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	Bayesian Item Response Theory in Politics	Ideal Point Estimation
Field	Political Science	Political Science
Family	Latent structure	Latent structure
Year of origin	2004	2004
Originator	Clinton, Jackman & Rivers (political IRT formulation); Treier & Jackman (latent-trait measurement)	Clinton, Jackman & Rivers (Bayesian formulation); Poole & Rosenthal (spatial tradition)
Type	Latent-variable measurement model for binary and ordinal items	Latent-variable spatial model of binary choice data
Seminal source	Clinton, J., Jackman, S., & Rivers, D. (2004). The Statistical Analysis of Roll Call Data. American Political Science Review, 98(2), 355–370.	Clinton, J., Jackman, S., & Rivers, D. (2004). The Statistical Analysis of Roll Call Data. American Political Science Review, 98(2), 355–370.
Aliases	Bayesian IRT, Political item response model, Latent trait measurement model, Bayesian latent measurement in politics	Ideal point model, Item response theory for roll calls, Spatial voting model, Bayesian ideal points
Related	5	4
Summary	Bayesian item response theory (IRT) in political science measures latent traits — such as ideology, level of democracy, or political knowledge — from observed binary or ordinal items, treating each item's response probability as a function of a respondent's position on the latent scale. Formalized for politics by Clinton, Jackman, and Rivers (2004) for roll-call votes and extended by Treier and Jackman (2008) to measure democracy as a latent variable, the approach combines item characteristic curves with prior distributions and estimates everything jointly by Markov chain Monte Carlo, yielding full posterior uncertainty for every subject's latent score.	Ideal point estimation recovers the latent policy positions — ideal points — of political actors from their observed binary choices, most often legislators' yea/nay votes on roll calls. Building on the spatial theory of voting and formalized as a Bayesian item-response model by Clinton, Jackman, and Rivers in 2004, it places each legislator and each bill in a low-dimensional policy space and estimates positions so that the probability a legislator votes yea increases as the bill's 'yea' outcome moves closer to that legislator's ideal point.