Bert Gunter gunter.berton at gene.com
Thu Apr 2 17:16:17 CEST 2015

```This is a big topic. You might try looking for tutorials on "linear
models", with "rank" or "rank deficiency" as subtopics. One possible
book is:

http://www.amazon.com/Linear-Models-Chapman-Statistical-Science/dp/1439887330/ref=sr_1_5?s=books&ie=UTF8&qid=1427987551&sr=1-5&keywords=linear+models+in+statistics

... but there are dozens.

Better yet, consult a local statistical expert for help. Trying to
educate yourself is laudable, but may be unrealistic.

Cheers,
Bert

Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
Clifford Stoll

On Thu, Apr 2, 2015 at 7:20 AM, Fix Ace <acefix at rocketmail.com> wrote:
> Thank you very much for the response. Then what does it mean? I am not a stat person, but have to use it for my project. :(
>
>
>      On Wednesday, April 1, 2015 10:58 AM, Michael Dewey <lists at dewey.myzen.co.uk> wrote:
>
>
>  This is really a question about statistics rather than R but see below
>
> On 01/04/2015 06:28, Fix Ace wrote:
>> I tried to run the sample code from R:
>> dd <- data.frame(a = gl(3,4), b = gl(4,1,12))  a b
>> 1  1 1
>> 2  1 2
>> 3  1 3
>> 4  1 4
>> 5  2 1
>> 6  2 2
>> 7  2 3
>> 8  2 4
>> 9  3 1
>> 10 3 2
>> 11 3 3
>> 12 3 4
>> options("contrasts")
>> model.matrix(~ a + b, dd)(Intercept) a2 a3 b2 b3 b4
>> 1            1  0  0  0  0  0
>> 2            1  0  0  1  0  0
>> 3            1  0  0  0  1  0
>> 4            1  0  0  0  0  1
>> 5            1  1  0  0  0  0
>> 6            1  1  0  1  0  0
>> 7            1  1  0  0  1  0
>> 8            1  1  0  0  0  1
>> 9            1  0  1  0  0  0
>> 10          1  0  1  1  0  0
>> 11          1  0  1  0  1  0
>> 12          1  0  1  0  0  1
>> when I tried to remove the intercept from the matrix, I used the following codemodel.matrix(~ 0+a + b, dd)
>>  a1 a2 a3 b2 b3 b41 1 0 0 0 0 02 1 0 0 1 0 03 1 0 0 0 1 04 1 0 0 0 0 15 0 1 0 0 0 06 0 1 0 1 0 07 0 1 0 0 1 08 0 1 0  0 0 19 0 0 1 0 0 010 0 0 1 1 0 011 0 0 1 0 1 012 0 0 1 0 0 1 when I tried to remove the intercept
>>
>
> That got mangled but
>
> In your matrix below try forming the sum of a1+a2+a3 and the sum of
> b1+b2+b3+b4. I think you will find they are linearly related.
>
>> Here I noticed that, all levels of a, a1, a2, and a3, were included. I wonder how  I can include the "b1" in the matrix as well?  a1 a2 a3 b1 b2 b3 b4
>> 1  1  0  0  1  0  0  0
>> 2  1  0  0  0  1  0  0
>> 3  1  0  0  0  0  1  0
>> 4  1  0  0  0  0  0  1
>> 5  0  1  0  1  0  0  0
>> 6  0  1  0  0  1  0  0
>> 7  0  1  0  0  0  1  0
>> 8  0  1  0  0  0  0  1
>> 9  0  0  1  1  0  0  0
>> 10  0  0  1  0  1  0  0
>> 11  0  0  1  0  0  1  0
>> 12  0  0  1  0  0  0  1
>>
>>     [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> --
> Michael
> http://www.dewey.myzen.co.uk/home.html
>
>
>
>         [[alternative HTML version deleted]]
>
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