I have position data for fish in a river relative to a point-source pollutant coming from upstream. When pollution levels are high, I expect the fish to either move downstream, deeper, or both. My response variable is therefore a two dimensional lattice and I would like to model this as a function of the pollution levels.. conceptually a generalized additive model such as
y ~ s(effect)
where y is a two dimensional array (latitude, depth),
(latitude, depth) ~ s(pollution)
which ultimately will be extended to
(latitude, depth) ~ s(pollution) + s(hour) + s(yday) + s(ID, bs="re")
I have looked at models in which the response variable is concatenated using cbind (or mvbind in brms), but these do not seem to provide the correct response.
I would then be able to draw predictions about the animal distributions as a function of time of year and pollution levels in the system.
Is what I am describing possible? Or am I thinking about the question incorrectly?