Dimension/number of priors for 2D-splines

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.


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I am no expert on splines, but the spline constructions in brms are inherited from mgcv and seem to be reasonably well described by the references in mgcv documentation. From briefly scanning Straightforward intermediate rank tensor product smoothing in mixed models, it seems that section 3.2.1 describes the case you are seeing:


Best of luck with your model!

Thank you! This is exactly what I was looking for.

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