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.
Factorial invariance in multilevel confirmatory factor analysis
Article first published online: 17 MAY 2013
© 2013 The British Psychological Society
British Journal of Mathematical and Statistical Psychology
Volume 67, Issue 1, pages 172–194, February 2014
How to Cite
Ryu, E. (2014), Factorial invariance in multilevel confirmatory factor analysis. British Journal of Mathematical and Statistical Psychology, 67: 172–194. doi: 10.1111/bmsp.12014
- Issue published online: 13 JAN 2014
- Article first published online: 17 MAY 2013
- Manuscript Accepted: 8 APR 2013
- Manuscript Revised: 28 MAR 2013
- Manuscript Received: 17 JAN 2012
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.