Modifying the Wide Format Approach To Multilevel Structural Equation Modeling To Mitigate Estimation Problems

Abstract

In psychology and the education sciences, multilevel data is omnipresent. In this data structure observational units are nested within higher level units, such as students within classes. A powerful tool for estimating parameters across these different levels is multilevel structural equation modeling (SEM). Multilevel data can be arranged in two data formats, long (LF) and wide (WF) format, and for both, multilevel SEM approaches are available. While both approaches are applicable within the established lavaan package in the free and open-source software R, the major advantage of the WF approach is its modifiability. Within my thesis, I first (1) redefine „small samples“ for multilevel data and compare the performance of both approaches here. I then show that the WF approach can be modified to mitigate estimation problems such as non-convergence and inaccuracy under conditions of (2) small samples and (3) heterogeneous variances. Findings suggest that both approaches exhibit comparable performance in small samples and that the proposed extensions of the WF approach offer an accessible avenue for researchers dealing with multilevel analysis, particularly when data acquisition is limited or heterogeneous populations are under investigation.