How do I structure my data in a time-lagged, multilevel mediation? I am analyzing a repeated measures experiment using a multilevel growth curve in SPSS. I want to test a time-lagged, multilevel mediation model. My X variable is linear time in weeks (week 1, week 2, week 3, etc.) My mediator (M variable) is a measure of ruminative thinking, and my dependent variable (Y variable) is depressive symptoms. I want to test if changes in ruminative thinking each week predict subsequent changes in depressive symptoms. In other words, changes in the mediator at time t are predicting changes in Y at time t + 1. So the conceptual model would be: X (linear time) --> M (changes in rumination) --> Y (changes in depression)
My questions are:

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*How do I properly capture change in M & Y when including them in a mediation model with a linear effect of time? Will raw scores capture change from week to week, or do I need to compute difference/change scores and use those in my mediation model?


*Do I need to person-mean center (within-person center) M & Y?
Advice on either of these questions would be greatly appreciated.
Edit (1/18/21): My X variable is a linear effect of time, measured in weekly intervals (0, 1, 2, 3, etc.) Both my M variable (ruminative thinking) and my Y variable (depressive symptoms) are continuous variables measured each week for 5 weeks. I am wanting to capture whether there is 1) A linear decrease in ruminative thinking over the course of the 5 weeks (path a), and 2) Whether these weekly decreases in ruminative thinking predict subsequent weekly decreases in depressive symptoms (path b), and 3) whether the indirect effect (path_a*path_b) is significant. Path b will be time-lagged. So, for example, the change in ruminative thinking from week 1 to week 2 would predict change in depressive symptoms from week 2 to week 3, and so on. So I'm only interested in the within-person relationship between M & Y. I believe what I'm stuck on is how to accurately estimate path b of my mediation model (i.e., the M --> Y effect). I know that for path a (X --> M), I can just use raw scores for M, and the linear coding of Time will give me the average weekly decrease in ruminative thinking. But for path b, would raw scores for M & Y capture how weekly change in M is associated with weekly change in Y, or do I need to enter difference/change scores into the model instead? If I do need to use change scores, then do I also need to enter a change score for M in path a of my model (rather than raw scores)?
Please let me know if I can clarify further, as I'm new to multilevel modeling and could be leaving important info out.
 A: I'm not sure this is a mediation model as much as it's a growth curve model with a slight twist. You want to know if prior week's rumination level is associated with subsequent week's depression. Is that right?
If so, then just create a "lagged" version of ruminate such that a row of data associated with week 2 has a version of ruminate that is its value from week 1. Obviously this means that you cannot include the week 1 depression because you do not have a "lagged" version of rumination. However, you still have enough data to run a growth curve model (starting w/ week 2 through week 5).
To incorporate GreggH's idea, you could also calculate a person mean of the lagged rumination variable and include that as a predictor of both the intercept and the slope (via an interaction between week and person mean lagged rumination). This tests whether people who have higher average prior rumination have higher average depression (fixed effect on the intercept) and have greater/lesser change in depression (interaction effect).
The coefficient on the lagged rumination tells you the association between prior rumination and the following week's depression score, accounting for an individual's linear growth in depression (random slope for time/week) and their trait depression (random intercept).
If instead you want to assess whether prior week's rumination is associated with changes in depression from prior week to present week, then you likely need a different modeling approach. I'd suggest structural equation modeling for that purpose.
