Сравнение методов

	Тестирование инвариантности порядковых измерений	Теория отклика на задания (IRT)
Область	Психометрия	Психометрия
Семейство	Latent structure	Latent structure
Год появления	1984–2011	1952–1968
Автор метода	Roger Millsap; Bengt Muthén	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Тип	Multi-group model comparison	Probabilistic measurement model
Основополагающий источник	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.
Другие названия	ordinal MI, measurement invariance for ordinal data, ordinal CFA invariance, categorical measurement invariance	IRT, latent trait theory, item characteristic curve theory, modern test theory
Связанные	6	5
Сводка	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.