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On Matters of Invariance in Latent Variable Models: Reflections on the Concept, and its Relations in Classical and Item Response Theory

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Statistical Models for Data Analysis

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Abstract

An overview is provided of the author’s program of research on measurement invariance. Two questions are addressed. First, when do theoreticians and practitioners talk about invariance, and what is it that we are talking about? Second, is invariance only a property of latent variable models such as IRT and is there invariance in classical test theory? If so, what is it for the: observed score, and latent variable formulations.

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Author information

Authors and Affiliations

  1. Department of ECPS (also Department of Statistics, and Institute of Applied Mathematics), University of British Columbia, Vancouver, BC, Canada

    Bruno D. Zumbo

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  1. Bruno D. Zumbo
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Correspondence to Bruno D. Zumbo .

Editor information

Editors and Affiliations

  1. Department of Economics, and Management, University of Pavia, Via San Felice 7, Pavia, 27100, Italy

    Paolo Giudici

  2. Department of Economics, and Business, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Ingrassia

  3. , Department of Statistics, University of Rome "La Sapienza", Piazzale Aldo Moro 5, Rome, 00185, Italy

    Maurizio Vichi

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Zumbo, B.D. (2013). On Matters of Invariance in Latent Variable Models: Reflections on the Concept, and its Relations in Classical and Item Response Theory. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_45

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