ABSTRACT
In the years since the printing of my rst AMOS book (Byrne, 2001), there has been a steady, yet moderate increase in reported ndings from tests for multigroup equivalence. A review of the SEM literature, however, reveals most tests for invariance to have been based on the analysis of covariance structures (COVS), as exemplied in Chapters 7 and 9 of this volume. Despite Sörbom’s (1974) introduction of the mean and covariance structures (MACS) strategy in testing for latent mean differences over 30 years ago, only a modicum of studies have been designed to test for latent mean differences across groups based on real (as opposed to simulated) data (see, e.g., Aikin, Stein, & Bentler, 1994; Byrne, 1988b; Cooke, Kosson, & Michie, 2001; Little, 1997; Marsh & Grayson, 1994; Reise, Widaman, & Pugh, 1993; Widaman & Reise, 1997). The aim of this chapter, then, is to introduce you to basic concepts associated with the analysis of latent mean structures, and to walk you through an application that tests for their invariance across two groups. Specically, we test for differences in the latent means of general, academic, English, and mathematics self-concepts across high-and low-track secondary school students. The example presented here draws from two published papers-one that focuses on methodological issues related to testing for invariant covariance and mean structures (Byrne et al., 1989), and one oriented toward substantive issues related to social comparison theory (Byrne, 1988b).
