Modeling and Multivariate Methods - SAS

Chapter 20 Performing Discriminant Analysis 493
Introduction
Introduction
Discriminant Analysis is an alternative to logistic regression. In logistic regression, the classification variable
is random and predicted by the continuous variables, whereas in discriminant analysis the classifications are
fixed, and the Y variables are realizations of random variables. However, in both cases, the categorical value
is predicted by the continuous.
There are several varieties of discriminant analysis. JMP implements linear and quadratic discriminant
analysis, along with a method that blends both types. In linear discriminant analysis, it is assumed that the Y
variables are normally distributed with the same variances and covariances, but that there are different
means for each group defined by X. In quadratic discriminant analysis, the covariances can be different
across groups. Both methods measure the distance from each point in the data set to each group's
multivariate mean (often called a centroid) and classify the point to the closest group. The distance measure
used is the Mahalanobis distance, which takes into account the variances and covariances between the
variables.
Discriminating Groups
Fisher's Iris data set is the classic example of discriminant analysis. Four measurements are taken from a
sample consisting of three different species. The goal is to identify the species accurately using the values of
the four measurements. Open Iris.jmp, and select Analyze > Multivariate Methods > Discriminant to
launch the Discriminant Analysis platform. The launch dialog in Figure 20.1 appears.
Figure 20.1 Discriminant Launch Dialog
If you want to find which variables discriminate well, click the checkbox for Stepwise Variable Selection.
Otherwise, the platform uses all the variables you specify. In this example, specify the four continuous
variables as Y, Covariates and Species as X, Categories.