If we use a model with an 2D-spline, e.g. the model
brm(rentsqm ~ t2(area, yearc) + (1|district), data = rent99, chains = 2, cores = 2)
from vignette(“brms_multilevel”, package = “brms”), the prior of class “sds” for the wiggliness parameters has 3 dimensions (and there are 3 posterior estimates).
One is for the wiggliness in the first direction, one is for the wiggliness in the second direction, but what is the function of the third one?
In theoretical papers and books about 2D-splines and tensor products, I could only find two wiggliness parameters but not a third.