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.