R help - Mar 2007 - Model matrix with redundant columns included

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Hello,

Normally when you call model.matrix, you get a matrix that has
aliased/redundant columns deleted. For example:
> m <- expand.grid(a=factor(1:3), b=factor(1:3))
> model.matrix(~a + b, m)
  (Intercept) a2 a3 b2 b3
1           1  0  0  0  0
2           1  1  0  0  0
3           1  0  1  0  0
4           1  0  0  1  0
5           1  1  0  1  0
6           1  0  1  1  0
7           1  0  0  0  1
8           1  1  0  0  1
9           1  0  1  0  1
attr(,"assign")
[1] 0 1 1 2 2
attr(,"contrasts")
attr(,"contrasts")$a
[1] "contr.treatment"

attr(,"contrasts")$b
[1] "contr.treatment"

The result is a matrix with 5 columns including the intercept.

However, for my purposes I need a matrix that includes all columns,
including those that would normally be redundant. Is there any way to do
this? For the example, this would be something like

  a1 a2 a3 b1 b2 b3
1  1  0  0  1  0  0
2  0  1  0  1  0  0
3  0  0  1  1  0  0
4  1  0  0  0  1  0
5  0  1  0  0  1  0
6  0  0  1  0  1  0
7  1  0  0  0  0  1
8  0  1  0  0  0  1
9  0  0  1  0  0  1

Including -1 as part of the model formula removes the intercept and adds
the column for the base level of the first variable, but not the rest.

Thanks,


-- 
Hong Ooi
Senior Research Analyst, IAG Limited
388 George St, Sydney NSW 2000
+61 (2) 9292 1566

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On Wed, 2007-03-14 at 14:57 +1100, Hong Ooi wrote:
> Hello,
> 
> Normally when you call model.matrix, you get a matrix that has
> aliased/redundant columns deleted. For example:
> 
> > m <- expand.grid(a=factor(1:3), b=factor(1:3))
> > model.matrix(~a + b, m)
>   (Intercept) a2 a3 b2 b3
> 1           1  0  0  0  0
> 2           1  1  0  0  0
> 3           1  0  1  0  0
> 4           1  0  0  1  0
> 5           1  1  0  1  0
> 6           1  0  1  1  0
> 7           1  0  0  0  1
> 8           1  1  0  0  1
> 9           1  0  1  0  1
> attr(,"assign")
> [1] 0 1 1 2 2
> attr(,"contrasts")
> attr(,"contrasts")$a
> [1] "contr.treatment"
> 
> attr(,"contrasts")$b
> [1] "contr.treatment"
> 
> The result is a matrix with 5 columns including the intercept.
> 
> However, for my purposes I need a matrix that includes all columns,
> including those that would normally be redundant. Is there any way to do
> this? For the example, this would be something like
> 
>   a1 a2 a3 b1 b2 b3
> 1  1  0  0  1  0  0
> 2  0  1  0  1  0  0
> 3  0  0  1  1  0  0
> 4  1  0  0  0  1  0
> 5  0  1  0  0  1  0
> 6  0  0  1  0  1  0
> 7  1  0  0  0  0  1
> 8  0  1  0  0  0  1
> 9  0  0  1  0  0  1
> 
> Including -1 as part of the model formula removes the intercept and adds
> the column for the base level of the first variable, but not the rest.
> 
> Thanks,

There may be a better way, but this seems to work:
> m
  a b
1 1 1
2 2 1
3 3 1
4 1 2
5 2 2
6 3 2
7 1 3
8 2 3
9 3 3

MAT <- do.call("cbind", lapply(m, function(x) model.matrix(~ x -
1)))
> MAT
  x1 x2 x3 x1 x2 x3
1  1  0  0  1  0  0
2  0  1  0  1  0  0
3  0  0  1  1  0  0
4  1  0  0  0  1  0
5  0  1  0  0  1  0
6  0  0  1  0  1  0
7  1  0  0  0  0  1
8  0  1  0  0  0  1
9  0  0  1  0  0  1

colnames(MAT) <- names(unlist(lapply(m, levels)))
 
> MAT
  a1 a2 a3 b1 b2 b3
1  1  0  0  1  0  0
2  0  1  0  1  0  0
3  0  0  1  1  0  0
4  1  0  0  0  1  0
5  0  1  0  0  1  0
6  0  0  1  0  1  0
7  1  0  0  0  0  1
8  0  1  0  0  0  1
9  0  0  1  0  0  1


You can cbind() the (Intercept) column back in if you require.

HTH,

Marc Schwartz