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Bugs? when dealing with contrasts

7 messages · Peter Dalgaard, Gabor Grothendieck, Berwin A Turlach

Original
Gabor Grothendieck
# 
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Below are two cases where I don't seem to be getting contr.sum
contrasts even though they were specified.  Are these bugs?

The first case is an interaction between continuous and factor variables.

The second case contrasts= was specified as an arg to lm.  The second
works ok if we set the contrasts through options but not if we set it
through an lm argument.
[1] "contr.sum"  "contr.poly"
[1] -2 -1  0  1  2 -2 -1  0  1  2 -2 -1  0  1  2
[1] 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3
Levels: 1 2 3
(Intercept) scores:fac1 scores:fac2 scores:fac3
1            1          -2           0           0
2            1          -1           0           0
3            1           0           0           0
4            1           1           0           0
5            1           2           0           0
6            1           0          -2           0
7            1           0          -1           0
8            1           0           0           0
9            1           0           1           0
10           1           0           2           0
11           1           0           0          -2
12           1           0           0          -1
13           1           0           0           0
14           1           0           0           1
15           1           0           0           2
attr(,"assign")
[1] 0 1 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.sum"
fac1 fac2
1  1   -2    0
2  1   -1    0
3  1    0    0
4  1    1    0
5  1    2    0
6  1    0   -2
7  1    0   -1
8  1    0    0
9  1    0    1
10 1    0    2
11 1    2    2
12 1    1    1
13 1    0    0
14 1   -1   -1
15 1   -2   -2
[1] "contr.treatment" "contr.poly"
(Intercept) fac2 fac3
1            1    0    0
2            1    0    0
3            1    0    0
4            1    0    0
5            1    0    0
6            1    1    0
7            1    1    0
8            1    1    0
9            1    1    0
10           1    1    0
11           1    0    1
12           1    0    1
13           1    0    1
14           1    0    1
15           1    0    1
attr(,"assign")
[1] 0 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.treatment"
(Intercept) fac2 fac3
1            1    0    0
2            1    0    0
3            1    0    0
4            1    0    0
5            1    0    0
6            1    1    0
7            1    1    0
8            1    1    0
9            1    1    0
10           1    1    0
11           1    0    1
12           1    0    1
13           1    0    1
14           1    0    1
15           1    0    1
attr(,"assign")
[1] 0 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.treatment"
(Intercept) fac1 fac2
1            1    1    0
2            1    1    0
3            1    1    0
4            1    1    0
5            1    1    0
6            1    0    1
7            1    0    1
8            1    0    1
9            1    0    1
10           1    0    1
11           1   -1   -1
12           1   -1   -1
13           1   -1   -1
14           1   -1   -1
15           1   -1   -1
attr(,"assign")
[1] 0 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.sum"
[1] "R version 2.10.1 (2009-12-14)"
[1] "Windows Vista (build 6002) Service Pack 2"
Peter Dalgaard
#
Gabor Grothendieck wrote:
In case #2, I think you just failed to read the help page.
(Intercept) fac1 fac2
1            1    1    0
2            1    1    0
3            1    1    0
4            1    1    0
5            1    1    0
6            1    0    1
7            1    0    1
8            1    0    1
9            1    0    1
10           1    0    1
11           1   -1   -1
12           1   -1   -1
13           1   -1   -1
14           1   -1   -1
15           1   -1   -1
attr(,"assign")
[1] 0 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.sum"

As for case #1, the rules are tricky in cases where interactions are
present without main effects, but AFAICS, what you observe is
essentially the same effect as
fac1 fac2 fac3
1     1    0    0
2     1    0    0
3     1    0    0
4     1    0    0
5     1    0    0
6     0    1    0
7     0    1    0
8     0    1    0
9     0    1    0
10    0    1    0
11    0    0    1
12    0    0    1
13    0    0    1
14    0    0    1
15    0    0    1
attr(,"assign")
[1] 1 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.sum"


I.e., that R reverts to using indicator variables when the intercept is
absent.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gabor Grothendieck
    

    

      
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On Wed, Apr 21, 2010 at 4:26 PM, Peter Dalgaard <pdalgd at gmail.com> wrote:

            

      
      
      
    

        
Is there any nice way of getting contr.sum coding for the interaction
as opposed to the ugly code in my post that I used to force it? i.e.
cbind(1, model.matrix(~ fac)[,2:3] * scores)

  
  


  


      

    

    

      
      

        


  

        

      Berwin A Turlach
    

    

      
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G'day Gabor,

On Wed, 21 Apr 2010 14:00:33 -0400

        
Gabor Grothendieck <ggrothendieck at gmail.com> wrote:

        

            

      
      
      
    

        
Short answer: no. :)

            

      
      
      
    

        
When creating the model matrix, the various levels of a factor are
first coded as indicator variables (for creation of the main effects
and for creation of interactions).  The contrast matrix is then
applied to remove redundant columns from the design matrix; that is,
columns that are known to be redundant due to the *design* (i.e. model
formula as a whole), depending on whether data is available for all
levels of a factor (or combinations of levels if several factors are in
the model) you can still end up with a design matrix that does not have
full column rank.

In this case, since there is no main effect fac, the three columns that
are put into the design matrix due to the score:fac term do not create
a singularity, hence the contrast matrix is not applied to these three
columns.

The above description is probably a bit rough and lacking in detail (if
not even wrong in some details).  IMHO, the best explanation of how R
goes from the model formula to the actual design matrix (for linear
models) can still be found in MASS; though, if I am not mistaken,
current versions of R seem to proceed slightly different to that
description in more complicated models (i.e. several factors and
continuous explanatory variables).

            

      
      
      
    

        
If you wish to have the design matrix that contains the interaction
terms as if the model had the main effects too but without the columns
corresponding to the main effects, then just instruct R that you want
to have such a matrix:

R> model.matrix(~ scores*fac)[,-(2:4)]
   (Intercept) scores:fac1 scores:fac2
1            1          -2           0
2            1          -1           0
3            1           0           0
4            1           1           0
5            1           2           0
6            1           0          -2
7            1           0          -1
8            1           0           0
9            1           0           1
10           1           0           2
11           1           2           2
12           1           1           1
13           1           0           0
14           1          -1          -1
15           1          -2          -2

Though, I am not sure why one wants to fit such a model.

            

      
      
      
    

        
No bug either, but wrong use of the optional argument "contrasts" for 
"lm".  Please read the help page of "lm", which points you to the help
page of "model.matrix.default", which contains pertinent examples; in
your case:

R> model.matrix(lm(seq(15) ~ fac, contrasts = list(fac="contr.sum")))  
   (Intercept) fac1 fac2
1            1    1    0
2            1    1    0
3            1    1    0
4            1    1    0
5            1    1    0
6            1    0    1
7            1    0    1
8            1    0    1
9            1    0    1
10           1    0    1
11           1   -1   -1
12           1   -1   -1
13           1   -1   -1
14           1   -1   -1
15           1   -1   -1
attr(,"assign")
[1] 0 1 1
attr(,"contrasts")
attr(,"contrasts")$fac
[1] "contr.sum"

HTH.

Cheers,

	Berwin

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      Gabor Grothendieck
    

    

      
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On Wed, Apr 21, 2010 at 11:38 PM, Berwin A Turlach

        
<berwin at maths.uwa.edu.au> wrote:

            

      
      
      
    

        
To save on degrees of freedom.

I had reduced it to the minimum needed to illustrate but in fact its
closer to this (except the coding is not the one needed):

options(contrasts = c("contr.sum", "contr.poly"))
tab <- as.table(matrix(1:21, 7))
dimnames(tab) = list(X = letters[1:7], Y = LETTERS[1:3])
rr <- factor(row(tab))
cc <- factor(col(tab))
scores <- rep(seq(-3,3), 3)
model.matrix( ~ rr + cc + scores:cc)

so the main effects are rr and cc but scores takes the place of rr in
the interaction.

Your description of the process seems right since it would predict
that the following gives the required coding and it does:

model.matrix(~ scores*cc + rr)[,-2]

Thanks.

  
  


  


      

    

    

      
      

        


  

        

      Peter Dalgaard
    

    

      
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Gabor Grothendieck wrote:

            

      
      
      
    

        
...

            

      
      
      
    

        
I think not. In general, an interaction like ~fac:scores indicates three
lines with a common intercept and three different slopes, and changing
the parametrization is not supposed to change the model, whereas your
model inserts a restriction that the slopes sum to zero (if I understand
correctly). So if you want to fit "ugly" models, you get to do a little
ugly footwork.

(A similar, simpler, issue arises if you want to have a 2x2 design with
no effect in one column and/or one row (think clinical trial, placebo
vs. active, baseline vs. treated. You can only do this us explicit dummy
variables, not with the two classifications represented as factors.)

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gabor Grothendieck
    

    

      
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On Thu, Apr 22, 2010 at 2:32 AM, Peter Dalgaard <pdalgd at gmail.com> wrote:

            

      
      
      
    

        
OK. Thanks.  I guess that's fair.