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 <ace...@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. :( > Could you please recommend some readings about it? Thanks a lot! > > > On Wednesday, April 1, 2015 10:58 AM, Michael Dewey > <li...@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@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > > -- > Michael > http://www.dewey.myzen.co.uk/home.html > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
