[R] Reconstructing LD function

[Prof Brian Ripley]

On Fri, 1 Jul 2005 usenet at s-boehringer.de wrote:

> On Mon, 2005-06-27 at 13:18, Prof Brian Ripley wrote:
>> On Mon, 27 Jun 2005 usenet at s-boehringer.de wrote:
>>
>>> in an LDA analysis with n groups n-1 LD functions result. Implicitly this
>>> defines an LD fucntion for the last group. Does there exist code already
>>> to explictly construct this LD function?
>
> Thank you for the quick reply.
>
>> What `LDA analysis' are our discussing here?  (LDA is usually
>> `linear discriminant analysis', so what did you mean and what R function
>> are you nor referring to?)
>
>> R has lda in package MASS, and that works with n LD functions.  To reduce
>> it to n-1, subtract the last one from the others, in which case LD_n == 0.
> Indeed I have been using the MASS::lda package.
>
>> Anything you do in LD analysis only depends on differences in LD
>> functions, and there really are n of them.  With two groups one is
>> conventionally taken to be zero (the first, usually, not the last).

> How is the classifcation decision reached from the LD functions? Are
> those what is known as "linear Fisherian discriminant functions"? If so,
> I'm not positive about why one of these functions can be set to 0.

What I did say:

`Anything you do in LD analysis only depends on differences in LD 
functions'

So subtracting any one function from the others does not change the 
differences.

LD is not about classification, and Fisher did not do classification, nor 
did he use more than 2 classes.  I suspect your difficulty is going to be 
clearing your preconceptions. lda() is support software for a book which 
does explain the relationship between Fisher's discrimination and 
classification: please consult it for the background.


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595