Discriminant Function Analysis

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Discriminant function analysis is concerned with the problem of assigning individuals (on whom several variables have been measured) to certain groups that are already identified in the sample. This problem is quite different from that of classifying a set of individuals into clusters (see Chapter 7), where the objective is to build the most homogeneous groups.
IDAMS module Discran performs stepwise linear discriminant analysis, wherein at each step the most powerful variable is entered into the discriminant function. The criterion used for variable selection depends upon the number of groups selected (number of groups can vary between 2 and 20). In the case of two groups, Mahalanobis distance is used; in the case of three or more groups, the variable selection criterion is the trace of the product of the covariance matrix of all the variables involved and between groups covariance matrix at a particular step. This is a generalization of Mahalanobis distance defined for two groups.
Besides executing the main discriminant analysis on a basic sample, the program offers two optional possibilities: (i) checking the power of the discriminant function(s) with the help of a test sample, in which the group assignment of the cases is known (as in the basic sample), but those cases were not used in the analysis, and (ii) classifying the cases (with the help of the discriminant function provided by prior analysis) in an anonymous sample, where the group assignment of the cases is unknown, or at least is not used.