Spatio-temporal smoother implimentation in sdmTMB

[matteba]

Hi
I was wondering if it is possible to use a spatio-temporal smoother in a sdmTMB model. The smoother should represents a function of a given density in space (coordinates) as a thin plate regression spline and time (month) as a cyclic cubic regression spline. Using the sintax of mgcv R package, it should be a tensor product smooth of the formula te(x,y,month, d =c(2,1)) + bs=c("tp,""cc"))
Thanks,

[ericward-noaa]

Good question. Yes -- this should work, though you'll want to turn SPDE spatial effects off and use the t2() smoother instead of te(). Here's an example that works:

mesh <- make_mesh(pcod, c("X", "Y"), cutoff = 20)
pcod$month <- sample(1:12, size = nrow(pcod), replace=T) # dummy values, not in orig. data

fit <- sdmTMB(
  density ~ t2(X,Y,month, d =c(2,1), bs = c("tp","cc")),
  data = pcod, mesh = mesh,
  spatial = "off",
  family = tweedie(link = "log")
)

[matteba]

Thanks a lot ericward. just to understand if i got it right. The reason why the spatial effect must be turned off is becasue the tensor procuct would build an "upper" spatial structure on the SPDE?

[ericward-noaa]

I think of the SPDE as implementing one version of spatial smoothing, and so turning it off is important when the tensor smooth is trying to approximate something very similar. I should have also clarified that by turning the SPDE spatial part off, the remaining model is something you could also fit in mgcv::gam() . There's a couple nuanced features of sdmTMB that obviously aren't in mgcv (e.g. AR(1) processes on parameters) -- but should be equivalent