Cosinor Model (Halberg, Bingham) - Multiple components - Linear, Quadratic and Cubic trends

Dear Iva,
First it is normal politeness to identify yourself with name an affiliation at the end of your email to a list like this, many people will not answer anonymous e-mails.

It is a little unclear to me what you mean.

If you are alluding to quadratic or cubic terms in some variable 
you just include then in the model al

lm( y ~ I(z^2) + I(z^3), data=...)

But if you are referring to harmonic functions of higher order you can put hem in as separate sines and cosinse:

lm( y ~ I(cos(2*pi*t/T)) + I(sin(2*pi*t/T)) + I(cos(4*pi*t/T)) + I(sin(4*pi*t/T)) )

Here is a small function and a demo that shows what it does, maybe this is what you are looking for:

harm <-
function( mm, n )
{
  # Function to devise a n'th order harmonic from a
  # numerical vector, scaled to be in the range 0 to 1

  MM <- cbind(
  outer( mm * 2 * pi, 1:n, function(x,y) cos( x*y ) ),
  outer( mm * 2 * pi, 1:n, function(x,y) sin( x*y ) )
              )[,rep(1:n,each=2)+rep(0:1,n)*n]
  colnames( MM ) <- outer( c("cos","sin"), 1:n, paste, sep="" )
  MM
}

x <- seq(0,1,,100)
head( harm(x,3) )
matplot( x, harm(x,3), type="l", lty=1, lwd=2 ) 

Best regards
Bendix Carstensen
Epi package maintainer
______________________________________________

Bendix Carstensen 
Senior Statistician
Epidemiology
Steno Diabetes Center A/S
Niels Steensens Vej 2-4
DK-2820 Gentofte
Denmark
+45 44 43 87 38 (direct)
+45 30 75 87 38 (mobile)
bxc at steno.dk    http://BendixCarstensen.com
www.steno.dk

-----Original Message-----
From: r-sig-epi-bounces at r-project.org 
[mailto:r-sig-epi-bounces at r-project.org] On Behalf Of Iva P
Sent: 18. marts 2012 21:21
To: R-sig-epi at r-project.org
Subject: [R-sig-Epi] Cosinor Model (Halberg, Bingham) - 
Multiple components - Linear, Quadratic and Cubic trends



Hello!

I have a doubt in relation with the use of the cosinor model 
with R when I have not only multiple components, but also 
linear, quadratic and cubic trends.

I explain the details:

In simple cosinor:


Y = M + A * cos(2
* ?* t / T + ?) + error

T knowed: y = M + ?* X1 + ?* X2 + error,
?
Where X1 = cos (2 * ?* t / T) and X2 = sin(2
* ?* t / T)
?
In this
case, I use lm(y ~ X1 + X2) .
?
For the
multiple components case:
?
y = M + ?Aj * cos(2 * ? * t /Tj + ?j) + error
?
In this
case I use:? lm(y ~ X1tot + X2tot)
?
However, in
the generalized model case (linear, quadratic and cubic 
trends), I don?t know how to analyze with R.
?
I include
the situacion formula:
?
y = M + ?1 * t + ?2 * t2 + ?3 * t3+ ?Aj *
cos(2 *?* t /Tj + ?2) + error
?
What
function in R can I use, as I used lm for the simple cosinor 
model and the multiple components model?.
?
How can I
obtain global information and separated information?. I refer 
to obtain information for each contribution (linear tren, 
quadratic trend, ? and so on).
?
Thank you
very much for your help.
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