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	Wielopoziomowy model Rascha	Model Rascha
Dziedzina	Psychometria	Psychometria
Rodzina	Latent structure	Latent structure
Rok powstania	1997	1960
Twórca	Adams, Wilson & Wu	Georg Rasch
Typ	Hierarchical item response model	Item Response Theory / Latent trait model
Źródło pierwotne	Adams, R. J., Wilson, M. & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22(1), 47–76.	Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Danish Institute for Educational Research, Copenhagen.
Inne nazwy	hierarchical Rasch model, random-effects Rasch model, multilevel IRT Rasch, MRCML model	1PL IRT, one-parameter logistic model, Rasch Modeli — 1PL IRT, 1PL model
Pokrewne	5	6
Podsumowanie	The multilevel Rasch model extends the standard Rasch model to data with a nested structure — for example, students within classrooms within schools — by embedding person ability parameters inside a hierarchical linear model. It yields item difficulty estimates on a logit scale while simultaneously partitioning person-ability variance across cluster levels and correcting standard errors for non-independence.	The Rasch model, introduced by Georg Rasch in 1960, is the simplest member of the Item Response Theory (IRT) family. It assigns a single difficulty parameter to each test item and places both item difficulties and person abilities on the same logit scale, enabling direct, sample-independent comparison of items and persons.