Chapter 7: N-Level Structural Equation Model of Student Achievement Data Nested with Repeated Teachers, Schools, and Districts

Modeling growth in student achievement across years invariably involves a complex set of dependencies due to changing classroom nesting structures and student mobility. Traditional multilevel cross-classified models for such data make restrictive assumptions particularly regarding persistent class-room/teacher effects across grades. Furthermore, the specification of the model itself tends to be unwieldy with many levels and complex dependencies. A general n-level structural equation modeling (NL-SEM) for complex dependent data is introduced. NL-SEM allows models with arbitrary number of levels. Each level may include a complete SEM model with observed and latent variables. Regression among observed and latent variables is allowed across any two levels that share a parent–child relationship. In effect, a full NL-SEM model is a DAG of SEM models. An empirical example illustrating alternative NL-SEM specifications of “persistent teacher-effects” is presented using a large dataset of students’ reading outcome from grades 1 through 3. Interestingly, the data include ID variables for kindergarten teacher even though student outcome data were not collected in kindergarten. The results indicate that kindergarten classrooms/teachers continue to have strong and persistent effect on student outcome. Classrooms in later grades have a relatively smaller effect. Implications for “value-added models” of teacher effects are discussed.