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What does PCOORD do ?
Program PCOORD produces a reduced-space ordination following the
method of principal coordinates analysis
(Gower, 1966). Like principal
components analysis, this is a metric multidimensional scaling
method. The computations, however, are made on a similarity or
distance matrix instead of a raw data table; this is also the
case with the methods of nonmetric multidimensional
scaling.
Each distance d is first transformed into a new distance
d' = -d^2/2 before centering the
matrix using the formula
alpha = d' - d'bari - d'barj +
d'bar
where d'bari and
d'barj are respectively the mean of row
i and of column j in distance matrix d',
while d'bar is the mean of all the values in the matrix. The
new coordinates of the objects in reduced space are the eigenvectors of
that centered matrix, after normalization to the square root of their
eigenvalues.
There are in principle no limits to the size of the matrices that can
be analyzed by the Macintosh version; the program occupies all the
available RAM space in the computer, so that the size of the matrices
that can be analyzed is, in practice, a function not only of the size
of the memory available in the machine, but also of the simultaneous
use of MultiFinder, of a RAM cache, or of other programs.
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