Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation
Open accessAbstract
Logistic regression models have been used in political science for estimating ideal points of legislators and Supreme Court justices. These models present estimation and identifiability challenges, such as improper variance estimates, scale and translation invariance, reflection invariance, and issues with outliers. We address these issues using Bayesian hierarchical modeling, linear transformations, informative regression predictors, and explicit modeling for outliers. In addition, we explore new ways to usefully display inferences and check model fit.
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Ideal points can be multiplied by any nonzero constant, with the normalizing constant divided by its square, leaving the model predictions unchanged.
“similarly i or j can be multiplied by any nonzero constant, with divided by its square, leaving the model predictions unchanged.”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Bafumi et al. 2005
Section 2.2.2 describes multiplicative aliasing, but its compensating scale factor is linear, not squared. It says multiplying the c parameters by a constant while dividing both the a and b parameters by that same constant preserves the likelihood; it does not support dividing a normalizing constant by the constant’s square. (LLM, conf=0.88)
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Experimental — accuracy not yet measuredAny constant can be added to all ideal point parameters without changing the model's predictions.
“any constant can be added to all the parameters i and j without changing the predictions of the model”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Bafumi et al. 2005
The model described by equation (1) is unidentified.
“The model described by equation ( 1) is unidentified: any constant can be added to all the parameters i and j without changing the predictions of the model; and similarly i or j can be multiplied by any nonzero constant, with divided by its square, leaving the model predictions unchanged.”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Bafumi et al. 2005
These indeterminacies are common to item-response theory models and are called additive aliasing and scaling invariance.
“These indeterminacies, which are common to item-response theory models, are sometimes called "additive aliasing" and "scaling invariance" (see, e.g., Bafumi et al. 2005; Londregan 1999).”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Bafumi et al. 2005
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Self-citationParameter expansion to accelerate EM: the PX-EM algorithm
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Research works printed but not linked: 8
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Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data
Barberá, P. (2015) · Political Analysis · doi:10.1093/pan/mpu011 · Cited by 982 · see citing works
Identification, Interpretability, and
Lauretig, A. (2019) · Proceedings of the Third Workshop on Natural Language Processing and Computational Social Science · doi:10.18653/v1/w19-2102 · Cited by 9 · see citing works
- Authors
- Bafumi, J., Gelman, A., Park, D. K., & Kaplan, N.
- Affiliations
- Columbia University (US)
- Washington University in St. Louis (US)
- University of Houston (US)
- Venue
- Political Analysis
- Publisher
- Cambridge University Press (CUP)
- Published
- 2005
- Volume
- 13
- Issue
- 2
- Pages
- 171-187
- ISSN
- 1047-1987 (ISSN-L)
- 1476-4989
- OpenAlex
- W2125917466
- Cited by
- 245
- References
- 2
- Citations by year
- 2026: 6 · 2025: 27 · 2024: 4 · 2023: 6 · 2022: 6 · 2021: 7 · 2020: 32 · 2019: 19 · 2018: 16 · 2017: 10 · 2016: 8 · 2015: 12 · 2014: 12 · 2013: 9 · 2012: 13
- FWCI
- 8.30
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Political Analysis (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Science Foundation (0318115)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Political Science and International Relations › Electoral Systems and Political Participation
- Social Sciences › General Social Sciences › Computational and Text Analysis Methods
- Keywords
- logistic regression, scale invariance, translation invariance, reflection invariance, outliers, hierarchical models, linear operators, model fit, legislators, Supreme Court justices
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