I find the simplest way to interpret a *linear* model formula, as used by lm()
and aov() is to take the left hand side as specifying the response variable (or
variables) and to take the right hand side as specifying the *columns of the
model matrix* in a coded way. Notice that the parameters are implicit and do
not occur anywhere in the formula.
To take your example, yin ~ I(sin(x)), [which you could simply write as yin ~
sin(x)] would specify yin as the response and the model matrix had two columns
namely 1 for the intercept term and sin(x)
X = [1 sin(x)]
So the model you would be fitting, in a more conventional notation, would be
Y = a + b*sin(x) + error.
lm() and aov() accommodate only *linear* parameters. You can recoginse a
linear parameter by the fact that when you differentiate the right hand side of
the model formula with respect to it, the result does not depend on that
parameter.
To take your other model
Y = a + b*sin(d*x + phi) + error
(you left out the error, BTW), clearly a and b are linear parameters but d and
phi are not, so you cannot fit this model directly with lm() or aov(). If you
knew d and phi, of course, you could fit it since the remaining parameters are
all linear and you would specify it using y ~ sin(d*x+phi) where d and phi
would need to have values at the time of fitting.
The simplest way to fit this kind of model is to use nls(). You can even
exploit the fact that a and b are linear parameters by using the "plinear"
algorithm, but I'll leave you to sort that one out. You can also re-write the
model so that you have just one non-linear parameter, but again, you can sort
that out.
_______
I think the reason why people were perhaps looking a little askance at your
this kind of question on R help is that there are plenty of books around where
this sort of issue is really done to death. The introduction to R from the
help menu of R is one place where you might start, but there are better ones
and now plenty of them.
Bill Venables
http://www.cmis.csiro.au/bill.venables/
-----Original Message-----
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of Carl Witthoft
Sent: Tuesday, 13 January 2009 8:58 AM
To: r-help@r-project.org
Subject: Re: [R] lm: how are polynomial functions interpreted?
Well..... *_* ,
I think it should have been clear that this was not a question for which
any code exists. In fact, I gave two very specific examples of function
calls. The entire point of my question was not "what's up with my
(putative) code and data " but rather to try to understand the
overarching philosophy of the way lm() treats the function it's given.
I do understand the sneaky ways to make it do a linear fit with or
without forcing the origin. And, sure, I could have run a data set thru
a bunch of different quadratic-like functions to try to see what happens.
Let me pick a more complicated example. The general case of a sin fit
might be Y = a + b*sin(d*x+phi) .(where, to be pedantic, x is the only
data input. All others are coefficients to be found)
If I try y<-lm(yin~I(sin(x))), what is the actual fit function? And so on.
That's why I was hoping for a more general explanation of what lm() does.
Charles C. Berry wrote:
> On Mon, 12 Jan 2009, c...@witthoft.com wrote:
>
> [nothing deleted]
>
> matplot(1:100, lm(rnorm(100)~poly(1:100,4),x=T)$x ) # for example
>
>>
>> ______________________________________________
>> R-help@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
>
> Ahem!
>
>> and provide commented, minimal, self-contained, reproducible code.
> ......^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> Charles C. Berry (858) 534-2098
> Dept of Family/Preventive
> Medicine
> E mailto:cbe...@tajo.ucsd.edu UC San Diego
> http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
>
>
>
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