INVARIANCE ANALYSES IN LARGE-SCALE STUDIES - OECD Education Working Paper No. 201 - A working paper authorised by OECD

Sep 17, 2026

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Large-scale education surveys such as PISA, TALIS, and PIAAC rely on advanced statistical models to estimate latent trait scores from multiple observed responses. Cross-group comparisons are valid only when the same estimated parameters apply across surveyed groups, making measurement invariance central. This paper addresses parameter invariance through model fit indices that reflect how likely a single set of parameters can be used for all groups. It examines theoretical and practical issues in evaluating invariance, especially for cognitive and non-cognitive scales using confirmatory factor analysis and item response theory.

LanguageEnglish

CategoryResearch & Report

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Pages111

Reading Time4 h 40 min

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Acknowledgements

Abstract

Measurement invariance and model fit indices

Invariance across respondent groups

Evaluating invariance for cognitive and non-cognitive scales

OECD Education Working Papers No. 201 Invariance analyses in large-scale studies Fons J. R. Van de Vijver, Francesco Avvisati, Eldad Davidov, Michael Eid, Jean-Paul Fox, Noémie Le Donné, Kimberley Lek, Bart Meuleman, Marco Paccagnella, Rens van de Schoot [https://dx.doi.org/10.1787/254738dd-en](https://dx.doi.org/10.1787/254738dd-en) Organisation for Economic Co-operation and Development EDU/WKP(2019)9 Unclassified English text only 30 April 2019 DIRECTORATE FOR EDUCATION AND SKILLS INVARIANCE ANALYSES IN LARGE-SCALE STUDIES OECD Education Working Paper No. 201 Fons J. R. van de Vijver (Tilburg University, Editor); Francesco Avvisati (OECD); Eldad Davidov (University of Cologne and University of Zurich); Michael Eid (Free University of Berlin); Jean-Paul Fox (University of Twente); Noémie Le Donné (OECD); Kimberley Lek (Utrecth University); Bart Meuleman (KU Leuven); Marco Paccagnella (OECD); and Rens van de Schoot (Utrecht University) This working paper has been authorised by Andreas Schleicher, Director of the Directorate for Education and Skills, OECD. Francesco Avvisati ([francesco.avvisati@oecd.org](francesco.avvisati@oecd.org)); Noémie Le Donné ([noemie.ledonne@oecd.org](noemie.ledonne@oecd.org)); and Marco Paccagnella ([marco.paccagnella@oecd.org](marco.paccagnella@oecd.org)) JT03446903 This document, as well as any data and map included herein, are without prejudice to the status of or sovereignty over any territory, to the delimitation of international frontiers and boundaries and to the name of any territory, city or area. OECD Education Working Papers Series OECD Working Papers should not be reported as representing the official views of the OECD or ofits member countries. The opinions expressed and arguments employed herein are those of the author(s) . Working Papers describe preliminary results or research in progress by the author(s) and are published to stimulate discussion on a broad range of issues on which the OECD works. Comments on Working Papers are welcome, and may be sent to the Directorate for Education and Skills, OECD, 2 rue André-Pascal, 75775 Paris Cedex 16, France. This document, as well as any data and map included herein, are without prejudice to the status of or sovereignty over any territory, to the delimitation of international frontiers and boundaries and to the name of any territory, city or area. The statistical data for Israel are supplied by and under the responsibility of the relevant Israeli authorities. The use of such data by the OECD is without prejudice to the status of the Golan Heights, East Jerusalem and Israeli settlements in the West Bank under the terms of international law. You can copy, download or print OECD content for your own use, and you can include excerpts from OECD publications, databases and multimedia products in your own documents, presentations, blogs, websites and teaching materials, provided that suitable acknowledgement of OECD as source and copyright owner is given. All requests for public or commercial use and translation rights should be [submitted to](submitted to rights@oecd.org)[ ](submitted to rights@oecd.org)[rights@oecd.org](submitted to rights@oecd.org). Comment on the series is welcome, and should be sent to [edu.contact@oecd.org](edu.contact@oecd.org). This working paper has been authorised by Andreas Schleicher, Director of the Directorate for Education and Skills, OECD. [www.oecd.org/edu/workingpapers](www.oecd.org/edu/workingpapers) © OECD 2018 Acknowledgements This report is the result of the work conducted by a group of experts, contracted by the OECD to provide advice and guidance on how to address the issue of measurement invariance in international surveys. Francesco Avvisati, Miloš Kankaraš, Noémie Le Donné and Marco Paccagnella followed and co-ordinated the work of the group. Chapter 1 has been drafted by Fons van de Vijver, who chaired and supervised the work of

FAQs

Why is measurement invariance required for comparing survey results across groups?

Cross-group comparisons are valid only when the same set of estimated parameters holds in each surveyed group. Without invariance, differences may reflect model misfit rather than true score differences.

How does the paper frame scale invariance across respondent groups?

Scale invariance is typically framed as how well a single model fits the responses of all groups. Model fit indices are used to gauge the likelihood that one parameter set can be applied universally.

Which statistical frameworks are highlighted for evaluating invariance in large-scale surveys?

The paper describes common procedures developed within confirmatory factor analysis and item response theory for evaluating invariance of cognitive and non-cognitive scales.

Sep 17, 2026

Uploaded by Elsa