Path: Janda's Home Page > Workshop > Discriminant Analysis > Outline
Discriminant Analysis with a Trichotomy
  • Let's return to the 1992 Presidential election, with Perot as a third choice:
Reported 1992 presidential vote for a 7% sample of respondents

Frequency
Valid Percent
Clinton
49
46.6
Perot
18
17.1
Bush
38
36.3
Total
105
100
  • And let's add more predictors: post-election feeling thermometers for Clinton, Bush, and Perot.
  • The new variables yield two discriminant functions, not one
    • The functions can be interpreted with reference to the Structure Matrix.
    • It offers the best interpretation of the discriminant functions.
    Structure Matrix

    Function 1
    Function 2
    Bush: Post-El Feeling Therm
    0.707
    -0.049
    Clinton: Post-El Feeling Therm
    -0.615
    -0.22
    Party Identification
    0.548
    0.217
    Perot: Post-El Feeling Therm
    -0.071
    0.829


    Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions

    Variables ordered by absolute size of correlation within function.

  • Here's the new classification table, based now on four predictors:

Predicted Group Membership (Vote in 1992) Ns
Actual vote in 1992
Clinton
Perot
Bush
Total
Clinton
41
1
4
46
Perot
1
14
3
18
Bush
2
2
34
38
Ungrouped cases
21
5
6
33

Predicted Group Membership (Vote in 1992) %
Clinton
89.4
1.4
9.2
100
Perot
4.9
77.3
17.8
100
Bush
4.7
4.5
90.8
100
Ungrouped cases
65.7
14.8
19.6
100
87.8% of original grouped cases correctly classified.
Discriminant Analysis also produces a "Territorial Map" of the results.