Aim 2c

Goal: To identify student subgroups for which PA is differentially effective

Hypothesis: Clear and recognizable groups of students exists, separated by their response to PA, and that these groups will express different levels of PA effectiveness.

Latent Trajectory Analysis (LTA) will be used, following the process outlined by Jung and Wickrama (2008), to test potential predictors of growth in individual student outcomes. In these LTA models, DV is a variable that represents the amount of outcome change experienced or expressed by a student. For example, in Figure 8 the DV (e.g., change in self-esteem) and IV (e.g., race) are identified in the model along with the latent construct that identifies group/class membership (C, class membership identified by the model) and the two latent constructs that capture the intercept and slope of one time-variant predictor variable. Therefore, a time-invariant moderator (e.g., race) and a time-variant (T) variable (e.g., social engagement) can be modeled to group students according to their change in a DV (e.g., self-esteem). It is hypothesized that there exists a set of observed variables (either time-invariant, time- variant, or both) that will effectively identify groupings of students by their distal PA effect.

Using Figure 8 as an example, many LTA procedures will be conducted and their findings compared to better understand the clustering of students based on trajectories in SECD and changes in student outcomes. In addition, the findings from our LTA analyses will increase the understanding of how student reports are related to student outcomes.