Correcting for regression to the mean in mixed effects model of longitudinal data?

#1
Hey everyone,

I know you can correct for regression to the mean for two time points, in a before and after scenario. But does anyone know how to do this when there are more than two time points, let's say there are about 10 points in a time series. I was hoping to model the longitudinal data with a random effects model, where each individual has a random intercept and slope, but I am not sure as to how to take into account the 'regression to the mean' effect.

I know that looking at the correlation between the random slope and random intercept will help assess the relationship with the 'regression to the mean' effect in play, but is there a way I can do this without this RTM effect?

Would centering the dependent variable help? because then the intercept of a centered variable becomes the mean and when you look at the correlation between random intercept and random slope, it's no longer the baseline but the mean and slope - and therefore, less susceptible to 'regression to the mean' effects?
 
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