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The Asymptotic Power of the Lagrange Multiplier Tests for Misspecified IRT Models

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Quantitative Psychology (IMPS 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 353))

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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.

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Author information

Authors and Affiliations

  1. University of Bologna, Bologna, Italy

    Lucia Guastadisegni & Silvia Cagnone

  2. London School of Economics and Political Science, London, UK

    Irini Moustaki

  3. Athens University of Economics and Business, Athens, Greece

    Vassilis Vasdekis

Authors
  1. Lucia Guastadisegni
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  2. Silvia Cagnone
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  3. Irini Moustaki
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  4. Vassilis Vasdekis
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Corresponding author

Correspondence to Lucia Guastadisegni .

Editor information

Editors and Affiliations

  1. Department of Statistics, USBE, Umeå University, Umeå, Västerbottens Län, Sweden

    Marie Wiberg

  2. Department of Psychology, University of Amsterdam, Amsterdam, The Netherlands

    Dylan Molenaar

  3. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

    Jorge González

  4. Kellogg School of Management, Northwestern University, Evanston, IL, USA

    Ulf Böckenholt

  5. Department of Educational Psychology, University of Wisconsin-Madison, Madison, WI, USA

    Jee-Seon Kim

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Guastadisegni, L., Cagnone, S., Moustaki, I., Vasdekis, V. (2021). The Asymptotic Power of the Lagrange Multiplier Tests for Misspecified IRT Models. In: Wiberg, M., Molenaar, D., González, J., Böckenholt, U., Kim, JS. (eds) Quantitative Psychology. IMPS 2020. Springer Proceedings in Mathematics & Statistics, vol 353. Springer, Cham. https://doi.org/10.1007/978-3-030-74772-5_25

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