Assessing factorial invariance in ordered-categorical measures

The factor analysis of ordered-categorical measures has been described in the literature on factor analysis, but the extension of the analysis to the multiple-population case is less well-known. For example, a comprehensive statement of identification conditions for the multiple-population case seems absent in the literature. We review this multiple-population extension here, with an emphasis on model specification and identification. The use of the method in the study of factorial invariance is described. New results on identification are given for a variety of factor structures and types of measures. Two widely-available software packages, LISREL 8.52 (Joreskog & Sorbom, 1996) and Mplus 2.12 (Muthen & Muthen, 1998), are applied in simulated data to illustrate the method. The two programs are shown to have different model specifications for this method, leading to different fit results in some cases. The final section discusses some remaining problems facing researchers who wish to study factorial invariance in ordered-categorical data.