On the relationship between sources of within- and between-group differences and measurement invariance in the common factor model

• Published in: Intelligence (Norwood) 2003-01, Vol.31 (6), p.543-566
• Main Authors: Lubke, Gitta H., Dolan, Conor V., Kelderman, Henk, Mellenbergh, Gideon J.
• Format: Article
• Language: English
• Subjects: Between-group differences; Biological and medical sciences; Common factor model; Confirmatory factor analysis; Fundamental and applied biological sciences. Psychology; Group dynamics; Ingroup-Outgroup differentiation; Intelligence; Intergroup bias; Measurement invariance; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Statistics. Mathematics; Within-group differences
• ISSN: 0160-2896; 1873-7935
• DOI: 10.1016/S0160-2896(03)00051-5

Investigating sources of within- and between-group differences and measurement invariance (MI) across groups is fundamental to any meaningful group comparison based on observed test scores. It is shown that by placing certain restrictions on the multigroup confirmatory factor model, it is possible to investigate the hypothesis that within- and between-group differences are due to the same factors. Moreover, the modeling approach clarifies that absence of measurement bias implies common sources of within- and between-group variation. It is shown how the influence of background variables can be incorporated in the model. The advantages of the modeling approach as compared with other commonly used methods for group comparisons is discussed and illustrated by means of an analysis of empirical data.