# [R] physical constraint with gam

Simon Wood simon.wood at bath.edu
Fri May 13 12:32:18 CEST 2016

```On 11/05/16 17:11, Dominik Schneider wrote:
> Hi Simon, Thanks for this explanation.
> To make sure I understand, another way of explaining the y axis in my
> original example is that it is the contribution to snowdepth relative
> to the other variables (the example only had fsca, but my actual case
> has a couple others). i.e. a negative s(fsca) of -0.5 simply means
> snowdepth 0.5 units below the intercept+s(x_i), where s(x_i) could
> also be negative in the case where total snowdepth is less than the
> intercept value.
>
- Yes, this looks right.

> The use of by=fsca is really useful for interpreting the marginal
> impact of the different variables. With my actual data, the term
> s(fsca):fsca is never negative, which is much more intuitive. Is it
> appropriate to compare magnitudes of e.g. s(x2):x2 / mean(x2) and
> s(x2):x2 / mean(x2)  where mean(x_i) are the mean of the actual data?
>
- I guess so (similarly to lm/glm).

> Lastly, how would these two differ: s(x1,by=x2); or
> s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and i'm
> not sure if a linear combination is enough.
>
- you'd probably use te(x1,x2) unless x1 and x2 are really on the same
scale, in which case s(x1,x2) might be appropriate. The `by' variable
trick is probably not going to work so well for interactions, however
(it's not so clear what the by variable should be).

--
Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
+44 (0)117 33 18273     http://www.maths.bris.ac.uk/~sw15190

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