Consequences of misspecifying across-cluster time-specific residuals in multilevel latent growth curve models

This Monte Carlo study evaluates, in the context of multilevel latent growth curve models, the consequences of under- and overspecifying across-cluster time-specific residuals (i.e., Θb) on the estimation of the fixed effects, their corresponding standard errors, the variances and covariances of the random effects, Type I error rates, and the statistical power of detecting fixed effects. The results show that underspecifying Θb with all elements of Θb fixed at zero results in a large underestimation of the between- and within-level random effect and standard errors of fixed effect estimates, which, in turn, leads to serious bias in significant testing. Underspecifying Θb with diagonal elements of Θb constrained to equality, or overspecifying Θb with diagonal elements of Θb constrained to equality or freely estimated and residual covariances fixed at zero also leads to bias in the estimation of the between- and within-level random effects. Implications of the compensatory relationship occurring at the covariance level are discussed.