The Factorial Invariance of Responses by Males and Females to a Multidimensional Self-Concept Instrument: Substantive and Methodological Issues

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Abstract
The factorial invariance of responses by preadolescent males and females to a multidimensional self-concept instrument was examined for responses to the Self Description Questionnaire (SDQ). Sets of responses by 500 males and by 500 females were each randomly divided in half to form four groups (M1, M2, Fl, and F2). The factorial invariance of an a priori structure demonstrated the replicability of the structure across cross-validation groups (M1 and M2, F1 and F2) and the generality of the structure across sex (M1 and Fl, M2 and F2). Additional a posteriori structures that better fit the data were derived on the basis of the initial analyses, but the estimated values of the new parameters were not invariant across cross-validation groups or across sex. This suggests that some of the improved fit was illusory and due to capitalizing on chance. However, factor loadings and factor correlations were invariant across sex for a priori and a posteriori structures. Hence the results support the replicability of ...