[R] evaluation of discriminant functions+multivariate homoscedasticity

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Jan 20 15:37:36 CET 2004

These topics are not much used by trained statisticians.  In particular, 
the tests such as 1) are so sensitive to multivariate normality as to be 
almost no practical use.

Even if the assumptions of multivariate normality hold, the standard
arguments of the robustniks hold here too:  the departure from the
homogeneity assumptions hurts you before statistical signifcance is
reached, and it is better to act as if the homoscedasticity does not hold
(so use QDA or a regularized version of it).  But then multivariate
normality almost never comes close to holding true outside simulation
experiments.  We do teach LDA and QDA, but mainly to point out that
logistic discrimination is a much safer procedure.

If you want to do statistics like SPSS does, I suggest you use SPSS.
R is not a substitute for SPSS -- in particular it lacks a lot of
legacy material that the much older packages have.  But as R is highly 
programmable, you can add these tests if you want to.

On Tue, 20 Jan 2004, Janke ten Holt wrote:

> Hello,
> I am switching from SPSS-Windows to R-Linux. My university is very 
> SPSS-oriented so maybe that's the cause of my problems. I am a beginner 
> in R and my assignments are SPSS-oriented, so I hope I don't annoy 
> anyone with my questions...
> Right now I've got 2 problems:
> -I have to evaluate discriminant functions I have calculated with 
> lda(MASS). I can't find a measure that evaluates their significance 
> (Wilk's lambda in my textbook (Stevens,(2002),"Applied multivariate 
> statistics for the social sciences")and in SPSS). Is there a Wilk's 
> lambda for discriminant functions in R? or can I use an alternative 
> measure? or am I thinking in the wrong direction? I have searched the 
> help-archive to find similar questions to mine but no answer to them.
> -My second problem: to check the assumption of multivariate 
> homoscedasticity I have to test if the variance-covariance matrices for 
> my variables are homogene. My textbook suggests Box's M test. I can't 
> find this statistic in R. Again I have found similar questions in the 
> help-archives, but no answers. Is there a way to calculate Box's M in R? 
> Or is there an alternative way to check for multivariate homoscedasticity?
> Any suggestion would be greatly appreciated!
> Cheers,
> Janke ten Holt

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

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