A two-stage approach to account for measurement error when using empirical Bayes estimates of random slopes

Psychological researchers have increasingly used individual- or cluster-specific slopes, also called random slopes in multilevel models, to operationalize dynamic constructs, such as individual growth, emotion inertia, and stress reactivity. However, the empirical Bayes estimates of random slopes, commonly used as predictors of cluster-level outcomes, are generally not reliable and could lead to biased results. Whereas multilevel structural equation modeling (MSEM) accounts for such measurement error, we propose a flexible two-stage approach that uses separate multilevel modeling and single-level structural equation modeling, which is computationally more efficient and gives similar estimates to MSEM. The proposed approach is demonstrated through an empirical example of stress reactivity. Results from three simulation studies show that the two-stage approach gives accurate estimates and inferences across a wide range of conditions, has substantially shorter computational time than MSEM for large cluster sizes, and has improved convergence when using penalized estimation in the first stage. (PsycInfo Database Record (c) 2026 APA, all rights reserved).