Discriminant Function Analysis - Discriminant Functions

Discriminant Functions

Discriminant analysis works by creating one or more linear combinations of predictors, creating a new latent variable for each function. These functions are called discriminant functions. The number of functions possible is either N_g-1 where N_g = number of groups, or p (the number of predictors), whichever is smaller. The first function created maximizes the differences between groups on that function. The second function maximizes differences on that function, but also must not be correlated with the previous function. This continues with subsequent functions with the requirement that the new function not be correlated with any of the previous functions.

Given group, with sets of sample space, there is a discriminant rule such that if ∈, then ∈ . Discriminant analysis then, finds “good” regions of to minimize classification error, therefore leading to a high percent correct classified in the classification table.

Each function is given a discriminant score to determine how well it predicts group placement.

• Structure Correlation Coefficients: The correlation between each predictor and the discriminant score of each function. This is a whole correlation.
• Standardized Coefficients: Each predictor’s unique contribution to each function, therefore this is a partial correlation. Indicates the relative importance of each predictor in predicting group assignment from each function.
• Functions at Group Centroids: Mean discriminant scores for each grouping variable are given for each function. The farther apart the means are, the less error there will be in classification.