Linganisha mbinu

	Upimishaji wa uhakikisho wa kipimo cha ordinal	Nadharia ya Itikio la Kipengee (IRT)
Nyanja	Saikometriki	Saikometriki
Familia	Latent structure	Latent structure
Mwaka wa asili	1984–2011	1952–1968
Mwanzilishi	Roger Millsap; Bengt Muthén	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Aina	Multi-group model comparison	Probabilistic measurement model
Chanzo asilia	Millsap, R. E. (2011). Statistical Approaches to Measurement Invariance. Routledge. ISBN: 978-1848728936	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Majina mbadala	ordinal MI, measurement invariance for ordinal data, ordinal CFA invariance, categorical measurement invariance	IRT, latent trait theory, item characteristic curve theory, modern test theory
Zinazohusiana	6	5
Muhtasari	Ordinal measurement invariance testing evaluates whether a multi-group confirmatory factor model holds equivalent measurement properties across groups when scale items are ordinal — such as Likert-type response scales. It uses polychoric correlations and categorical estimators (WLSMV/DWLS) rather than Pearson-based methods, correcting the systematic bias that arises when ordinal data are treated as continuous.	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.