The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Assessing Factorial Invariance in Ordered-Categorical Measures
Open accessAbstract
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 multiplepopulation 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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Alternative Ways of Assessing Model Fit
Browne, M. W., & Cudeck, R. (1992) · Sociological Methods & Research · doi:10.1177/0049124192021002005 · Cited by 27,200
Measurement Invariance, Factor Analysis and Factorial Invariance
Meredith, W. (1993) · Psychometrika · doi:10.1007/bf02294825 · Cited by 4,536
A comparison of some methodologies for the factor analysis of non‐normal Likert variables
Muthén, B., & Kaplan, D. (1985) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1985.tb00832.x · Cited by 1,778 · cited 1×
“While WLS estimation was used in the examples, this method is known to require very large samples for adequate performance (Boomsma & Hoogland, 2001; Muthén & Kaplan, 1985).”
MethodLatent Variable Models and Factor Analysis: A Unified Approach
Bartholomew, D., Knott, M., & Moustaki, I. (2011) · Wiley Series in Probability and Statistics · doi:10.1002/9781119970583 · Cited by 842
Item bias and item response theory
Mellenbergh, G. J. (1989) · International Journal of Educational Research · doi:10.1016/0883-0355(89)90002-5 · Cited by 553 · cited 1×
“This approach is consistent with general definitions of measurement invariance that rely on conditional probability (Mellenbergh, 1989; Meredith, 1993; Meredith & Millsap, 1992).”
Multiple Group IRT Modeling: Applications to Item Bias Analysis
Muthén, B., & Lehman, J. (1985) · Journal of Educational Statistics · doi:10.3102/10769986010002133 · Cited by 97 · cited 1×
“For discussions of the relationship between the IRT and common-factor models, see Lord and Novick (1968), Takane and de Leeuw (1987), Muthén and Lehman (1985), or McDonald (1999).”
Method
Research works printed but not linked: 32
- Anderson, T. W. & Rubin, H. (1956). Statistical inference in factor analysis. In J. Neyman (Ed.), Proceedings of the third Berkeley symposium on mathematical statistics and probability, (pp. 111-150). Berkeley, CA: University of California Press.
- Babakus E., 1987, Journal of Marketing Research, 37, 72
- Bartholomew D. J., 1980, Series B, 42, 293
- Bartholomew D. J., 1984, Series B, 46, 120
- 10.1037//0033-2909.105.3.467 · DOI · Paper page
- Bock R. D., 1981, Psychometrika, 46, 443, 10.1007/BF02293801 · DOI · Paper page
- Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley. · DOI · Paper page
- Bollen K. A., 1985, Sociological Methods and Research, 14, 155, 10.1177/0049124185014002003 · DOI
- Boomsma, A. & Hoogland, J. J. (2001). The robustness of LISREL modeling revisited. In R. Cudeck, S. Du Toit & D. Sorbom (Eds.), Structural equation modeling: Present and future. (pp. 139-168). Lincolnwood, IL: Scientific Software Inc.
- Browne, M. W. & Arminger, G. (1995). Specification and estimation of mean and covariance structure models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 185-249). New York: Plenum. · DOI · Paper page
- Christoffersson A., 1975, Psychometrika, 40, 5, 10.1007/BF02291477 · DOI · Paper page
- Joreskog, K. G. (1979). A general approach to confirmatory factor analysis with addendum. In K. G. Joreskog, D. Sorbom, & J. Magidson (Eds.), Advances in factor analysis and structural equation models (pp. 21-43). New York: Abt Associates.
- 10.1007/BF00152012 · DOI · Paper page
- Joreskog, K. G. (1993). Latent variable modeling with ordinal variables. In K. Haagen, D. J. Bartholomew, & M.Deistler (Eds.), Statistical modeling and latent variables (pp. 163-171). Amsterdam: North-Holland.
- 10.1207/S15327906347-387 · DOI · Paper page
- Lee S. Y., 1989, Psychometrika, 54, 63, 10.1007/BF02294449 · DOI
- Lord, F. M. & Novick, M. E. (1968). Statistical theories of mental test scores. Reading: Addison-Wesley.
- Meredith W., 1992, Psychometrika, 57, 289, 10.1007/BF02294510 · DOI · Paper page
- 10.1207/S15328007SEM0801_1 · DOI
- Mislevy R. J., 1986, Journal of Educational Statistics, 11, 3, 10.3102/10769986011001003 · DOI · Paper page
- Muthen B. O., 1978, Psychometrika, 43, 551, 10.1007/BF02293813 · DOI · Paper page
- Muthen B. O., 1984, Psychometrika, 49, 115, 10.1007/BF02294210 · DOI · Paper page
- Muthen B. O., 1981, Psychometrika, 46, 407, 10.1007/BF02293798 · DOI · Paper page
- Olsson U. H., 1979, Multivariate Behavioral Research, 14, 485, 10.1207/s15327906mbr1404_7 · DOI · Paper page
- 10.1016/0167-9473(90)90100-V · DOI
- Rigdon E. E., 1991, Journal of Marketing Research, 28, 491, 10.1177/002224379102800412 · DOI · Paper page
- Satorra, A. (1992). Asymptotic robust inferences in the analysis of mean and covariance structures. In P. V. Marsden (Ed.), Sociological methodology 1992 (pp. 249-278). Oxford: Blackwell Publishers. · DOI
- Satorra, A. (1993a). Asymptotic robust inferences in multiple-group analysis of augmentedmoment structures. In C. M. Cuadras & C. R. Rao (Eds.), Multivariate analysis: Future directions 2 (pp. 211-229). Amsterdam: Elsevier. · doi:10.1016/b978-0-444-81531-6.50018-0
- Satorra, A. (1993b). Multi-sample analysis of moment structures: Asymptotic validity of inferences based on second-order moments. In K. Haagen, D. J. Bartholomew, & M. Deistler (Eds.), Statistical modeling and latent variables (pp. 283-298). Amsterdam: North-Holland.
- Satorra, A. & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications to developmental research (pp. 399-419). Newbury Park: Sage.
- Shapiro, A. (1985). Identifiability of factor analysis: Some results and open problems. Linear Algebra and its Applications, 70, 1-7. · doi:10.1016/0024-3795(85)90038-2
- Takane Y., 1987, Psychometrika, 52, 393, 10.1007/BF02294363 · DOI · Paper page
Cited by
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012) · Psychological Methods · doi:10.1037/a0029315 · Cited by 2,816
Rutkowski, L., & Svetina, D. (2014) · Educational and Psychological Measurement · doi:10.1177/0013164413498257 · Cited by 767
Eaton, N. R., Keyes, K. M., Krueger, R. F., Balsis, S., Skodol, A. E., Markon, K. E., Grant, B. F., & Hasin, D. S. (2012) · Journal of Abnormal Psychology · doi:10.1037/a0024780 · Cited by 701
Sass, D. A. (2011) · Journal of Psychoeducational Assessment · doi:10.1177/0734282911406661 · Cited by 531
Karaca, O., Çalışkan, S. A., & Demir, K. (2021) · BMC Medical Education · doi:10.1186/s12909-021-02546-6 · Cited by 377
Metadata
- Authors
- Millsap, R. E., & Yun-Tein, J.
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 2004-07
- Volume
- 39
- Issue
- 3
- Pages
- 479-515
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W1969027278
- Cited by
- 862
- References
- 6
- FWCI
- 5.76
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Assessing Factorial Invariance in Ordered-Categorical Measures. https://app.cochat.ai/papers/10.1207/s15327906mbr3903_4
- The paper
- Millsap, R. E., & Yun-Tein, J. (2004). Assessing Factorial Invariance in Ordered-Categorical Measures. Multivariate Behavioral Research. https://doi.org/10.1207/s15327906mbr3903_4
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
