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	Bayesian Item Response Theory in Politics	NOMINATE
Field	Political Science	Political Science
Family	Latent structure	Latent structure
Year of origin	2004	1985
Originator	Clinton, Jackman & Rivers (political IRT formulation); Treier & Jackman (latent-trait measurement)	Keith T. Poole and Howard Rosenthal
Type	Latent-variable measurement model for binary and ordinal items	Spatial scaling model of roll-call voting
Seminal source	Clinton, J., Jackman, S., & Rivers, D. (2004). The Statistical Analysis of Roll Call Data. American Political Science Review, 98(2), 355–370.	Poole, K. T., & Rosenthal, H. (1985). A Spatial Model for Legislative Roll Call Analysis. American Journal of Political Science, 29(2), 357–384.
Aliases	Bayesian IRT, Political item response model, Latent trait measurement model, Bayesian latent measurement in politics	DW-NOMINATE, W-NOMINATE, Nominal Three-Step Estimation, Poole-Rosenthal scores
Related	5	3
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.	NOMINATE — Nominal Three-step Estimation — is the family of spatial scaling procedures developed by Keith Poole and Howard Rosenthal to recover legislators' ideological positions from roll-call votes. Each legislator and the yea and nay outcomes of each vote are placed in a low-dimensional space, and a normal (Gaussian) deterministic utility plus a random shock governs choices. Fitted by maximum likelihood, NOMINATE produces the canonical ideal-point coordinates used to chart polarization across two centuries of the U.S. Congress, with the dynamic DW-NOMINATE variant allowing positions to drift smoothly over time.