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Measurement invariance, factor analysis and factorial invariance
 William Meredith
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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.
Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.
 Birnbaum, M. H. (1985) Relationships among models of salary bias. American Psychologist 40: pp. 8626
 Bloxom, B. (1972) Alternative approaches to factorial invariance. Psychometrika 37: pp. 42540
 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. Educational Testing Service, Princeton, NJ
 Gregory, K. (1991) A reconsideration of bias in employment testing from the perspective of factorial invariance. 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: pp. 6581
 Horn, J. L. Remodeling old models of intelligence. In: Wolman, B. B. eds. (1985) Handbook of intelligence. Wiley, New York
 Horn, J. L. Intellectual ability concepts. In: Sternberg, R. J. eds. (1986) Advances in the psychology of human intelligence (Vol. 3). Erlbaum, Hillsdale, NJ
 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: pp. 17988
 Jöreskog, K. G. (1971) Statistical analysis of sets of congeneric tests. Psychometrika 36: pp. 109133
 Jöreskog, K. G., Sörbom, D. (1988) LISREL 7: A guide to the program and applications. SPSS, Chicago
 Junker, B. W. (1991) Essential independence and likelihood based ability estimation for polytomous items. Psychometrika 56: pp. 25578
 Kearns, R. J. (1971) Latent class models for response emission tests. University of California at Berkeley, Berkeley, CA
 Lord, F. M. (1952) A theory of test scores. Psychometric Society, New York
 Lord, F. M. (1980) Applications of item response theory to practical testing problems. Erlbaum, Hillsdale, NJ
 Lord, F. M., Novick, M. R. (1968) Statistical theories of mental test scores. AddisonWesley, Reading, MA
 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: pp. 50211
 Mellenbergh, G. J. (1989) Item bias and item response theory. International Journal of Educational Research 13: pp. 12743
 Meredith, W. (1964) Notes on factorial invariance. Psychometrika 29: pp. 17785
 Meredith, W. (1971) Poisson distributions of error in Mental Test Theory. British Journal of Mathematical and Statistical Psychology 24: pp. 4982
 Meredith, W., Millsap, R. E. (1992) On the misuse of manifest variables in the detection of measurement bias. Psychometrika 57: pp. 289311
 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: pp. 55788
 Muthén, B., Lehman, J. (1985) Multiple group IRT modeling: Applications to item bias analysis. Journal of Educational Statistics 10: pp. 13342
 Sands, L., Terry, H., Meredith, W. (1989) Change and stability in adult intellectual functioning assessed by Wechsler item responses. Psychology and Aging 2: pp. 7987
 Shealy, R., Stout, W. An item response theory model for test bias and differential test functioning. In: Holland, P. W., Wainer, H. eds. (1993) Differential item functioning: Theory and practice. Erlbaum, Hillsdale, NJ
 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: pp. 293325
 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: pp. 22939
 Tryon, R. C. (1958) General dimensions of individual differences: Cluster analysis vs. factor analysis. Educational & Psychological Measurement 18: pp. 44795
 Wechsler, D. (1981) Wechsler Adult Intelligence ScaleRevised. Harcourt, Brace, Jovanovich, New York
 Title
 Measurement invariance, factor analysis and factorial invariance
 Journal

Psychometrika
Volume 58, Issue 4 , pp 525543
 Cover Date
 19931201
 DOI
 10.1007/BF02294825
 Print ISSN
 00333123
 Online ISSN
 18600980
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 measurement invariance
 test bias
 item bias
 factor analysis
 factorial invariance
 selection
 group differences
 fairness
 equity
 Industry Sectors
 Authors

 William Meredith ^{(1)}
 Author Affiliations

 1. Department of Psychology, University of California, 3210 Tolman Hall, 94720, Berkeley, CA