Linganisha mbinu

	Mfumo wa Rasch wa Ngazi Nyingi	Nadharia ya Itikio la Kipengee (IRT)
Nyanja	Saikometriki	Saikometriki
Familia	Latent structure	Latent structure
Mwaka wa asili	1997	1952–1968
Mwanzilishi	Adams, Wilson & Wu	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Aina	Hierarchical item response model	Probabilistic measurement model
Chanzo asilia	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.	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Majina mbadala	hierarchical Rasch model, random-effects Rasch model, multilevel IRT Rasch, MRCML model	IRT, latent trait theory, item characteristic curve theory, modern test theory
Zinazohusiana	5	5
Muhtasari	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.	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.