A systematic approach for identifying level-1 error covariance structures in latent growth modeling

Abstract

It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which, however, is not systematically addressed in the literature. In this study, we first discuss characteristics of various covariance structures and their nested relations, based on which we then propose a systematic approach to facilitate identifying a plausible covariance structure. A test for stationarity of an error process and the sequential chi-square difference test are conducted in the approach. Preliminary simulation results indicate that the approach performs well when sample size is large enough. The approach is illustrated with empirical data. We recommend that the approach be used in LGM empirical studies to improve the quality of the specification of the error covariance structure.

The Optimal Starting Model to Search for the Accurate Growth Trajectory in Latent Growth Models

“…Given that the misspecified error variance structure has detrimental impacts on the inferences about growth parameters (Ferron et al, 2002 ; Kwok et al, 2007 ), searching for the correct or adequate error variance structure should be followed by specifying the optimal growth trajectory. Recently published simulation study by Ding et al ( 2017 ) has provided a systematic approach to facilitate identifying a plausible covariance structure. Although they have conducted a study based on unconditional growth models, the guideline given in the study can be used as another starting point for searching the adequate error variance structure in LGM.…”