On Sun, Nov 8, 2009 at 11:28 AM, Peter Dalgaard <p.dalga...@biostat.ku.dk> wrote: > Gabor Grothendieck wrote: >> >> On Sun, Nov 8, 2009 at 11:59 AM, Peng Yu <pengyu...@gmail.com> wrote: >>> >>> On Sun, Nov 8, 2009 at 10:11 AM, Duncan Murdoch <murd...@stats.uwo.ca> >>> wrote: >>>> >>>> On 08/11/2009 11:03 AM, Peng Yu wrote: >>>>> >>>>> I'm wondering which textbook discussed the various contrast matrices >>>>> mentioned in the help page of 'contr.helmert'. Could somebody let me >>>>> know? >>>> >>>> Doesn't the reference on that page discuss them? >>> >>> It does explain what the functions are. But I need a more basic and >>> complete reference. For example, I want to understand what 'Helmert >>> parametrization' (on page 33 of 'Statistical Models in S') is. >>> >> >> Just google for: Helmert contrasts > > Or, > >> contr.helmert(5) > [,1] [,2] [,3] [,4] > 1 -1 -1 -1 -1 > 2 1 -1 -1 -1 > 3 0 2 -1 -1 > 4 0 0 3 -1 > 5 0 0 0 4 > >> MASS::fractions(MASS::ginv(contr.helmert(5))) > [,1] [,2] [,3] [,4] [,5] > [1,] -1/2 1/2 0 0 0 > [2,] -1/6 -1/6 1/3 0 0 > [3,] -1/12 -1/12 -1/12 1/4 0 > [4,] -1/20 -1/20 -1/20 -1/20 1/5 > > and apply brains. > > I.e., except for a slightly odd multiplier, the parameters represent the > difference between each level and the average of the preceding levels.
I realized that my questions are what a contrast matrix is and how it is related to hypothesis testing. For a give hypothesis, how to get the corresponding contrast matrix in a systematical way? There are some online materials, but they are all diffused. I have also read the book Applied Linear Regression Models, which doesn't give a complete descriptions on all the aspects of contrast and contrast matrix. But I would want a textbook that gives a complete description, so that I don't have to look around for other materials. ______________________________________________ R-help@r-project.org mailing list 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.