[R] LDA once again

Prof Brian Ripley ripley at stats.ox.ac.uk
Sun May 25 09:38:14 CEST 2003

Do read the reference: MASS (the book), *and* the code.  Your question is 
addressed in the primary reference for the function, with references to 
the original papers.

On Sun, 25 May 2003, Edoardo M Airoldi wrote:

>  i have one more question about LDA.  just to make surei understand,
> suppose we have two classes, then if i specify a prior=c(.3,.7) in
> lda(...) this will affect my between classes covariance matrix as in:
>  SB = (.3*m1 - .7*m2) %*% inv(Sigma) %*% t(.3*m1 - .7*m2)
>  [is Sigma affected ?] and the threshold to decide which class to assign
> 'test' data = log(.3/.7)

Sigma is undefined!  That symbol is normally used to indicate the 
*population* within-class covariance matrix.  But no, you do not seem to 
understand, so please consult your local statistical experts (since you 
seem inexplicably loath to read our book).

Overview for well-informed readers:  the `Fisher' view of LDA has no
priors: the Rao and Bryan views do, and they differ.  In practice it only
matters if LDA is used when the within-class covariances are not common
but the conventional theory assumes the model is correct.

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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