonica’s CF (Campaign Finance) scores. Our results provide an optimistic assessment of the electorate’s ability to develop ideological profiles of legislators and candidates that are in line with their roll call voting records and sources of campaign contributions. Citizens can ideologically distinguish not only Democrats from Republicans, but between centrist and non-centrist Democratic/Republican elites.


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The American Journal of Political Science (AJPS) is the flagship journal of the Midwest Political Science Association and is published by Wiley.