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	Bayesian Item Response Theory in Politics	Pemodelan Berbilang Aras
Bidang	Political Science	Statistik Penyelidikan
Keluarga	Latent structure	Process / pipeline
Tahun asal	2004	1992
Pengasas	Clinton, Jackman & Rivers (political IRT formulation); Treier & Jackman (latent-trait measurement)	Anthony Bryk and Stephen Raudenbush
Jenis	Latent-variable measurement model for binary and ordinal items	Method
Sumber perintis	Clinton, J., Jackman, S., & Rivers, D. (2004). The Statistical Analysis of Roll Call Data. American Political Science Review, 98(2), 355–370.	Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE Publications.
Alias	Bayesian IRT, Political item response model, Latent trait measurement model, Bayesian latent measurement in politics	HLM, mixed-effects models, random effects models, MLM
Berkaitan	5	3
Ringkasan	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.	Multilevel modeling (also called hierarchical linear modeling, mixed-effects modeling) is a statistical framework for analyzing data organized in nested or clustered structures—students within schools, patients within hospitals, repeated measures within individuals. Developed by Bryk and Raudenbush (1992), it accounts for dependency among observations and partitions variance into levels (within-cluster and between-cluster), enabling valid inference and revealing context effects. Essential in education, medicine, organizational research, and any field where data have natural hierarchies.