Discriminant Analysis

The mathematical objective of discriminant analysis is to weight and linearly combine the discriminating variables in some fashion so that the groups are forced to be as statistically distinct as possible.

The functions are formed in such a way as to maximize the separation of the groups.

Two things can then be done -- analysis & classification.

Analysis
How is the material to be interpreted i.e., are there any differences between the groups and which variables make the differences?

Classification
If a set of variables is found which provide satisfactory discrimination, classification equations can be derived, their use checked out through hit/rate tables, and if good, they can be used to classify new subjects who were not in the original analysis.

Assumptions

Have at least 2x number of subjects as variables.
Each groups has at least N=# of variables.
Groups have the same variance/covariance structures.
All variables are normally distributed.

Equivalent of the PRE in regression is multi omega squared given by the following formula.

Typical Discrim Output from SYSTAT.