Thanks a lot for you explanations.
Only to complete this:
I am using glm with a quasi-poisson distribution for count data
variables and I still have problems to interpret the table that I get
back.
But that is probably more a problem of lacking statistical knowledge.
Greets
Birgit
Am 16.05.2008 um 19:10 schrieb Doran, Harold:
Dear Berwin:
Indeed, it seems I was incorrect. Using your data, it seems that
only in
the case that the variables are numeric would my earlier statements be
true, as you note. For example, if we did
lm(y ~ as.numeric(N)+as.numeric(M), dat)
lm(y ~ as.numeric(N)*as.numeric(M), dat)
lm(y ~ as.numeric(N):as.numeric(M), dat)
Then the latter two are different, but only under the coercion to
numeric.
-----Original Message-----
From: Berwin A Turlach [mailto:[EMAIL PROTECTED]
Sent: Friday, May 16, 2008 12:27 PM
To: Doran, Harold
Cc: Birgit Lemcke; R Hilfe
Subject: Re: [R] glm model syntax
G'day Harold,
On Fri, 16 May 2008 11:43:32 -0400
"Doran, Harold" <[EMAIL PROTECTED]> wrote:
N+M gives only the main effects, N:M gives only the interaction, and
G*M gives the main effects and the interaction.
I guess this begs the question what you mean with "N:M gives
only the interaction" ;-)
Consider:
R> (M <- gl(2, 1, length=12))
[1] 1 2 1 2 1 2 1 2 1 2 1 2
Levels: 1 2
R> (N <- gl(2, 6))
[1] 1 1 1 1 1 1 2 2 2 2 2 2
Levels: 1 2
R> dat <- data.frame(y= rnorm(12), N=N, M=M) dim(model.matrix(y~N+M,
R> dat))
[1] 12 3
R> dim(model.matrix(y~N:M, dat))
[1] 12 5
R> dim(model.matrix(y~N*M, dat))
[1] 12 4
Why has the model matrix of y~N:M more columns than the model
matrix of y~N*M if the former contains the interactions only
and the latter contains main terms and interactions? Of
course, if we leave the dim() command away, we will see why.
Moreover, it seems that the model matrix constructed from
y~N:M has a redundant column.
Furthermore:
R> D1 <- model.matrix(y~N*M, dat)
R> D2 <- model.matrix(y~N:M, dat)
R> resid(lm(D1~D2-1))
Shows that the column space created by the model matrix of
y~N*M is completely contained within the column space created
by the model matrix of y~N:M, and it is easy to check that
the reverse is also true. So it seems to me that y~N:M and
y~N*M actually fit the same models. To see how to construct
one design matrix from the other, try:
R> lm(D1~D2-1)
Thus, I guess the answer is that y~N+M fits a model with main
terms only while y~N:M and y~N*M fit the same model, namely a
model with main and interaction terms, these two formulations
just create different design matrices which has to be taken
into account if one tries to interpret the estimates.
Of course, all the above assumes that N and M are actually
factors, something that Birgit did not specify. If N and M
(or only one of
them) is a numeric vector, then the constructed matrices
might be different, but this is left as an exercise. ;-)
(Apparently, if N and M are both numeric, then your summary
is pretty much correct.)
Cheers,
Berwin
=========================== Full address
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Berwin A Turlach Tel.: +65 6515 4416
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Faculty of Science FAX : +65 6872 3919
National University of Singapore
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Birgit Lemcke
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[EMAIL PROTECTED]
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