ABSTRACT
This chapter represents an extension to Chapter 28 in this volume on basic structural equation modeling (SEM). Here we consider the development and testing of theoretical models in two more advanced contexts. First, multiple sample SEM (MS-SEM) considers the invariance (or equality) of parameters across populations (i.e., equivalence of covariance structures). For example, Jöreskog and Sörbom (1993, Example 10) tested whether the same factor structure of the SAT verbal and math sections is present in two groups of students (e.g., by examining invariance of factor loadings, the factor correlation, and the measurement error variances). Second, structured means SEM (SM-SEM) additionally assesses mean differences between populations (i.e., intercept parameters). For example, Jöreskog and Sörbom (1993, Example 13) examined mean differences between academic and nonacademic boys on the latent variables of verbal ability at grades 5 and 7.
