In longitudinal studies with three or more measurement waves, growth curve modeling can provide an understanding of individual change (Laird & Ware, 1982; McArdle & Nesselroade, 2003; Muthen & Khoo, 1998). Researchers may study individual growth trajectories and relate variations in the growth trajectories to covariates that vary between individuals. They may also get better estimates of true growth by studying the effects of covariates that vary over time within individuals. We use the hierarchical modeling framework here to describe the models.
Conceptually, growth curve modeling has two levels denoted as Level 1 (within individuals) and Level 2 (between individuals). At Level 1 we describe each individual's growth using a regression equation. We focus here on the simplest model, linear growth. With linear growth we express the measure Y(j of an individual i at time t as the sum of the individual's linear growth plus a residual eti that represents random error at occasion t,
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