9.1 Key terms and concepts

Discriminant variables are the independent variables. These are also called predictors.

This is the dependent variable, which is the object of classification efforts.

A discriminant function, also called a canonical root, is a latent variable, which is treated as a linear combination of discriminant (independent) variables. The discriminant function is estimated using ordinary least-squares method.

Discriminant score is the value resulting from applying a discriminant function formula to the data for a given case.

If the discriminant score of the function is less than or equal to the cutoff, the case is classed as 0, or if above the cutoff it is classed as 1. When group sizes are equal, the cutoff is the mean of the two centroids (for two-group discriminant analysis). If the groups are unequal, the cutoff is the weighted mean.

Group centroid is the mean value for the discriminant scores for a given category of the dependent variable. Two-group discriminant analysis has two centroids, one for each group.

There is one discriminant function for 2-group discriminant analysis, but for higher order discriminant analysis, the number of functions (each with its own cut-off value) is equal to (g - 1), where g is the number of groups, or p, the number of discriminant variables, whichever is less. Each discriminant function is orthogonal to the others.

The classification table, also called a confusion matrix or table, is used to assess the performance of discriminant analysis. This is simply a table in which the rows are the observed categories of the dependent variable and the columns are the predicted categories of the dependent variable. When prediction is perfect, all cases will lie on the diagonal. The percentage of cases on the diagonal is the percentage of correct classifications.

Mahalanobis D square is an index of the extent to which the discriminant functions discriminate between criterion groups.

Eigenvalues are called the characteristic roots: There is one eigenvalue for each discriminant function. The ratio of the eigenvalues indicates the relative discriminating power of the discriminant functions