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Factorial invariance in multilevel confirmatory factor analysis

Authors

  • Ehri Ryu

    Corresponding author
    1. Department of Psychology, Boston College, Chestnut Hill, USA
    • Correspondence should be addressed to Ehri Ryu, Department of Psychology, Boston College, Chestnut Hill, MA 02467, USA (e-mail: ehri.ryu.1@bc.edu).

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  • An earlier version of this paper was presented at the 8th International Amsterdam Multilevel Conference, Amsterdam Netherlands, March 2011. The author would like to thank Stephen G. West for his comments on the earlier version.

Abstract

This paper presents a procedure to test factorial invariance in multilevel confirmatory factor analysis. When the group membership is at level 2, multilevel factorial invariance can be tested by a simple extension of the standard procedure. However level-1 group membership raises problems which cannot be appropriately handled by the standard procedure, because the dependency between members of different level-1 groups is not appropriately taken into account. The procedure presented in this article provides a solution to this problem. This paper also shows Muthén's maximum likelihood (MUML) estimation for testing multilevel factorial invariance across level-1 groups as a viable alternative to maximum likelihood estimation. Testing multilevel factorial invariance across level-2 groups and testing multilevel factorial invariance across level-1 groups are illustrated using empirical examples. SAS macro and Mplus syntax are provided.

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