Discriminant Analysis

Discriminant analysis is a method of predicting some level of a one-way classification based on known values of the responses. The technique is based on how close a set of measurement variables are to the multivariate means of the levels being predicted. Discriminant analysis is more fully implemented using the Discriminant Platform (see the Multivariate Methods book).

In JMP you specify the measurement variables as Y effects and the classification variable as a single X effect. The multivariate fitting platform gives estimates of the means and the covariance matrix for the data, assuming that the covariances are the same for each group. You obtain discriminant information with the Save Discrim option in the popup menu next to the MANOVA platform name. This command saves distances and probabilities as columns in the current data table using the initial E and H matrices.

For a classification variable with k levels, JMP adds k distance columns, k classification probability columns, the predicted classification column, and two columns of other computational information to the current data table.

Example of the Save Discrim Option

Examine Fisher’s Iris data as found in Mardia, Kent, and Bibby (1979). There are k = 3 levels of species and four measures on each sample.

1.	Select Help > Sample Data Library and open Iris.jmp.

2.	Select Analyze > Fit Model.

3.	Select Sepal length, Sepal width, Petal length, and Petal width and click Y.

4.	Select Species and click Add.

5.	Next to Personality, select Manova.

6.	Click Run.

7.	From the red triangle menu next to Manova Fit, select Save Discrim.

The following columns are added to the Iris.jmp sample data table:


SqDist[0]	Quadratic form needed in the Mahalanobis distance calculations.
SqDist[setosa]	Mahalanobis distance of the observation from the Setosa centroid.
SqDist[versicolor]	Mahalanobis distance of the observation from the Versicolor centroid.
SqDist[virginica]	Mahalanobis distance of the observation from the Virginica centroid.
Prob[0]	Sum of the negative exponentials of the Mahalanobis distances, used below.
Prob[setosa]	Probability of being in the Setosa category.
Prob[versicolor]	Probability of being in the Versicolor category.
Prob[virginica]	Probability of being in the Virginica category.
Pred Species	Species that is most likely from the probabilities.

Now you can use the new columns in the data table with other JMP platforms to summarize the discriminant analysis with reports and graphs. For example:

1.	From the updated Iris.jmp data table (that contains the new columns) select Analyze > Fit Y by X.

2.	Select Species and click Y, Response.

3.	Select Pred Species and click X, Factor.

Click OK.

The Contingency Table summarizes the discriminant classifications. Three misclassifications are identified.

Contingency Table of Predicted and Actual Species