Linganisha mbinu

	Multilevel Differential Item Functioning	Nadharia ya Itikio la Kipengee (IRT)
Nyanja	Saikometriki	Saikometriki
Familia	Latent structure	Latent structure
Mwaka wa asili	2001	1952–1968
Mwanzilishi	Kamata (2001) and subsequent multilevel IRT/DIF literature	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Aina	Bias detection / multilevel measurement model	Probabilistic measurement model
Chanzo asilia	French, B. F., & Finch, W. H. (2008). Multigroup confirmatory factor analysis: Locating the invariant referent sets. Structural Equation Modeling: A Multidisciplinary Journal, 15(1), 96–113.	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Majina mbadala	multilevel DIF, hierarchical DIF analysis, cross-level DIF, ML-DIF	IRT, latent trait theory, item characteristic curve theory, modern test theory
Zinazohusiana	5	5
Muhtasari	Multilevel DIF analysis detects whether individual test or survey items function differently across groups when respondents are clustered within higher-level units — such as students nested in schools, employees in organizations, or patients in clinics. By accounting for hierarchical data structure, it separates genuine item bias from artificial DIF signals caused by ignoring clustering.	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.