Repeated measures with different cohorts

Dear all,

I have data from 3 different art groups (orchestra, dance, musical theatre) collected in 3 different times of measure. Data is questionnaire based. I am interested in if X variable is predicted by Y and Z, and if this relation holds for these three different domains. So I am only going to conduct regression analyses.

The problem with my data is, in each time of measure there are different participants from different art domains. In other words, some participants have attended the study only one time, some have attended three times. I have managed to get three measures from same orchestra members, but I have different dancer participants in three measures. Groups are student societies, so attendance was not strict. So I'm very confused on how to analyse the data.

I have cleaned the data and removed people who haven't taken part in all of the measurements. There is no mean difference between any of the variables I measured in terms of time (In other words, there is no within difference). But this meant significant sample loss of course. I am thinking of doing separate analyses for each time of measurement: 1st, 2nd and 3rd. in order to keep sample power. What else I can do? I am more interested in domain related differences rather than time related differences.

Any thoughts, feedback, suggestions would be very helpful.

Thank you very much :)