Cross-level covariance approach to the disaggregation of between-person effect and within-person effect.

Abstract

In longitudinal studies, researchers are often interested in investigating relations between variables over time. A well-known issue in such a situation is that naively regressing an outcome on a predictor results in a coefficient that is a weighted average of the between-person and within-person effect, which is difficult to interpret. This article focuses on the cross-level covariance approach to disaggregating the two effects. Unlike the traditional centering/detrending approach, the cross-level covariance approach estimates the within-person effect by correlating the within-level observed variables with the between-level latent factors; thereby, partialing out the between-person association from the within-level predictor. With this key device kept, we develop novel latent growth curve models, which can estimate the between-person effects of the predictor's change rate. The proposed models are compared with an existing cross-level covariance model and a centering/detrending model through a real data analysis and a small simulation. The real data analysis shows that the interpretation of the effect parameters and other between-level parameters depends on how a model deals with the time-varying predictors. The simulation reveals that our proposed models can unbiasedly estimate the between- and within-person effects but tend to be more unstable than the existing models. (PsycInfo Database Record (c) 2023 APA, all rights reserved).