Abstract
Several concepts are introduced and defined: measurement invariance, structural bias, weak measurement invariance, strong factorial invariance, and strict factorial invariance. It is shown that factorial invariance has implications for (weak) measurement invariance. Definitions of fairness in employment/admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness/equity to exist. Implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Birnbaum, M. H. (1985). Relationships among models of salary bias.American Psychologist, 40, 862–6.
Bloxom, B. (1972). Alternative approaches to factorial invariance.Psychometrika, 37, 425–40.
Chang, H. & Mazzeo, J. (1993, June). The identifiability of expected score in conceptualizations of differential item functioning for polytomously scored items. Paper presented at Psychometric Society Annual Meeting.
French, J. W., Ekstrom, R. B., & Price, L. A. (1963).Kit of reference tests for cognitive factors. Princeton, NJ: Educational Testing Service.
Gregory, K. (1991).A reconsideration of bias in employment testing from the perspective of factorial invariance. Unpublished doctoral dissertation, University of California at Berkeley, Berkeley, CA.
Guttman, L. (1955). The determinacy of factor score matrices with implications for five basic problems in common factor theory.British Journal of Statistical Psychology, 8, 65–81.
Horn, J. L. (1985). Remodeling old models of intelligence. In B. B. Wolman (Ed.),Handbook of intelligence. New York: Wiley.
Horn, J. L. (1986). Intellectual ability concepts. In R. J. Sternberg (Ed.),Advances in the psychology of human intelligence (Vol. 3). Hillsdale, NJ: Erlbaum.
Horn, J. L., McArdle, J. J., Mason, R. (1983). When is invariance not invariant: A practical scientist's look at the ethereal concept of factor invariance.The Southern Psychologist, 1, 179–88.
Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests.Psychometrika, 36, 109–133.
Jöreskog, K. G. & Sörbom, D. (1988).LISREL 7: A guide to the program and applications (2nd ed.). Chicago: SPSS.
Junker, B. W. (1991). Essential independence and likelihood based ability estimation for polytomous items.Psychometrika, 56, 255–78.
Kearns, R. J. (1971).Latent class models for response emission tests. Unpublished doctoral dissertation, University of California at Berkeley, Berkeley, CA.
Lord, F. M. (1952). A theory of test scores. New York: Psychometric Society;Psychometric Monograph, No. 7.
Lord, F. M. (1980).Applications of item response theory to practical testing problems. Hillsdale, NJ: Erlbaum.
Lord, F. M. & Novick, M. R. (1968).Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
Mazzeo, J. & Chang, H. (1993, June).Detection of differential item functioning for polytomously scored items. An adaptation of Shealy and Stout's SIBTEST procedure. Paper presented at Psychometric Society Annual Meeting.
McArdle, J. J. & Cattell, R. B. (in press). Structural equation models of factorial invariance in parallel proportion profiles and oblique confactor problems.Multivariate Behavioral Research.
McCallum, R. C. & Tucker, L. R. (1991). Representing sources of error in the common factor model: Implications for theory and practice.Psychological Bulletin, 109, 502–11.
Mellenbergh, G. J. (1989). Item bias and item response theory.International Journal of Educational Research, 13, 127–43.
Meredith, W. (1964). Notes on factorial invariance.Psychometrika, 29, 177–85.
Meredith, W. (1971). Poisson distributions of error in Mental Test Theory.British Journal of Mathematical and Statistical Psychology, 24, 49–82.
Meredith, W. & Millsap, R. E. (1992). On the misuse of manifest variables in the detection of measurement bias.Psychometrika, 57, 289–311.
Millsap, R. E. & Meredith, W. (in press). Statistical evidence in salary discrimination studies: Nonparametric inferential conditions.Applied Psychological Measurement.
Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations.Psychometrika, 54, 557–88.
Muthén, B. & Lehman, J. (1985). Multiple group IRT modeling: Applications to item bias analysis.Journal of Educational Statistics, 10, 133–42.
Sands, L., Terry, H., & Meredith, W. (1989). Change and stability in adult intellectual functioning assessed by Wechsler item responses.Psychology and Aging, 2, 79–87.
Shealy, R. & Stout, W. (1993a). An item response theory model for test bias and differential test functioning. In P. W. Holland & H. Wainer.Differential item functioning: Theory and practice. Hillsdale, NJ: Erlbaum.
Shealy, R. & Stout, W. (1993b). A model based standardization approach that separates true bias/DIF as well as item bias/DIF.Psychometrika, 159–194.
Silny, F. & Meredith, W. (1973). Test of a model for response emission tests.Proceedings, 81st Annual Convention, American Psychological Association.
Stout, W. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation.Psychometrika, 55, 293–325.
Sörbom, D. (1974). A general method for studying differences in factor means and factor structures between groups.British Journal of Mathematical and Statistical Psychology, 28, 229–39.
Tryon, R. C. (1958). General dimensions of individual differences: Cluster analysis vs. factor analysis.Educational & Psychological Measurement, 18, 447–95.
Wechsler, D. (1981).Wechsler Adult Intelligence Scale-Revised. New York: Harcourt, Brace, Jovanovich.
Author information
Authors and Affiliations
Additional information
Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.
Rights and permissions
About this article
Cite this article
Meredith, W. Measurement invariance, factor analysis and factorial invariance. Psychometrika 58, 525–543 (1993). https://doi.org/10.1007/BF02294825
Issue Date:
DOI: https://doi.org/10.1007/BF02294825