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	Multilevel Item Response Theory	項目応答理論 (IRT)
分野	Education	心理測定学
系統	Latent structure	Latent structure
提唱年	2010	1952–1968
提唱者	Adams, Wilson & Wu; Fox & Glas; De Boeck & Wilson	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
種類	Item response models with a multilevel structure on the latent ability	Probabilistic measurement model
原典	Fox, J.-P. (2010). Bayesian Item Response Modeling: Theory and Applications. Springer.	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
別名	Multilevel IRT, MLIRT, Hierarchical IRT, Explanatory Item Response Models	IRT, latent trait theory, item characteristic curve theory, modern test theory
関連	4	5
概要	Multilevel item response theory (MLIRT) joins two powerful frameworks: an IRT measurement model that turns item responses into a latent ability, and a multilevel structural model that explains how that ability varies across nested groups such as classrooms, schools, or countries. Instead of first scoring a test and then running a multilevel regression on the scores, MLIRT does both at once, so that measurement error in ability is properly carried into the group-level analysis. It is the rigorous way to study how student and school characteristics relate to a latent trait measured by a test.	Item response theory models the probability that a respondent answers an item correctly (or endorses it) as a function of the respondent's latent trait level and the item's own statistical properties — difficulty, discrimination, and guessing. Unlike classical test theory, IRT places persons and items on the same scale, yielding measurement that is sample-independent for items and test-independent for persons.