I have data of compassion ratings in response to stimuli (pictures). The stimuli can be described by two factors, valence (categorical: positive, negative) and arousal (continuous). All n=145 subjects rated all 44 pictures. The ratings are continuous from 0 to 100 and are normally distributed for both positive and negative pictures. Here is what the data looks like for the first 3 subjects and 2 stimuli:
> df subject stimulus arousal valence 1 sub-1 pic-1 0.25 pos 2 sub-2 pic-1 0.25 pos 3 sub-3 pic-1 0.25 pos 4 sub-1 pic-2 0.48 neg 5 sub-2 pic-2 0.48 neg 6 sub-3 pic-2 0.48 neg
I want to analyse this data with a linear mixed model, however, I am a bit unsure about the random effects. In my experiments before, I always modelled both stimulus and subject as random effects, so my first instinct was to do somthing like this:
formula = rating ~ valence * arousal + (1|subject) + (1|stimulus)
However, since I have also an effect of interest continuously describing the stimuli, I am unsure if this is correct. Since I have an effect of interest describing each oft the stimuli with exactly one value, is the stimulus then still random? Or would it be better to only use subjects as a random effect, e.g., like this:
formula = rating ~ valence * arousal + (1|subject)
Does anyone know which model is better suited to analyse my data? Or generally has suggestions which model to use to analyse this data?