Hello everyone,

I am struggling with the correct interpretation of an interactive term (the moderator is time) and appropriate model for my issue.
It might be simple but I couldn't find any similiar case to help me understand.

I am trying to estimate whether the community reponse in different areas in a virtual community positively impacts the users' probability to participate longer.

So among the three independant variables v1 v2 v3 is for example: the cumulative ratio of how many of my emails received a response (since the underlying thought is, how much feedback do I get in regard to what I give). My dependant variable is the respective active month of the user (lenght_of_participation). Additionally to the effect of the variables v1 v2 v3, I am interested how the effect varies over time. The variable time represents the first 12 months (1 in the first month, 2 in the second month..) and is 13 afterwards.

However, I was wondering if it is even possible to test for the moderating effect of time, since the dependant variable is also "the time"? Is it nonsense or is v1 the overall effect whereas the i.time#c.v1 splits for the effects of the respective month? Estat gof in order to check for overdispension and choose the model.

Code:
xtset user_id year_month
poisson lenght_of_participation v1 v2 v3 i.time#c.v1 i.time#c.v2 i.time#c.v3 $control, vce(cluster user_id)
estat gof
nbreg lenght_of_participation v1 v2 v3 i.time#c.v1 i.time#c.v2 i.time#c.v3 $control, vce(cluster user_id)
Alternatively I though to construct a survival analysis with a cox model, where censor is the last active month and hence the dependant variable the probability to exit. Here the dependant variables would not be the cumulative ratio, but the ratio within the year_month (since I thougth its like deciding every month: how was my feedback, should I continue?)

Code:
stset year_month, id(user_id) failure(censor==1)
stcox v1 v2 v3 i.time#c.v1 i.time#c.v2 i.time#c.v3 $control, nohr vce(cluster user_id)
Is the survival regression the only way for me to check for the effect over time? Or is there something crucial I am misunderstanding?

I hope you can give me some thinking hint on where to go with my thoughts.
Thank you very much in advance!
Karin