Estimating Legislators' Preferred Points
Open accessAbstract
This paper shows that agnostic spatial models that simultaneously attempt to estimate legislators' preferred points and ideological locations for the proposals on which they vote, such as the well-known NOMINATE model of Poole and Rosenthal, are not identified. The problem arises because the agnostic estimators inherit the granularity of the voting data and, so, cannot recapture the underlying continuous parameter space. I propose an alternative estimator that achieves identification by modeling the agenda.
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Any 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 Londregan 1999
Section 3.2, “First-Order” Identifying Restrictions (page unavailable), treats the location of the ideological scale as arbitrary and normalizes one legislator’s position to zero. But Eq. (10) in Section 2.2 shows that voting depends on the difference between a legislator’s ideal point and a proposal’s midpoint. Adding a constant to legislators’ ideal points alone would change that difference; the prediction is unchanged if the proposal locations shift with them. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThese 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 Londregan 1999
Section 3, “Issues in Model Identification” (page unavailable), says spatial voting models and their psychometric cousins, Rasch models, are not identified without further restrictions. Section 2.2 equates a spatial-model voting condition with one from an educational-testing model. The copy does not identify the indeterminacies as “additive aliasing” and “scaling invariance,” so it supports the shared identification problem but not those specific characterizations. (LLM, conf=0.82)
Experimental — accuracy not yet measuredIdeal 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 Londregan 1999
Section 3.2 (“First-Order” Identifying Restrictions; page not provided) supports the need to normalize the scale of legislators’ ideal points in the Ladha and linear-probability models. It does not state that dividing a normalizing constant by the square of any nonzero multiplier leaves predictions unchanged; for the Poole–Rosenthal model, it instead says β can be pinned down. (LLM, conf=0.82)
Experimental — accuracy not yet measuredExisting studies on ideal point estimation use two strategies to identify the model: applying two linearly independent restrictions on ideal point parameters, or applying a unit variance restriction.
“Existing studies on ideal point estimation employ two different strategies to identify the model.One is to apply two linearly independent restrictions on the ideal point parameters, u or f in this case.”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Londregan 1999
Section 3.2 (“First-Order” Identifying Restrictions; page not provided) describes identifying models by imposing two restrictions on legislators’ preferred-point locations, including setting one location to zero and another to one in the Ladha and linear-probability models. The passages do not describe a unit-variance restriction as a second strategy, so that part of the attributed claim is unsupported. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe 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 Londregan 1999
The usual procedure for the first identification strategy is to constrain the ideal points of two legislators (liberal and conservative) at arbitrary positions, such as -1 and +1.
“In particular, the usual procedure is to constrain the ideal points of two legislators (liberal and conservative) at arbitrary positions, such as À1 and þ1 (see, e.g., Londregan 1999; Clinton, Jackman, and Rivers 2004).”
From Birds of the Same Feather Tweet Together: Bayesian Ideal Point Estimation Using Twitter Data (2015) · cites this paper as Londregan 1999
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Cites
Cox, D. R., & Hinkley, D. V. (1974) · doi:10.1007/978-1-4899-2887-0 · Cited by 3,089 · see citing works
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Research works printed but not linked: 11
- Birnbaum, A. 1968. "Some Latent Trait Models and Their Use in Inferring an Examinee's Ability." In Statistical Theories of Mental Test Scores, eds. F. M. Lord and M. R. Novick. Reading, MA: Addison Wesley. https://doi.org/10.1093/oxfordjournals.pan.a029804 Published online by Cambridge University Press
- Gerhard H. Fischer. New York: Springer Verlag.
- Haberman, S. J. 1977. "Maximum Likelihood Estimates in Exponential Response Models." Annals of Statistics 5:815-841.
- Hinich, Melvin J., Lawerence Cahoon, and Peter C. Ordeshook. 1978. "A Statistical Multidimensional Scaling Method Based on the Spatial Theory of Voting." In Graphical Representation of Multivariate Data, ed. P. C. Wang. New York: Harwood, pp. 243-279.
- Londregan, John B. 2000. Legislative Institutions and Ideology in Chile's Democratic Transition. New York: Cambridge University Press.
- Maddala, G. S. 1986. Limited Dependent and Qualitative Variables in Econometrics. New York: Cambridge.
- Poole, Keith T., and Howard Rosenthal. 1991. "Patterns of Congressional Voting." American Journal of Political Science 35:228-278.
- Poole, Keith T., and Howard Rosenthal. 1996. Congress: A Political-Economic History of Roll Call Voting. New York: Oxford University Press.
- Rasch, Georg. 1961. "On General Laws and the Meaning of Measurement in Psychology." Proceedings of the IV Berkeley Symposium on Mathematical Statistics and Probability 4:321-333.
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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
- Authors
- Londregan, J.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Londregan, John
- ORCID
- Londregan, John
- Venue
- Political Analysis
- Publisher
- Cambridge University Press (CUP)
- Published
- 1999
- Volume
- 8
- Issue
- 1
- Pages
- 35-56
- ISSN
- 1047-1987 (ISSN-L)
- 1476-4989
- OpenAlex
- W2053720373
- Cited by
- 159
- References
- 1
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 1 · 2022: 3 · 2021: 4 · 2019: 2 · 2018: 1 · 2017: 4 · 2016: 3 · 2015: 3 · 2014: 6 · 2013: 6 · 2012: 10
- FWCI
- 34.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Political Analysis (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- University of Cambridge
- Topics
- Social Sciences › Political Science and International Relations › Electoral Systems and Political Participation
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Game Theory and Voting Systems
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- legislator preferences, ideological positions, spatial modeling, identification problem, legislative voting
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