I have a question concerning the approriate modeling approach for my research question.
The situation is as follows: I have longitudinal cognitive data of approx 2500 individuals measured on 6 timepoints (baseline and 5 follow-ups at 1.5 years interval). The sample can be subcategorized into 4 different diagnostic groups (G1-G4) with varying sample size in each groups (G1=1200, G2=300, G3=300, G4=700). Within the whole group there is cognitive decline which also differs between diagnostic groups. Further their is difference in the intercepts (baseline cognition)
I would now like to test whether a specific independent variable (physical activity) influences the rate of cognitive decline DIFFERENTIALLY in the subgroups. My hyopthesis is that activity is a predictor of slower cognitive decline in group 1 and 2 but not in group 3 and 4 (the latter are more progressed in their cognitive status at baseline).
I wonder if and how this idea can be adressed with growth curve modeling?
Thank you for your reply Linda. In fact, I also thought about this idea but wondered whether this is possible when the actual slopes of decline do also differ between the groups (i.e. there is almost no decline in one group but a steeper decline in the other). So given the hypothetical result that I find differing effects of physical activity on the slopes in two groups, can this be confounded by different rates of decline (different slope growth factors) in the respective groups?
Would I go for a Multigroup Model or is this a case for application of a Growth Mixture Model (with known classes)?