Our first application examines a first-order confirmatory factor analysis (CFA) model designed to test the multidimensionality of a theoretical construct. Specifically, this application tests the hypothesis that self-concept (SC), for early adolescents (grade 7), is a multidimensional construct composed of four factors-General SC (GSC), Academic SC (ASC), English SC (ESC), and Mathematics SC (MSC). The theoretical underpinning of this hypothesis derives from the hierarchical model of SC proposed by Shavelson, Hubner, and Stanton (1976). The example is taken from a study by Byrne and Worth Gavin (1996) in which four hypotheses related to the Shavelson et al. model were tested for three groups of children-preadolescents (grade 3), early adolescents (grade 7), and late adolescents (grade 11). Only tests bearing on the multidimensional structure of SC, as it relates to grade 7 children, are relevant in the present chapter. This study followed from earlier work in which the same four-factor structure of SC was tested for adolescents (see Byrne & Shavelson, 1986) and was part of a larger study that focused on the structure of social SC (Byrne & Shavelson, 1996). For a more extensive discussion of the substantive issues and the related findings, readers should refer to the original Byrne and Worth Gavin article.