I’m reaching the limits of my statistical understanding here when it comes to model specification in BRMS.
I’m an ecologist researching how different drivers of species distribution (generalised into three categories, Biotic, Abiotic and Space) change across scale (e.g. from 1km up to 10km).
To do this I have run some Joint Species Distribution Models and partitioned the variance in my models to understand the variance contribution of each category across my resolutions. According to ecological theory, I should be expecting to see the variance attributed to Environment increase as scale increases, and Biotic (potential species interactions) decrease as scale increases. A visual snapshot for three of my species (15 species in total) for my data is below.
Ideally I would like to show how scale is associated with a % increase or decrease in each variance explained category across all species.
After some discussion myself and my supervisor think this should be modelled multinomially as below. Is this appropriate?
C[Biotic VE, Environment VE, Spatial VE] ~ Scale + (1|Species)
My values are bounded between 0-1 so could run a beta regression on each variance category individually but I’m also aware that the composition of each variance category isn’t independent from each other.
I initially thought a Dirichlet regression might work well as explained by Andrew Heiss (Guide to understanding the intuition behind the Dirichlet distribution | Andrew Heiss), but am now aware that would require all my categories to sum to 1, which would mean re-scaling everything to fit. I’m somewhat hesitant to do this as total variance explained for each species is also interpreted as an indicator of model fit.
Is there an alternate distribution that would be more suitable for this?
Thanks in advance.