Hi everyone,

I ran two economics experiments and I am having trouble making the correct inference. In EXP1, over 100 subjects were asked questions over different rounds. My testable hypothesis is whether the probability that a question is answered truthfully depends on the round number. To do this, I can do things (truth is a 1-0 variable, round is an integer):

xtmelogit truth round || id :
xtlogit truth round, fe

In both regressions, I obtain the coefficient associated with round, which if significant tells me that the round number does affect the probability of receiving a truthful answer. My first question is: which of the two regressions above makes more sense to run? I ran both and the coefficients are very very similar, although not identical.

My second question is regarding EXP2, in which the goal is to also identify the effect of the round number on the probability of receiving a truthful answer. However, in EXP2 subjects make decisions in groups of 3, and one could argue that the regression should look like

xtmelogit truth round || id groupsession:

However, running this second regression to account for the potential correlation of the replies made by groups who shared the same session would drastically reduce my sample size. Is there another alternative? Ideas are most welcomed.