ABSTRACT
Multilevel structural equation models (SEM) have become increasingly popular in the psychometric literature (Goldstein & McDonald, 1988; Longford & Muthén, 1992; McDonald & Goldstein, 1989; Muthén & Sattora, 1989; Muthén, 1989,1994). The rapid growth of multilevel modeling stems from the importance of accounting for population heterogeneity to make valid inferences from data that have a nested or hierarchical structure. Such nested data structures are common in the social sciences. Here are some examples:
• In the educational literature, student performance data are often collected from a cluster sample obtained by first drawing a random sample of schools and then drawing a random sample of students from within each selected school. For example, in the Second International Mathematics Study (SIMS; Crosswhite, Dossey, Swafford, McKnight, & Cooney 1985), a national probability sample of school districts was selected, a sample of schools was drawn from within district, and a sample of two classes were selected from within each school. Here students are nested within classrooms, classrooms are nested within schools, and schools are nested within districts, thus forming a four-level nesting structure. Background vari-ables are observed at all the four levels of the hierarchy, and interest
could be in understanding how district-level, school-level, class-level, and studentspecific variables influence test performance.
