Discriminant analysis attempts to classify observations described by values on continuous variables into groups. Group membership, defined by a categorical variable X, is predicted by the continuous variables. These variables are called covariates and are denoted by Y.
Discriminant analysis differs from logistic regression. In logistic regression, the classification variable is random and predicted by the continuous variables. In discriminant analysis, the classifications are fixed, and the covariates (Y) are realizations of random variables. However, in both techniques, the categorical value is predicted by the continuous variables.
The Discriminant platform provides four methods for fitting models. All methods estimate the distance from each observation to each group's multivariate mean (centroid) using Mahalanobis distance. You can specify prior probabilities of group membership and these are accounted for in the distance calculation. Observations are classified into the closest group.
Fitting methods include the following:
• Linear—Assumes that the within-group covariance matrices are equal. The covariate means for the groups defined by X are assumed to differ.
• Quadratic—Assumes that the within-group covariance matrices differ. This requires estimating more parameters than does the Linear method. If group sample sizes are small, you risk obtaining unstable estimates.
• Regularized—Provides two ways to impose stability on estimates when the within-group covariance matrices differ. This is a useful option if group sample sizes are small.
• Wide Linear—Useful in fitting models based on a large number of covariates, where other methods can have computational difficulties. It assumes that all covariance matrices are equal.