To Be Long or To Be Wide: How Data Format Influences Convergence and Estimation Accuracy in Multilevel Structural Equation Modeling

A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their cols:rows is related to the magnitude of eigenvalue bias in sample covariance matrices. Previous studies have shown similar performance for both approaches, but they were limited to settings where cols≪rows in both data formats. We conducted a Monte Carlo study to investigate whether varying cols:rows result in differing performances. Specifically, we examined the p:N (cols:rows) effect on convergence and estimation accuracy in multilevel settings. Our findings suggest that (1) the LF approach is more likely to achieve convergence, but for the models that converged in both, (2) the LF and WF approach yield similar estimation accuracy, which is related to (3) differential cols:rows effects in both approaches, and (4) smaller ICC values lead to less accurate between-group parameter estimates.