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	Multidimensional Item Response Theory	因子分析
分野	Education	研究統計
系統	Latent structure	Process / pipeline
提唱年	2009	1931
提唱者	Mark Reckase; foundations in factor analysis of items (Bock, McDonald)	Louis Leon Thurstone
種類	Item response model with multiple latent ability dimensions	Method
原典	Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer.	Thurstone, L. L. (1947). Multiple Factor Analysis. University of Chicago Press.
別名	MIRT, Multidimensional IRT, Compensatory MIRT, Bifactor IRT	EFA, CFA, latent variable modeling
関連	4	3
概要	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.	Factor analysis is a statistical technique for identifying latent (unobserved) dimensions underlying observed variables, developed by Louis Leon Thurstone in the 1930s and formalized by Jöreskog (1969). Exploratory factor analysis (EFA) discovers unknown factor structure from data; confirmatory factor analysis (CFA) tests hypothesized relationships between observed and latent variables. Essential in psychometrics (test development), organizational research (measuring constructs like leadership style), and biomedicine (identifying disease subtypes), factor analysis reduces dimensionality while revealing conceptual organization in multivariate data.