Thanks for your reply, very helpful!

> -mrr 's(Time,k=7)+s(Time,by=Group,k=7)+Age+Gender'
According to the 3dMSS, I would create a pred.txt that include label, Time and Group (binarized).
Are Age and Gender okay to only be in the dataTable (not the pred.txt), and would Gender have to binarized for 3dMSS?

> With this specification, you would be able to assess the association of each outcome with your outcome variable.
> However, I'm confused with your word "correcting": What do you mean "correcting for them"?

Maybe it is due to my superficial knowledge of statistics, but I was under the impression that if I include a (confounding) variable as covariate, like Age,
I am correcting my model for the effect of this variable. Basically taking out the effect of Age out of the Group*Time effect.
(Like the questions asked here: [stats.stackexchange.com] or [stats.stackexchange.com])

For example, in R, a model with var1~Group*Time+ReactionTime+(1|Subj) produces different fixed effects estimates for Time and Group and Group:Time than a model with only var1~Group*Time+(1|Subj). Therefore, I am assuming it has removed the effect from the Group*Time effect.

So if I changed
Time*Group+Age+Gender+(Time|Subj)
to
Time*Group+Age+Gender+outcome1+outcome2+outcome3+(Time|Subj)
, my guess is that the Group*Time effect would look differently.

Similarily, I think adding them all into one 3dLMEr model would probably produce a different result than assessing the association of outcome1, 2 and 3 each in a separate 3dLMEr model (like Time*Group+Age+Gender+outcome1+(Time|Subj), and another model being Time*Group+Age+Gender+outcome2 +(Time|Subj), ...etc.)

Do these thoughts make any sense?

-Agent007