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

[Peng Yu]

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.