Assessing factorial invariance in ordered-categorical measures

Roger E. Millsap, Jenn-Yun Tein

Research output: Contribution to journalReview articlepeer-review

597 Scopus citations


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 (Jöreskog & Sörborn, 1996) and Mplus 2.12 (Muthén & Muthén, 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.

Original languageEnglish (US)
Pages (from-to)479-515
Number of pages37
JournalMultivariate Behavioral Research
Issue number3
StatePublished - 2004

ASJC Scopus subject areas

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)


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