# [Rd] model.matrix bug? Nested factor yields singular design matrix.

From: Steven McKinney <smckinney_at_bccrc.ca>
Date: Thu, 17 May 2007 11:41:02 -0700

Hi all,

I believe this is a bug in the model.matrix function. I'd like a second opinion before filing a bug report.

If I have a nested covariate B with multiple values for just one level of A, I can not get a non-singular design matrix out of model.matrix

> df <- data.frame(A = factor(c("a", "a", "x", "x"), levels = c("x", "a")),

```+                  B = factor(c("b", "x", "x", "x"), levels = c("x", "b")))
```

>
> df

A B
1 a b
2 a x
3 x x
4 x x

So of course the full design matrix is singular, this is expected.

> model.matrix(~ A * B, df)

(Intercept) Aa Bb Aa:Bb

```1           1  1  1     1
2           1  1  0     0
3           1  0  0     0
4           1  0  0     0
```

attr(,"assign")
[1] 0 1 2 3
attr(,"contrasts")
attr(,"contrasts")\$A
[1] "contr.treatment"

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

I'd like to drop the B main effect column, but get the unexpected result of a column of zeroes.

> model.matrix(~ A * B - B, df)

(Intercept) Aa Ax:Bb Aa:Bb

```1           1  1     0     1
2           1  1     0     0
3           1  0     0     0
4           1  0     0     0
```

attr(,"assign")
[1] 0 1 2 2
attr(,"contrasts")
attr(,"contrasts")\$A
[1] "contr.treatment"

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

>
>

This does not happen in S-PLUS.

> info()

S info file C:\DOCUME~1\kilroy\LOCALS~1\Temp\S0107EB.tmp will be removed at session end \$Sinfo:
Enterprise Developer Version 7.0.6 for Microsoft Windows : 2005

```SHOME:                                               C:/PROGRAMFILES/INSIGHTFUL/splus70
prog.name:                               SPLUS.EXE
load.date:                                 Sun Dec 04 23:15:59 2005
date:                                         Thu May 17 07:38:16 PDT 2007

```

> options(contrasts = c("contr.treatment", "contr.poly"))
> df <- data.frame(A = factor(c("a", "a", "x", "x"), levels = c("x", "a")),

```+                   B = factor(c("b", "x", "x", "x"), levels = c("x", "b")))
```

> model.matrix(~ A * B - B, df)

(Intercept) A A:B
```1           1 1   1
2           1 1   0
3           1 0   0
4           1 0   0
```

>

This is what I was expecting to get in R, but can not.

Alternate specifications in R continue to yield a singular design matrix

>
> model.matrix(~ A/B, df)

(Intercept) Aa Ax:Bb Aa:Bb

```1           1  1     0     1
2           1  1     0     0
3           1  0     0     0
4           1  0     0     0
```

attr(,"assign")
[1] 0 1 2 2
attr(,"contrasts")
attr(,"contrasts")\$A
[1] "contr.treatment"

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

> model.matrix(~ A + A:B, df)

(Intercept) Aa Ax:Bb Aa:Bb

```1           1  1     0     1
2           1  1     0     0
3           1  0     0     0
4           1  0     0     0
```

attr(,"assign")
[1] 0 1 2 2
attr(,"contrasts")
attr(,"contrasts")\$A
[1] "contr.treatment"

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

Why is the Ax:Bb column being included?

Have I missed a control parameter or some other way of specifying to model.matrix not to include this extra column?

Any feedback appreciated.

Best regards

Steven McKinney

Statistician
Molecular Oncology and Breast Cancer Program British Columbia Cancer Research Centre

email: smckinney_at_bccrc.ca

tel: 604-675-8000 x7561

BCCRC
Molecular Oncology
675 West 10th Ave, Floor 4
Vancouver B.C.
V5Z 1L3