Fig. 1.

Longitudinal trajectories measured at the individual level and at the group level using mixed effects modeling.

a. Level 1 Model: When the same child or adolescent is measured over time (e.g. age), individual parameters can be estimated that characterize the starting point (intercept) and the change (slope) of the fMRI BOLD signal for that specific subject (a.i.). Individual estimates of the longitudinal pattern of the fMRI BOLD signal will have greater precision when the number of timepoints is increased. With three timepoints, a simple linear model can be fit to estimate linear trajectory (a.ii), whereas with 4+ timepoints non-linear growth trajectories of a child or adolescent (such as quadratic and cubic) can be estimated (a.iii.).

b. Level 2 Model: Linear (b.i.), quadratic (b.ii.) and cubic (b.iii.) between-subject estimates can be assessed if a large age-range of children and adolescents are included in the sample. In this scenario, including a wide age-range allows more complex models (i.e. quadratic, cubic, etc.) to be fitted at a between-subject level.

c. i/ii/iii. With the inclusion of more timepoints, both linear (c.i) and non-linear (c.ii/iii) models can be fitted for both within- and between-subject levels.