Local Structural Equation Modeling for Longitudinal Data
In this chapter, we illustrate how local structural equation modeling can be used to study the moderation effects of continous context variables on developmental trajectories. More specifically, we investigated the effects of parental education on students' reading and math ability acquisition across four school years. We used data from the National Educational Panel Study: Starting Cohort Grade 5, which contains math and reading ability estimates of N = 2,037 German students from Grade 5 to Grade 9 across three measurement occasions. We used bivariate latent growth curve models to differentiate between initial levels and growth of math and reading competence, as well as study the interplay between these two developmental processes. Using local structural equation modeling, we moderated this model across a continous indicator of parental education levels. This approach allowed us to examine the effects of parental education on all parameters of the model (e.g., factor mean, variance, covariance), without imposing a restriction on the shape of the effect (e.g., linear). This combination of modeling approaches is thus particularly useful to determine which aspects of the developmental process are affected by the context variable, and which form this effect has. We provide R code and output examples and discuss other potential applications of local structural equation modeling.