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	Multidimensional Item Response Theory	Cognitive Diagnostic Modeling
Field	Education	Education
Family	Latent structure	Latent structure
Year of origin	2009	2010
Originator	Mark Reckase; foundations in factor analysis of items (Bock, McDonald)	Tatsuoka; DiBello, Roussos & Stout; Junker & Sijtsma; de la Torre
Type	Item response model with multiple latent ability dimensions	Restricted latent class models for diagnosing mastery of discrete skills
Seminal source	Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer.	Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. Guilford Press. ISBN: 9781606235270
Aliases	MIRT, Multidimensional IRT, Compensatory MIRT, Bifactor IRT	CDM, Diagnostic Classification Models, DCM, DINA / G-DINA Models
Related	4	4
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.	Cognitive diagnostic models (CDMs), also called diagnostic classification models, are restricted latent class models that report not a single ability score but a profile of which discrete skills or attributes a student has mastered. Each item is linked to the attributes it requires through a Q-matrix, and the model classifies every examinee into one of the possible binary mastery patterns. CDMs answer 'which specific skills does this student lack' rather than 'how much overall ability does this student have,' making them central to fine-grained diagnostic and formative assessment.