Dear Peng, I'm tempted to try to get an entry in the fortunes package but will instead try to answer your questions directly:
> -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf Of Peng Yu > Sent: November-08-09 7:41 PM > To: r-h...@stat.math.ethz.ch > Subject: Re: [R] reference on contr.helmert and typo on its help page. > > Dear John, > > I did read Section 9.1.2 and various other textbooks before posting my > questions. But each reference uses slightly different notations and > terminology. I get confused and would like a description that > summaries everything so that I don't have to refer to many different > resources. May I ask a few questions on the section in your textbook? > > Which variable in Section 9.1.2 is "a matrix of contrasts" mentioned > in the help page of 'contr.helmert'? Which matrix of contrast in R > corresponds to dummy regression? With different R formula, e.g. y ~ x > vs. y ~ x -1, $X_F$ (mentioned on page 189) is different and hence > $\beta_F$ (mentioned in eq. 9.3) is be different. So my understanding > is that the matrix of contrast should depend on the formula. But it is > not according to the help page of "contr.helmert". If the model is simply y ~ A, for the factor A, then cbind(1, contrasts(A)) is what I call X_B, the row-basis of the model matrix. As I explain in the section that you read, the level means are mu = X_B beta, and thus beta = X_B^-1 mu = 0 are the hypotheses tested by the contrasts. Moreover, if, as in Helmert contrasts, the columns of X_B are orthogonal, then so are the rows of X_B^-1, and the latter are simply rescalings of the former. That allows one conveniently to code the hypotheses directly in X_B; all this is also explained in that section of my book, and is essentially what Peter D. told you. In R, contr.treatment and contr.SAS provide dummy-variable (0/1) coding of regressors, differing only in the selection of the reference level. John > > Regards, > Peng > > On Sun, Nov 8, 2009 at 6:17 PM, John Fox <j...@mcmaster.ca> wrote: > > Dear Peng Yu, > > > > Perhaps you're referring to my text, Applied Linear Regression Analysis and > > Generalized Linear Models, since I seem to recall that you sent me a number > > of questions about it. See Section 9.1.2 on linear contrasts for the answer > > to your question. > > > > I hope this helps, > > John > > > > -------------------------------- > > John Fox > > Senator William McMaster > > Professor of Social Statistics > > Department of Sociology > > McMaster University > > Hamilton, Ontario, Canada > > web: socserv.mcmaster.ca/jfox > > > > > >> -----Original Message----- > >> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] > > On > >> Behalf Of Peng Yu > >> Sent: November-08-09 4:52 PM > >> To: r-h...@stat.math.ethz.ch > >> Subject: Re: [R] reference on contr.helmert and typo on its help page. > >> > >> 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. > > > > > > > > ______________________________________________ > 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. ______________________________________________ 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.
