the group centroid is the mean value for the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 07/29/2011 for the course STAT 202 at Stanford.

Ask a homework question - tutors are online