20-Discriminant2

# the rst discriminant function or variable

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Unformatted text preview: 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 are used in regression. * The group centroid is the mean value for the discriminant scores for a given category of the dependent. Two-group . . . . . . discriminant analysis has two...
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## This document was uploaded on 02/16/2014 for the course STATISTICS 3026 at Columbia.

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