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Discriminant Analysis

The objective of discriminant analysis is to classify persons or objects into two or more categories, using a set of intervally scaled predictor variables.

Multiple regression allows us to use an intervally scaled criterion variable such as sales, market share, relative price, or attitude. Often the criterion variable that we are interested in is nominal, that is, purchaser - nonpurchaser, heavy user - light user - nonuser, foreign - domestic car purchaser, credit card - cash purchase, and so forth. Regression analysis is inappropriate in such situations. Instead, discriminant analysis should be used.

The objective is to develop a model that will result in a large proportion of the cases being correctly classified. The discriminant equation can then be used to predict to which class a new case will belong, or, more importantly, to demonstrate which variables are most important in distinguishing between the classes.

Graph of the relationship between three variables. Variable x1 and x2 are independent variables. The dependent variable is membership in Group A or Group B.

The group means, called centroids, are calculated.

Along the x1 axis, the groups have high overlap, (high ratio of between-groups variance to within-group variance), and there is not much discrimination between them.

Similarly, along the x2 axis, the groups have high overlap, and there is not much discrimination between them.

Discriminant analysis finds the new axis, the discriminant axis, on which overlap is minimized.