I want to fit a spatiotemporal model where my dependent variable is in the range [>0,<1].
A beta regression seems suitable for this case.
I tried the betareg package, that works like a charm, but to my knowledge I cannot include complex interaction terms that occur e.g. in spatiotemporal datasets to account for autocorrelation.
I know that GAMs e.g. package mgcv support beta regression via the betar() family. To my knowledge the precision/variance parameter is held constant though and only the mean (mu) changes as a function of the predictors.
my model looks like this (it is conceptual so no example data needed):
mgcv::gam(Y~ te(latitude,longitude,day)+s(X1)+s(X2)+s(X3),family=betar())
The problem is that only mu is modelled but not phi / precision
In the betareg I can let vary phi with my predictors:
betareg::betareg(Y ~ X1+X2+X3+latitude+longitude | X1+X2+X3+latitude+longitude)
but this doesn´t let me model the spatiotemporal term as needed, because simple additive effects are not suitable for that and I need something like what is supported with the te() functionality from mgcv or any other kind of interaction term.
Is there any work around or a way to model phi but account for my spatiotemporal term either via mgcv or betareg or any other R package?
Thanks a lot!
