The initial input data do not have to be centered or

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Unformatted text preview: have to be centered or standardized before the analysis as is the case in principal components, the outcome of the final discriminant analysis will not be affected by the scaling. . . . . . . Discriminant Functions A discriminant function, also called a canonical root, is a latent variable which is created as a linear combination of discriminating (independent) variables, such that L = b1 x1 + b2 x2 + ... + bp xp + c, where the b's are discriminant coefficients, the x's are discriminating variables, and c is a constant. This is similar to multiple regression, but the b's are discriminant coefficients which maximize the distance between the means of the criterion (dependent) variable. Note that the foregoing assumes the discriminant function is estimated using ordinary least-squares, the traditional method, but there is also a version involving maximum likelihood estimation. . . . . . . Least Squares Method of estimation of Discriminant Functions The variance covariances matrix can be decomposed into two parts: one is the variance within each class and the other the variability between clases, or we can decompose the sum of squares and cross products (the same up to a constant factor) T = B+W T = X′ (In − P1n)X B = X′ (Pg − P1n)X between-class W = X′ (In − Pg)X within In is the identity matrix. P1n is the orthogonal projection in the space 1n . (i.e. P1n = 1n 1′ /n ). Such that (In − P1n)X is n the matrix of centered cases. Pg is the...
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This note was uploaded on 07/29/2011 for the course STAT 202 at Stanford.

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