Chapter 9: Disaggregating Within-Person and Between-Person Efects in Multilevel and Structural Equation Growth Models

Growth models are being used to study interindividual differences in intra-individual change at a rapidly increasing rate in the social sciences. These are most often estimated as either a structural equation model (SEM) or as a multilevel linear model (MLM), although other estimation methods are available (e.g., fixed effects growth, general estimating equations, etc.). Regardless of approach, the core concept behind a growth model is to use a set of repeated measures to infer the existence of one or more parameters that define an unobserved (or latent) trajectory over time. The functional form of the trajectories might be flat with respect to time (e.g., an intercept-only model), they might be linearly increasing or decreasing, or they might be some complex nonlinear function. Whatever the form, growth models typically estimate the fixed and random effects associated with stability and change over time. The fixed effects capture the mean of the trajectory pooling over all of the individuals within the sample and the random effects reflect individual variability around the mean trajectory. Smaller random effects suggest greater similarity in growth across individuals; larger random effects suggest greater individual heterogeneity in change over time.