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

[David Winsemius]

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

>
>>
>> Can anybody help please?
>>
>> Code and figures here:
>> https://docs.google.com/fileview?id=0B1cQ7z9xYFl2ZTZhMmMyMjAtYTA3Zi00N2QyLTkxNzMtOGYyMjdiOGU2ZWE4&hl=en
>>
>> Thank you,
>> Claudia
> -- 
>
> David Winsemius, MD
> West Hartford, CT
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT