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	Multidimensional Item Response Theory	Item Response Theory
Field	Education	Psychometrics
Family	Latent structure	Latent structure
Year of origin	2009	1952–1968
Originator	Mark Reckase; foundations in factor analysis of items (Bock, McDonald)	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Type	Item response model with multiple latent ability dimensions	Probabilistic measurement model
Seminal source	Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer.	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Aliases	MIRT, Multidimensional IRT, Compensatory MIRT, Bifactor IRT	IRT, latent trait theory, item characteristic curve theory, modern test theory
Related	4	5
Summary	Multidimensional item response theory (MIRT) generalizes IRT to tests that measure more than one latent ability at once. Instead of a single ability θ, each examinee is characterized by a vector of abilities, and each item by a vector of discriminations indicating how strongly it taps each dimension. MIRT unites the logic of item response theory with the structure of factor analysis, letting analysts model, for example, that a word-problem item draws on both reading and mathematics. Synthesized in Reckase's authoritative treatment, it underlies the analysis of complex, multi-skill assessments.	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.