# Re: [R] glm model syntax

From: Birgit Lemcke <birgit.lemcke_at_systbot.uzh.ch>
Date: Sat, 17 May 2008 19:00:28 +0200

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:berwin_at_maths.uwa.edu.au]
>> 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" <HDoran_at_air.org> 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
>>
>> =============================
>> Berwin A Turlach Tel.: +65 6515 4416
>> (secr)
>> Dept of Statistics and Applied Probability +65 6515 6650
>> (self)
>> Faculty of Science FAX : +65 6872 3919
>> National University of Singapore
>> 6 Science Drive 2, Blk S16, Level 7 e-mail:
>> statba_at_nus.edu.sg
>> Singapore 117546 http://www.stat.nus.edu.sg/
>> ~statba
>>

Birgit Lemcke
Institut für Systematische Botanik
Zollikerstrasse 107
CH-8008 Zürich
Switzerland
Ph: +41 (0)44 634 8351
birgit.lemcke_at_systbot.uzh.ch

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