Shrinking Small Sample Problems in Multilevel Structural Equation Modeling via Regularization of the Sample Covariance Matrix

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized estimation approach designed for scenarios with both a small number of groups and small group sizes, and a low ICC. The method employs the wide format approach to multilevel SEM, where, at first, the sample covariance matrix is replaced by a shrinkage estimate, and then, this estimate is used to fit the SEM. By means of a simulation study, we evaluated the effectiveness of our two-stage approach. Our findings demonstrate that this method consistently ensures model convergence, provides more accurate between-level estimates, and even improves accuracy of within-level estimates in cases of very small group sizes.