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Ends Against the Middle: Measuring Latent Traits when Opposites Respond the Same Way for Antithetical Reasons

Published online by Cambridge University Press:  09 January 2023

JBrandon Duck-Mayr Open the ORCID record for JBrandon Duck-Mayr [Opens in a new window]  and
Jacob Montgomery Open the ORCID record for Jacob Montgomery [Opens in a new window]
JBrandon Duck-Mayr*
Affiliation:
Department of Government, The University of Texas at Austin, 158 W 21st ST STOP A1800, Austin, TX 78712-1704, USA. e-mail: jbrandon.duckmayr@austin.utexas.edu
Jacob Montgomery
Affiliation:
Department of Political Science, Washington University in St. Louis, One Brookings Drive, Box 1063, St. Louis, MO 63130, USA. e-mail: jacob.montgomery@wustl.edu
*
Corresponding author JBrandon Duck-Mayr
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Abstract

Standard methods for measuring latent traits from categorical data assume that response functions are monotonic. This assumption is violated when individuals from both extremes respond identically, but for conflicting reasons. Two survey respondents may “disagree” with a statement for opposing motivations, liberal and conservative justices may dissent from the same Supreme Court decision but provide ideologically contradictory rationales, and in legislative settings, ideological opposites may join together to oppose moderate legislation in pursuit of antithetical goals. In this article, we introduce a scaling model that accommodates ends against the middle responses and provide a novel estimation approach that improves upon existing routines. We apply this method to survey data, voting data from the U.S. Supreme Court, and the 116th Congress, and show that it outperforms standard methods in terms of both congruence with qualitative insights and model fit. This suggests that our proposed method may offer improved one-dimensional estimates of latent traits in many important settings.

Keywords

measurementBayesian statisticsitem response

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Type
Article
Information
Political Analysis , Volume 31 , Issue 4 , October 2023 , pp. 606 - 625
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

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