I'm trying to run an intraclass-correlation (inter-rater agreement) for personality data I have collected. However, I work with animals and as such the data has been collected over a period of a year or so, I have, in some cases different numbers of raters per subject, and different raters (or more specifically, not all raters have rated all subjects; some raters have done some subjects, other raters have done other subjects (and some have done all)). So, I have 7-9 ratings per subject, with some overlap between raters and subjects, but not always.
Is this possible, and if so which ICC should I use?
Any advice would be gratefully received.