# [R] Cubic B-spline, how to numerically integrate?

David Winsemius dwinsemius at comcast.net
Fri May 14 18:36:26 CEST 2010

```On May 14, 2010, at 11:57 AM, David Winsemius wrote:

>
> On May 14, 2010, at 11:41 AM, Claudia Penaloza wrote:
>
>> (corrected version of previous posting)
>>
>> I fit a GAM to turtle growth data following methods in Limpus &
>> Chaloupka
>> 1997 (http://www.int-res.com/articles/meps/149/m149p023.pdf).
>>
>> I want to obtain figures similar to Fig 3 c & f in Limpus & Chaloupka
>> (1997), which according to the figure legend are "expected size-at-
>> age
>> functions" obtained by numerically integrating "size-specific
>> growth rate
>> functions derived using cubic B-spline fit to GAM predicted values".
>>
>> I was able to fit the cubic-B spline, but I do not know how to
>> "numerically
>> integrate" it.
>
> You need to give us the function and the appropriate limits of
> integration.

Maybe it is even easier than I thought. Assuming your interest lies
with the last fitted line ... the one on the third page ... you could
perhaps just see how successful this strategy would be:

# Presumably you have already done:
# requite(mgcv)

Int.fit <- seq(100, 600, by=0.1)*predict(bspline3,
newdata=data.frame(size=seq(100, 600,
by=0.1) ) )

You would need to do a sensibility check by comparing the result to a
back of the envelope estimate: say 55*500=27500 . I'm a bit concerned
that a dimensional analysis suggest this is an estimate of mm^2/yr,
although I suppose a yearly surface area increase could be a
meaningful value in some domain or another

>
>>
>>
>> Code and figures here:
>>
>> Thank you,
>> Claudia
> --
>
> David Winsemius, MD
> West Hartford, CT
>
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