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The asymptotic power of the Lagrange multiplier tests for misspecified IRT models

Authors :
Silvia Cagnone
Lucia Guastadisegni
Vassilis G. S. Vasdekis
Irini Moustaki
Wiberg, Marie
Molenaar, Dylan
González, Jorge
Böckenholt, Ulf
Kim, Jee-Seon
Wiberg M.
Molenaar D.
González J.
Böckenholt U.
Kim J.S.
Guastadisegni L.
Cagnone S.
Moustaki I.
Vadeskis I
Source :
Springer Proceedings in Mathematics & Statistics ISBN: 9783030747718
Publication Year :
2021
Publisher :
Springer Berlin / Heidelberg, 2021.

Abstract

This article studies the power of the Lagrange Multiplier Test and the Generalized Lagrange Multiplier Test to detect measurement non-invariance in Item Response Theory (IRT) models for binary data. We study the performance of these two tests under correct model specification and incorrect distribution of the latent variable. The asymptotic distribution of each test under the alternative hypothesis depends on a noncentrality parameter that is used to compute the power. We present two different procedures to compute the noncentrality parameter and consequently the power of the tests. The performance of the two methods is evaluated through a simulation study. They turn out to be very similar to the classic empirical power but less time consuming. Moreover, the results highlight that the Lagrange Multiplier Test is more powerful than the Generalized Lagrange Multiplier Test to detect measurement non-invariance under all simulation conditions.

Details

Language :
English
ISBN :
978-3-030-74771-8
ISBNs :
9783030747718
Database :
OpenAIRE
Journal :
Springer Proceedings in Mathematics & Statistics ISBN: 9783030747718
Accession number :
edsair.doi.dedup.....1a1754881752cf1e5ebbd291f9ae6e27