GDA Models Results - Functions Tab

Select the Functions tab of the GDA Models Results dialog to access options to produce summaries of the discriminant function analysis results. For example you can review the classification functions, the results of the canonical analysis, and the misclassification matrix for the analysis sample.

Class means for predictors

Click the Class means for predictors button to display a results spreadsheet containing the means for the predictor variables for each class (group) of the dependent variable. If categorical predictor effects are included in the design, then the means will pertain to the coded design vectors, using sigma-restricted coding of effects. See also the General Linear Models (GLM) Introductory Overview for details.

Class std deviations for predictors

Click the Class std deviations for predictors button to display a results spreadsheet containing the standard deviations for the predictor variables, for each class (group) of the dependent variable. If categorical predictor effects are included in the design, then the means will pertain to the coded design vectors, using sigma-restricted coding of effects. See also the General Linear Models (GLM) Introductory Overview for details.

Chi-square tests of successive roots

Click the Chi-square tests of successive roots button to display a spreadsheet containing a step-down test for canonical roots (and discriminant functions). The first row in that spreadsheet contains the test of significance for all roots combined. The second row contains the significance of the remaining roots, after removing the first root, and so on. Thus, this spreadsheet allows us to evaluate how many significant roots to interpret.

Standardized coefficients

Click the Standardized coefficients button to display a spreadsheet with the standardized discriminant (canonical) function coefficients.

Raw coefficients

Click the Raw coefficients button to display a spreadsheet containing the raw discriminant (canonical) function coefficients. These are the coefficients that can be used to compute the raw canonical scores for each case for each discriminant function. Also included in this spreadsheet will be the eigenvalues for each discriminant function and the cumulative proportion of (common) variance extracted by each discriminant function.

Factor structure coefficients

Click the Factor structure coefficients button to display a spreadsheet containing the pooled within-class (groups) correlations of predictor variables with the respective discriminant (canonical) functions. If you are familiar with factor analysis (see Factor Analysis), you can think of these correlations as the factor loadings of the respective variables on the discriminant functions.

Some authors have argued that to interpret the "meaning" of the discriminant functions, one should use these structure coefficients rather than the standardized discriminant function coefficients. Refer to the Introductory Overview of Discriminant Analysis for a discussion of this argument. The most important thing to remember is that the discriminant function coefficients denote the unique (partial) contribution of each variable to the discriminant functions, while the structure coefficients denote the simple correlations between the variables and the functions; therefore, the structure coefficients are usually more appropriate for substantive interpretations of functions.

Class means for canonical variables

Click the Class means for canonical variables button to display a spreadsheet containing the means for the discriminant functions, for each class (group). These means allow you to determine the groups that are best identified (discriminated) by each discriminant function.

Class squared Mahalanobis distances

Click the Class squared Mahalanobis distances button to display a results spreadsheet containing the squared Mahalanobis distances between the class (group) centroids. The Mahalanobis distance is similar to the standard Euclidean distance measure, except that it takes into account the correlations between variables. The larger the differences in this spreadsheet, the farther are the respective groups apart from each other, and the more discriminatory power does the current model possess for discriminating between the respective two groups.

Tests of significance of distances

Click the Tests of significance of distances button to display a spreadsheet containing statistical significance tests of the Class squared Mahalanobis distances (see above) between groups. For each pair of classes (groups) defined in the categorical dependent variable, the spreadsheet will show the F-value associated with the respective distance and the p-value. Those p-values should be interpreted with caution, unless one brings to the analysis strong a priori hypotheses concerning which pairs of groups should show particularly large (and significant) distances.

Classification function coefficients

Click the Classification function coefficients button to display a spreadsheet containing the classification functions. Classification functions are computed for each class (group) and can be used directly to classify cases. You could classify a case into the group for which it has the highest classification score. Refer to the Discriminant Analysis module for additional details concerning the interpretation of various standard results statistics for discriminant function analysis.

Analysis sample classification matrix

Click the Analysis sample classification matrix button to display a spreadsheet containing the classification matrix. The classification matrix contains information about the number and percent of correctly classified cases in each class (group). Note that only cases in the analysis sample (and not the cross validation or prediction samples) will be used to compute this classification matrix. To compute the classification matrix for a cross validation or prediction sample, use the Sample classification matrix button on the Cases tab. Also, the computations for the classification of cases will be based on a priori classification probabilities as specified on the Quick specs dialog, or in the Analysis wizard dialog.

See also GDA - Index.