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	बहु-समूह राश मॉडल	आइटम रिस्पांस थ्योरी (IRT)
क्षेत्र	मनोमिति	मनोमिति
परिवार	Latent structure	Latent structure
उद्भव वर्ष	1960 (Rasch); 1980s–1990s (multi-group extensions)	1952–1968
प्रवर्तक	Georg Rasch (single-group); extended to multi-group applications by Fischer, Molenaar, and others	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
प्रकार	Item response model / measurement invariance test	Probabilistic measurement model
मौलिक स्रोत	Fischer, G. H. & Molenaar, I. W. (Eds.) (1995). Rasch Models: Foundations, Recent Developments, and Applications. Springer. ISBN: 978-0387944296	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
उपनाम	MG-Rasch, Rasch measurement invariance, multi-group 1PL IRT, cross-group Rasch analysis	IRT, latent trait theory, item characteristic curve theory, modern test theory
संबंधित	6	5
सारांश	The multi-group Rasch model fits the one-parameter logistic item response model simultaneously across two or more distinct groups, testing whether item difficulty parameters are invariant across groups. It is the primary psychometric tool for establishing that a scale measures the same latent trait with the same metric in each group, a prerequisite for meaningful score comparisons.	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.