Use of the Lagrange Multiplier Test for Assessing Measurement Invariance under Model Misspecification

Autor/inn/en	Guastadisegni, Lucia; Cagnone, Silvia; Moustaki, Irini; Vasdekis, Vassilis
Titel	Use of the Lagrange Multiplier Test for Assessing Measurement Invariance under Model Misspecification
Quelle	In: Educational and Psychological Measurement, 82 (2022) 2, S.254-280 (27 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Cagnone, Silvia)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1644
DOI	10.1177/00131644211020355
Schlagwörter	Measurement; Statistical Analysis; Item Response Theory; Test Items; Statistical Distributions; Hypothesis Testing + Suchen Sie Ihr Suchwort? Messverfahren; Statistische Analyse; Item-Response-Theorie; Test content; Testaufgabe; Wahrscheinlichkeitsverteilung; Hypothesenprüfung; Hypothesentest
Abstract	This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01