[R] linear discriminant analysis in MASS

[Prof Brian Ripley]

On Mon, 20 Feb 2006, Alain Paquette wrote:

> Hello R people
>
> I now know how to run my discriminant analysis with the lda function in
> MASS:
> lda.alain=lda(Groupes ~ Ht.D0 + Lc.Dc + Ram + IDF, gr, CV = FALSE)
> and it works fine.

CV=FALSE is the default and so not needed.

> But I am missing a test and cannot find any help on how to get it, if it
> exist.
>
> The "S" equivalent:

There is no such function in S, and I rather object as the S equivalent is 
lda() (and as the author of both I should know).  Credit where credit is 
due: discrim() is an S-PLUS function, indebted to lda().

> discrim(structure(.Data = Groupes ~ Ht.D0 + Lc.Dc + Ram + IDF, class =
> "formula"), data = gr, family = Canonical(cov.structure =
> "homoscedastic"), na.action = na.omit, prior = "proportional")
> outputs a nice matrix of Mahalanobis distances between groups and even
> tests (Hotelling's T Squared) for significant distances.

Well, it seems not to.  That is part of the output of the summary() 
method, which itself calls the multicomp() method.

> Why don't I just take the "S" output you say?  Because like you, I'd
> rather put in my paper that I did it using R of course!

No `of course' applies. If you learnt of this output from S-PLUS, I urge 
you to credit it honestly and accurately.  (If you refer to lda, you 
should credit that, not just R.)

> Does anyone know of a way to get this test out of lda?  Or of another R
> package that does it?

Mahalanobis distance between groups is easy, as this is just Euclidean 
distance between group centres in the scaled space.  The test statistics 
can be produced, but

- they are critically dependent on the unrealistic assumptions of 
multivariate normality and variance homogeneity and

- there needs to be an adjustment for multiple comparisons.

-- 
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