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The CANDISC Procedure |
Computational Details |
Canonical discriminant analysis is equivalent to canonical correlation analysis between the quantitative variables and a set of dummy variables coded from the class variable. In the following notation the dummy variables are denoted by and the quantitative variables by
. The total sample covariance matrix for the
and
variables is
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When is the number of groups,
is the number of observations in group
, and
is the sample covariance matrix for the
variables in group
, the within-class pooled covariance matrix for the
variables is
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The canonical correlations, , are the square roots of the eigenvalues,
, of the following matrix. The corresponding eigenvectors are
.
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Let be the matrix with the eigenvectors
that correspond to nonzero eigenvalues as columns. The raw canonical coefficients are calculated as follows:
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The pooled within-class standardized canonical coefficients are
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The total sample standardized canonical coefficients are
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Let be the matrix with the centered
variables as columns. The canonical scores can be calculated by any of the following:
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For the multivariate tests based on ,
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where is the total number of observations.
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