Inference about H matrix with non-spatial data

[ericward-noaa]

Question from colleague:

I'm interested in fitting anisotropic models with the SPDE approach to 2D non-spatial data (think something like body size vs time). Has anybody done this with sdmTMB or other SPDE models? Are there challenges in interpreting the H matrix?

[ericward-noaa]

I haven't seen applications to non-spatial data. I think a challenge is that when working with the anisotropic models with space, we're assuming the units are the same in each direction (e.g. latitude, longitude). But if working with 2 variables on totally different scales (body size, time), I haven't thought beyond simple rescaling (standardization, quantiles) to get them on similar scales.

Also - I'm not sure that the SPDE approach is totally necessary here. It seems like if you aren't trying to make inference about spatial parameters (e.g. range), then you could fit some very flexible GAMs with 2D smooths (letting relationships vary continuously / discretely by year)