Testing factorial invariance across groups: A reconceptualization and proposed new method

Many cross-cultural researchers are concerned with factorial invariance; that is, with whether or not members of different cultures associate survey items, or similar measures, with similar constructs. Researchers usually test items for factorial invariance using confirmatory factor analysis (CFA). CFA, however, poses certain problems that must be dealt with. Primary among them is standardization, the process that assigns units of measurement to the constructs (latent variables). Two standardization procedures and several minor variants have been reported in the literature, but using these procedures when testing for factorial invariance can lead to inaccurate results. In this paper we review basic theory, and propose an extension of Byrne, Shavelson, and Muthen's (1989) procedure for identifying non-invariant items. The extended procedure solves the standardization problem by performing a systematic comparison of all pairs of factor loadings across groups. A numerical example based upon a large published data set is presented to illustrate the utility of the new procedure, particularly with regard to partial factorial invariance.