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Discriminant
Analysis with a Trichotomy
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- Let's return to the 1992 Presidential
election, with Perot as a third choice:
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Reported 1992 presidential vote for a 7%
sample of respondents
|
|
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Frequency
|
Valid Percent
|
|
Clinton
|
49
|
46.6
|
|
Perot
|
18
|
17.1
|
|
Bush
|
38
|
36.3
|
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Total
|
105
|
100
|
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- 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.
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Structure Matrix
|
|
|
Function 1
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Function 2
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Bush: Post-El Feeling
Therm
|
0.707
|
-0.049
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Clinton: Post-El Feeling
Therm
|
-0.615
|
-0.22
|
Party Identification
|
0.548
|
0.217
|
Perot: Post-El Feeling
Therm
|
-0.071
|
0.829
|
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Pooled within-groups correlations between
discriminating variables and standardized
canonical discriminant functions
|
|
Variables ordered by absolute size of
correlation within function.
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- Here's the new classification table,
based now on four predictors:
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|
|
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.
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Discriminant Analysis also produces a
"Territorial Map" of the results.
|