R help - Aug 2006 - Constrain coefs. in linear model to sum to 0

Hello!

I would like to use constrain to sum coeficients of a factor to 0 instead
of classical corner contraint i.e. I would like to fit a model like

lm(y ~ 1 + effectA + effectB)

and say get parameters

intercept
effectA_1
effectA_2
effectB_1
effectB_2
effectB_3

where effectA_1 represents deviation of level A_1 from intercept and 
sum(effectA_1, effectA_2) = 0 and the same for factor B.

Is this possible to do?

Lep pozdrav / With regards,
    Gregor Gorjanc

----------------------------------------------------------------------
University of Ljubljana     PhD student
Biotechnical Faculty        URI: http://www.bfro.uni-lj.si/MR/ggorjan
Zootechnical Department     mail: gregor.gorjanc <at> bfro.uni-lj.si
Groblje 3                   tel: +386 (0)1 72 17 861
SI-1230 Domzale             fax: +386 (0)1 72 17 888
Slovenia, Europe
----------------------------------------------------------------------
"One must learn by doing the thing; for though you think you know it,
 you have no certainty until you try." Sophocles ~ 450 B.C.

"Gorjanc Gregor" <Gregor.Gorjanc at bfro.uni-lj.si> writes:
> Hello!
> 
> I would like to use constrain to sum coeficients of a factor to 0 instead
> of classical corner contraint i.e. I would like to fit a model like
> 
> lm(y ~ 1 + effectA + effectB)
> 
> and say get parameters
> 
> intercept
> effectA_1
> effectA_2
> effectB_1
> effectB_2
> effectB_3
> 
> where effectA_1 represents deviation of level A_1 from intercept and 
> sum(effectA_1, effectA_2) = 0 and the same for factor B.
> 
> Is this possible to do?
This is what contr.sum does. There are multiple ways to set this
instead of the default contr.treatment:

(a) options(contrast=....) 

(b) contrasts(effectA) <-  contr.sum 

(c) lm(y~C(effectA,contr.sum)+.....)

Notice though that you only get parameters for a linearly independent
subset of groups (i.e. the first n-1 of them). The last one is defined
as -sum(the other levels).

-- 
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

Gorjanc Gregor asks:
> 
> Hello!
> 
> I would like to use constrain to sum coeficients of a factor to 0
instead
> of classical corner contraint i.e. I would like to fit a model like
> 
> lm(y ~ 1 + effectA + effectB)
> 
> and say get parameters
> 
> intercept
> effectA_1
> effectA_2
> effectB_1
> effectB_2
> effectB_3
> 
> where effectA_1 represents deviation of level A_1 from intercept and 
> sum(effectA_1, effectA_2) = 0 and the same for factor B.
> 
> Is this possible to do?
Yes, but not quite as simply as you would like.  If you set

options(contrasts = c("contr.sum", "contr.poly"))

for example, then factor models are parametrised as you wish above,
BUT you don't get all the effects directly

In your case above, for example, if fm is the fitted model object, then

coef(fm)

Will give you intercept, effectA_2, effectB_2, effectB_3.  The
remaining effects*_1 you will need to calculate as the negative of the
sum of all the others.

This gets a bit more complicated when you have crossed terms, a*b, but
the same principle applies.

Bill Venables.

> 
> Lep pozdrav / With regards,
>     Gregor Gorjanc
> 
> ----------------------------------------------------------------------
> University of Ljubljana     PhD student
> Biotechnical Faculty        URI: http://www.bfro.uni-lj.si/MR/ggorjan
> Zootechnical Department     mail: gregor.gorjanc <at> bfro.uni-lj.si
> Groblje 3                   tel: +386 (0)1 72 17 861
> SI-1230 Domzale             fax: +386 (0)1 72 17 888
> Slovenia, Europe
> ----------------------------------------------------------------------
> "One must learn by doing the thing; for though you think you know it,
>  you have no certainty until you try." Sophocles ~ 450 B.C.

Well, now's your chance!