Foundations of Longitudinal Data Analysis: Designs, Trajectories, and Causal Leverage

This chapter introduces longitudinal data analysis for population research. We distinguish cross-sectional, time-series, and event-history structures, emphasising repeated measures on subjects and the consequences for correlation, missingness, and unbalanced designs. Core data representations (wide and long) are presented with notation for trajectories and growth models. We review modelling strategies for within- and between-subject inference, fixed effects, random effects, mixed models, and generalised estimating equations, highlighting covariance structures, assumptions, and trade-offs for causal interpretation and prediction. Applications using Australian assets (PLIDA, HILDA) illustrate policy-relevant analyses of trajectories, interventions, and heterogeneity. This chapter provides foundations for principled model choice, robust diagnostics, and practical forecasting.