GDA Introductory Overview - Coding the Categorical Dependent Variable
Here is a simple illustration of the computational approach taken by GDA. Consider the following simple data file, with a single categorical dependent variable, with 3 groups, and 4 predictor variables.
| 1 | 2 | 3 | 4 | ||
| Group 1 | 2.3 | 5.4 | 4.4 | 3.3 | |
| Group 1 | 3.4 | 3.9 | 3.6 | 3.1 | |
| Group 1 | 5.6 | 1.2 | 4.3 | 5.6 | |
| Group 2 | 1.6 | 4.0 | 3.3 | 5.8 | |
| Group 2 | 2.3 | 9.8 | 3.0 | 5.3 | |
| Group 2 | 3.1 | 6.7 | 1.4 | 2.3 | |
| Group 3 | 8.7 | 7.5 | 1.3 | 3.4 | |
| Group 3 | 9.3 | 7.3 | 2.7 | 2.1 | |
| Group 3 | 3.2 | 7.7 | 1.7 | 6.7 |
The computational approach to performing a traditional discriminant function analysis on these data is documented in the Discriminant Analysis section (see also Jennrich, 1977, for a concise description for of the computations involved). In GDA, the program will "internally" rewrite the data in the following manner (of course, your input data file will not be changed):
| 1 | 0 | 0 | 2.3 | 5.4 | 4.4 | 3.3 | |
| 1 | 0 | 0 | 3.4 | 3.9 | 3.6 | 3.1 | |
| 1 | 0 | 0 | 5.6 | 1.2 | 4.3 | 5.6 | |
| 0 | 1 | 0 | 1.6 | 4.0 | 3.3 | 5.8 | |
| 0 | 1 | 0 | 2.3 | 9.8 | 3.0 | 5.3 | |
| 0 | 1 | 0 | 3.1 | 6.7 | 1.4 | 2.3 | |
| 0 | 0 | 1 | 8.7 | 7.5 | 1.3 | 3.4 | |
| 0 | 0 | 1 | 9.3 | 7.3 | 2.7 | 2.1 | |
| 0 | 0 | 1 | 3.2 | 7.7 | 1.7 | 6.7 |
The categorical dependent variable was converted into three different dependent variables, each containing a 1 to indicate that the respective case belongs to a particular group, or a 0 that it does not. The problem can now be considered a multivariate regression problem (see General Regression Models (GRM), and the standard univariate and multivariate regression results (see GRM) can be applied. Again, this recoding of the dependent variable(s) is done internally by the program, and, of course, your input data are not rewritten.
In addition to the regression-like results statistics described in the context of GRM, all standard discriminant function analysis statistics are computed; these are described in the context of the Quick Discriminant Analysis module. When analyzing standard discriminant function analysis problems, with (single degree of freedom) continuous predictor variables, the results computed by GDA and Quick Discriminant Analysis will be identical, except that GDA will also report the univariate and multivariate regression results, as described in the context of the General Regression Models (GRM) module.