Comparing personal trajectories and drawing causal inferences from longitudinal data.

This review considers statistical analysis of data from studies that obtain repeated measures on each of many participants. Such studies aim to describe the average change in populations and to illuminate individual differences in trajectories of change. A person-specific model for the trajectory of each participant is viewed as the foundation of any analysis having these aims. A second, between-person model describes how persons very in their trajectories. This two-stage modeling framework is common to a variety of popular analytic approaches variously labeled hierarchical models, multilevel models, latent growth models, and random coefficient models. Selected published examples reveal how the approach can be flexibly adapted to represent development in domains as diverse as vocabulary growth in early childhood, academic learning, and antisocial propensity during adolescence. The review then considers the problem of drawing causal inferences from repeated measures data.