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.

Lucia Guastadisegni, Silvia Cagnone, Irini Moustaki, Vassilis Vasdekis (2022). Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 82(2), 254-280 [10.1177/00131644211020355].

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

Lucia Guastadisegni
Primo
;
Silvia Cagnone
Secondo
;
2022

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.
2022
Lucia Guastadisegni, Silvia Cagnone, Irini Moustaki, Vassilis Vasdekis (2022). Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 82(2), 254-280 [10.1177/00131644211020355].
Lucia Guastadisegni; Silvia Cagnone; Irini Moustaki; Vassilis Vasdekis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/821406
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