Pg is the matrix projecting onto the subspace

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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.

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