An illustration of local structural equation modeling for longitudinal data: Examining differences in competence development in secondary schools

In this chapter, we discuss how a combination of longitudinal modeling and local structural equation modeling (LSEM) can be used to study how students’ context influence their growth in educational achievement. LSEM is a nonparametric approach that allows for the moderation of a structural equation model over a continuous variable (e.g., socio-economic status; cultural identity; age). Thus, it does not require the categorization of continuous moderators as applied in multi-group approaches. In contrast to regression-based approaches, it does not impose a particular functional form (e.g., linear) on the mean-level differences and can spot differences in the variance-covariance structure. LSEM can be used to detect nonlinear moderation effects, to examine sources of measurement invariance violations, and to study moderation effects on all parameters in the model. We showcase how LSEM can be implemented with longitudinal of the National Educational Panel Study (NEPS) using the R-package sirt. In more detail, we examine the effect of parental education on math and reading competence in secondary school across three measurement occasions, comparing LSEM to regression based approaches and multi-group confirmatory factor analysis. Results provide further evidence of the strong influence of the educational background of the family. This chapter offers a new approach to study inter-individual differences in educational development.