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	बहु-समूह राश मॉडल	बहु-समूह आइटम रिस्पांस थ्योरी (MG-IRT)
क्षेत्र	मनोमिति	मनोमिति
परिवार	Latent structure	Latent structure
उद्भव वर्ष	1960 (Rasch); 1980s–1990s (multi-group extensions)	1990s
प्रवर्तक	Georg Rasch (single-group); extended to multi-group applications by Fischer, Molenaar, and others	Multiple contributors; formalized by Birnbaum (1968) for IRT; multi-group extensions developed through 1980s–1990s
प्रकार	Item response model / measurement invariance test	Latent trait / measurement invariance
मौलिक स्रोत	Fischer, G. H. & Molenaar, I. W. (Eds.) (1995). Rasch Models: Foundations, Recent Developments, and Applications. Springer. ISBN: 978-0387944296	Embretson, S. E. & Reise, S. P. (2000). Item Response Theory for Psychologists. Lawrence Erlbaum Associates. ISBN: 978-0805828191
उपनाम	MG-Rasch, Rasch measurement invariance, multi-group 1PL IRT, cross-group Rasch analysis	MG-IRT, multiple-group IRT, multi-group latent trait model, IRT across groups
संबंधित	6	6
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.	Multi-group item response theory fits IRT models simultaneously across two or more defined groups — such as males and females, or different cultural samples — to determine whether item parameters are invariant across those groups. It is the primary IRT-based framework for testing measurement equivalence and detecting differential item functioning (DIF) at the model level.