ABSTRACT
This chapter focuses on analysis of longitudinal studies using mixed-effect growth-curve models for trials where time or other explantory variables are conceptualized as a continuous variable (e.g. time-driven design). Strategies for choosing between repeated measures and growth-curve models for longitudinal studies were discussed in the previous chapter. The most typical approach for modeling growth-curve models uses a mixed-effects model.∗ The term mixed refers to the mixture of fixed and random effects:
Yi = Xiβ︸︷︷︸ Fixed effects
+ Zidi︸︷︷︸ Random effects
+ ei︸︷︷︸ Residual error
(4.1)
The fixed-effects (Xiβ) model the average trajectory. The fixed-effects are illustrated in Figure 4.1 by the bold line. The fixed effects are also referred to as the mean response, the marginal expectation of the response [Diggle et al., 1994] and the average evolution [Verbeke and Molenberghs, 1997, 2000]. The random effects model the variation among individuals relative to the average trajectory. The difference between the bold and dashed lines in Figure 4.1 represent the random effects (Zidi). In the figure there is both variation in the initial values (intercepts) and the rates of change (slopes) among the subjects. The variance of the random effects is also referred to as the between-subjects variation. The final component is the residual error and is represented by the difference between the symbols and the dashed lines. The variance of the residual errors is also referred to as the within-subject variation.
