METHODS article

Front. Appl. Math. Stat.

Sec. Statistics and Probability

Basically tau-equivalent confirmatory factor analysis considering item particularities

  • 1. Goethe University Frankfurt, Frankfurt, Germany

  • 2. Zhejiang University, Hangzhou, China

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Abstract

We propose the basically tau-equivalent measurement model for confirmatory factor analysis that differs from the original tau-equivalent measurement model through the replacement of strict tau equivalence by basic tau equivalence enabling the account of item particularities. Considered in the framework of linear regression analysis, basic tau equivalence means a slope of zero across the set of factor loading, but without their restriction to exact correspondence. Allowing for deviations from correspondence enables the account of item particularities while zero slope keeps away systematic influences unrelated to the attribute of interest. This measurement model is illustrated using an example matrix and the data from two simulation studies. The fit results of two described methods for realizing basic tau equivalence are highly correlated withvalidate each other.

Summary

Keywords

confirmatory factor analysis1, congeneric5, factor loading replacementconstant7, item-position effect6, measurement mode2, tau equivalent3, tauequivalence4

Received

31 December 2025

Accepted

18 February 2026

Copyright

© 2026 Schweizer and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Karl Schweizer

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All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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