[R] reference on contr.helmert and typo on its help page.

[John Fox]

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-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Peng Yu
> Sent: November-08-09 7:41 PM
> To: r-help at 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 <jfox at 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-bounces at r-project.org
[mailto:r-help-bounces at r-project.org]
> > On
> >> Behalf Of Peng Yu
> >> Sent: November-08-09 4:52 PM
> >> To: r-help at 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.dalgaard at biostat.ku.dk> wrote:
> >> > Gabor Grothendieck wrote:
> >> >>
> >> >> On Sun, Nov 8, 2009 at 11:59 AM, Peng Yu <pengyu.ut at gmail.com>
wrote:
> >> >>>
> >> >>> On Sun, Nov 8, 2009 at 10:11 AM, Duncan Murdoch
<murdoch at 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 at 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.
> >
> >
> >
> 
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