Linganisha mbinu

	Mfumo wa Rasch wa Ngazi Nyingi	Uchanganuzi wa Kiwango-Nyingi wa Uhakiki wa Kipengele (MCFA)
Nyanja	Saikometriki	Saikometriki
Familia	Latent structure	Latent structure
Mwaka wa asili	1997	1994
Mwanzilishi	Adams, Wilson & Wu	Bengt O. Muthen
Aina	Hierarchical item response model	Latent variable model / 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.	Muthen, B. O. (1994). Multilevel covariance structure analysis. Sociological Methods & Research, 22(3), 376–398.
Majina mbadala	hierarchical Rasch model, random-effects Rasch model, multilevel IRT Rasch, MRCML model	MCFA, multilevel measurement model, two-level CFA, hierarchical CFA
Zinazohusiana	5	6
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.	Multilevel confirmatory factor analysis tests a pre-specified factor structure while simultaneously accounting for the non-independence of observations caused by clustered data. It decomposes item variance into within-group and between-group components, fitting a separate measurement model at each level, making it the standard tool for validating psychometric scales administered within natural groups such as classrooms, clinics, or organisations.