[19134] in s-news-athena
Re: [S] query on a more efficient method for writing a nonlinear
daemon@ATHENA.MIT.EDU (Bill Venables)
Tue Sep 7 20:06:57 1999
Message-Id: <199909080000.KAA25075@snowy.nsw.cmis.CSIRO.AU>
To: "Gene Felber" <gfelber@rxttm.com>
Cc: s-news@wubios.wustl.edu
In-Reply-To: Your message of "Tue, 07 Sep 1999 08:49:58 -0400."
<LOBBKJFMEMHLDHOLHNOFGENHCAAA.gfelber@rxttm.com>
Mime-Version: 1.0
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Date: Wed, 08 Sep 1999 09:58:40 +1000
From: Bill Venables <venables@acland.qld.cmis.csiro.au>
>
> Dear:
>
> I am using the function below to fit an nls model:
>
> sin.cos.fcn <- function(A,B,C1,C2,C3,C4,D1,D2,D3,D4,time)
> {
> A+B*time
> + (C1 * sin(2*1*pi*time/52)) + (D1 * cos(2*1*pi*time/52))
> + (C2 * sin(2*2*pi*time/52)) + (D2 * cos(2*2*pi*time/52))
> + (C3 * sin(2*3*pi*time/52)) + (D3 * cos(2*3*pi*time/52))
> + (C4 * sin(2*4*pi*time/52)) + (D4 * cos(2*4*pi*time/52))
> }
>
> Is there a more efficient method to write this function so that one could
> more easily change the summation of k=1:4 to 1:n without having to
> explicitly write (and obtain estimates for) each parameter?
Eh? This isn't a non-linear model at all, it's only a linear model, as you
should be delighted to discover. The way I would handle such a model with
variable numbers of terms in the approximating fourier series would be as
follows:
sin.cos.fcn <- function(k, time) {
X <- matrix(0, length(time), 2*k)
for(i in 1:k) {
X[,i] <- sin(i*2*pi*time/52)
X[,k+i] <- cos(i*2*pi*time/52)
}
X
}
m0 <- lm(y ~ time , data = mycat)
m1 <- lm(y ~ time + sin.cos.fcn(1, time), data = mycat)
m2 <- lm(y ~ time + sin.cos.fcn(2, time), data = mycat)
&c
anova(m0, m1, m2, .....)
If you do have a genuinely nonlinear model there are very useful ways to use
vector (as opposed to scalar) parameters that should be better known than they
are, but that's another fascinating story...
Bill Venables.
-----------------------------------------------------------------
Bill Venables, Statistician, CMIS Environmetrics Project.
Physical address: Postal address:
CSIRO Marine Laboratories, PO Box 120,
233 Middle St, Cleveland, Queensland Cleveland, Qld, 4163
AUSTRALIA AUSTRALIA
Telephone: +61 7 3826 7251 Email: Bill.Venables@cmis.csiro.au
Fax: +61 7 3826 7304
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