Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-07T14:59:13.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Measurement Invariance, Factor Analysis and Factorial Invariance

Published online by Cambridge University Press:  01 January 2025

William Meredith
William Meredith*
Affiliation:
University of California at Berkeley
*
Requests for reprints should be addressed to William Meredith, Department of Psychology, University of California, 3210 Tolman Hall, Berkeley, CA 94720.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

measurement invariancetest biasitem biasfactor analysisfactorial invarianceselectiongroup differencesfairnessequity
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 4 , December 1993 , pp. 525 - 543
Copyright
Copyright © 1993 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.

References

Birnbaum, M. H. (1985). Relationships among models of salary bias. American Psychologist, 40, 862–866.CrossRefGoogle Scholar
Bloxom, B. (1972). Alternative approaches to factorial invariance. Psychometrika, 37, 425–440.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
French, J. W., Ekstrom, R. B., & Price, L. A. (1963). Kit of reference tests for cognitive factors, Princeton, NJ: Educational Testing Service.Google Scholar
Gregory, K. (1991). A reconsideration of bias in employment testing from the perspective of factorial invariance, Berkeley, CA: University of California at Berkeley.Google Scholar
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.CrossRefGoogle Scholar
Horn, J. L. (1985). Remodeling old models of intelligence. In Wolman, B. B. (Eds.), Handbook of intelligence, New York: Wiley.Google Scholar
Horn, J. L. (1986). Intellectual ability concepts. In Sternberg, R. J. (Eds.), Advances in the psychology of human intelligence (Vol. 3), Hillsdale, NJ: Erlbaum.Google Scholar
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, 179–188.Google Scholar
Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36, 109–133.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. (1988). LISREL 7: A guide to the program and applications 2nd ed.,, Chicago: SPSS.Google Scholar
Junker, B. W. (1991). Essential independence and likelihood based ability estimation for polytomous items. Psychometrika, 56, 255–278.CrossRefGoogle Scholar
Kearns, R. J. (1971). Latent class models for response emission tests, Berkeley, CA: University of California at Berkeley.Google Scholar
Lord, F. M. (1952). A theory of test scores, New York: Psychometric Society.Google Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Erlbaum.Google Scholar
Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
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.Google Scholar
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.Google Scholar
McCallum, R. C., & Tucker, L. R. (1991). Representing sources of error in the common factor model: Implications for theory and practice. Psychological Bulletin, 109, 502–511.CrossRefGoogle Scholar
Mellenbergh, G. J. (1989). Item bias and item response theory. International Journal of Educational Research, 13, 127–143.CrossRefGoogle Scholar
Meredith, W. (1964). Notes on factorial invariance. Psychometrika, 29, 177–185.CrossRefGoogle Scholar
Meredith, W. (1971). Poisson distributions of error in Mental Test Theory. British Journal of Mathematical and Statistical Psychology, 24, 49–82.CrossRefGoogle Scholar
Meredith, W., & Millsap, R. E. (1992). On the misuse of manifest variables in the detection of measurement bias. Psychometrika, 57, 289–311.CrossRefGoogle Scholar
Millsap, R. E. & Meredith, W. (in press). Statistical evidence in salary discrimination studies: Nonparametric inferential conditions. Applied Psychological Measurement.Google Scholar
Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557–588.CrossRefGoogle Scholar
Muthén, B., & Lehman, J. (1985). Multiple group IRT modeling: Applications to item bias analysis. Journal of Educational Statistics, 10, 133–142.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Shealy, R., & Stout, W. (1993). An item response theory model for test bias and differential test functioning. In Holland, P. W. & Wainer, H. (Eds.), Differential item functioning: Theory and practice, Hillsdale, NJ: Erlbaum.Google Scholar
Shealy, R. & Stout, W. (1993b). A model based standardization approach that separates true bias/DIF as well as item bias/DIF. Psychometrika, 159–194.Google Scholar
Silny, F. & Meredith, W. (1973). Test of a model for response emission tests. Proceedings, 81st Annual Convention, American Psychological Association.Google Scholar
Stout, W. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293–325.CrossRefGoogle Scholar
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, 229–239.CrossRefGoogle Scholar
Tryon, R. C. (1958). General dimensions of individual differences: Cluster analysis vs. factor analysis. Educational & Psychological Measurement, 18, 447–495.CrossRefGoogle Scholar
Wechsler, D. (1981). Wechsler Adult Intelligence Scale-Revised, New York: Harcourt, Brace, Jovanovich.Google Scholar