Estimating multivariate longitudinal trajectories using mixed-effects models with crossed random effects

In this study we examine how a mixed-effects model with crossed random effects for individuals and variables estimates within- and between-variability in longitudinal multivariate trajectories from cohort-sequential designs. These designs are characterized by large proportions of planned missing data, and they usually require continuous-time metrics. Via simulations, we evaluated different model outcomes under various conditions regarding the size of clusters (individuals and variables) and the complexity of the trajectories. Results show that (a) this model can estimate the general trajectories (common to all individuals and variables) and their variability, plus the variable-specific trajectories through the predictions of the levels of the random factors; (b) the standard errors of the random effects are wide, yet they are important for making substantive decisions for specific variables; and (c) the model predictions can adequately forecast individual and variable-specific complete trajectories from just a few observations per individual. These results are supported in an empirical illustration using cognitive developmental data. These findings show that researchers can obtain complete individual trajectories for multiple variables throughout a target age range. The relative simplicity of this model in comparison with other alternatives makes it a promising and accessible tool for multivariate longitudinal data analysis.