I have conducted an experiment where I measured the pupil diameter of 100 participants in response to 9 sounds presented in a random order, all participants heard the same 9 sounds. I would like to run a mixed effects linear model where I predict pupil size from different ratings (e.g.
pupil_size ~ rating1 + rating2 + rating3). However, I would also like to account for each participant's natural pupil size as well as random fluctuations in the participant's pupil sizes due to low level properties of the sound (e.g. loudness, length, etc.).
I have been assuming that in this case stimuli (sound) and participant should be treated as crossed (
(1|stimuli) + (1|participant)) but I wonder whether since pupil size variation in response to the stimuli will depend on each participant's natural pupil size should it be treated as nested?