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# the group centroid is the mean value for the

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Unformatted text preview: e 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 centroids, one for each group. * Number of discriminant functions. There is one discriminant function for 2-group discriminant analysis, but for higher order DA, the number of functions (each with its own cut-off value) is the lesser of (g - 1), where g is the number of groups, or p,the number of discriminating (independent) variables. Each discriminant function is orthogonal to the others. . . . . . . Mahalonobis Distance Mahalanobis distances are used in analyzing cases in discriminant analysis. For instance, one might wish to analyze a new, unknown set of cases in comparison to an existing set of known cases. Mahalanobis distance is the distance between a case and the centroid for each group in attribute space (p-dimensional space deﬁned by p variables) taking into account the covariance of the variables. The population version: Suppose g groups, and p variable, and that the mean for group i is a vector µi = [µi1 , µi2 , . . . µip ], 1 ≤ i ≤ g, and call σ the variance-covariance matrix (which we suppose to be the same in all the groups). The Mahalanobis distance between group i and group j is: Dij = (µi − µj )′ Σ−1 (µi − µj ) . . . . . . The Mahalanobis distance is often used to compute the distance of a case x and the centre of the population as: D2 (x, µ) = (x − µ)′ Σ−1 (x − µ) When the distr...
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## This note was uploaded on 07/29/2011 for the course STAT 202 at Stanford.

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