Residual structures in latent growth curve modeling

Several alternatives are available for specifying the residual structure in latent growth curve modeling. Two specifications involve uncorrelated residuals and represent the most commonly used residual structures. The first, building on repeated measures analysis of variance and common specifications in multilevel models, forces residual variances to be invariant across measurement occasions. The second, generally arising from structural equation modeling perspectives, allows residual variances to be freely estimated across occasions. Usually an afterthought, alternate specifications of the residual structure can have sizable effects on variance and covariance estimates for the intercept and slope factors (Ferron, Dailey, & Yi, 2002; Kwok, West, & Green, 2007; Sivo, Fan, & Witta, 2005), the fit of the model, and model convergence. We propose additional residual structures in latent growth modeling arising from ideas regarding growth curve reliability. These structures allow residual variances to change across time, but in constrained ways. We provide three illustrations and highlight the importance of focusing on residual structures in latent growth curve modeling.