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Unformatted text preview: matrix projecting
onto the subspace generated by the columns of the binary
discriminating matrix G. This matrix has g columns and a one
on row i and column j if observaton i belongs to group j
a′ Ta = a′ Ba + a′ Wa.
. . . . . . The ﬁrst discriminant function (or variable or axis) is the
linear combination of the original variables that maximises:
a′ Ba/a′ Ta
This is equivalent to maximizing the quadratic form a′ Ba
under a constraint a′ Ta = 1. This is also equivalent to ﬁnding
the eigenvectors of BW−1 . . . . . . * The discriminant score, also called the DA score, is the
value resulting from applying a discriminant function formula
to the data for a given case. The Z score is the discriminant
score for standardized data.
* Cutoff: If the discriminant score of the function is less
than or equal to the cutoff, the case is classed as 0, or if
above it is classed as 1. When group sizes are equal, the
cutoff is the mean of the two centroids (for two-group DA).
If the groups are unequal, the cutoff is the weighted mean.
* Unstandardized discriminant coefﬁcients are used in the
formula for making the classiﬁcations in DA, much as b
coefﬁcients are used in regression in making predictions. The
product of the unstandardized coefﬁcients with the
observations yields the discriminant scores.
* Standardized discriminant coefﬁcients are used to compare
the relative importance of the independent variables, much as
beta weights ar...
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This note was uploaded on 07/29/2011 for the course STAT 202 at Stanford.