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Similar Results from Logistic Regression and Discriminant Analysis

Although these descriptions suggest that discriminant analysis would produce very different results from logistic regression, the main results are very similar, if not identical, in standard applications.

  • Consider the simplest case:
    • A dichotomous dependent variable: vote for Bush or Clinton in 1992
    • A single independent variable: party identification
    • Studying a 7% sample of about 150 cases from the 1992 NES survey.
    • Here's the distribution for 87 respondents who reported voting for Clinton or Bush:

Frequency
Valid Percent
Clinton
49
56.2
Bush
38
43.8
Total
87
100
Binary logistic regression in SPSS has many options. The analysis below was run
--treating Party ID by default as a covariate (interval scale), not opting to treat it as categorical (discrete)
--requesting a classification table and plot
Discriminant Analysis in SPSS also has many options. This analysis was run
--treating Party ID as a factor (either interval or discrete); there is no option
--requesting function coefficients
--requesting a summary (classification) table
--requesting probabilities equal to group proportions
  • The overall classification results for the two methods are identical
    • the equations differ because the dependent variables are scaled differently
    • in this instance, the plot from binary logistic analysis is unique
Binary Logistic Regression
Discriminant Analysis, two groups
Variables in the equation
(constant)-3.32 + .756Party Identification

Predicted Vote in 1992

% Correctly Predicted

Observed vote in 1992

Clinton
Bush

Clinton

40
8
82.8

Bush

8
30
78.9
Overall percentage correctly classified
81.1

 

 

Binary Logistic regression produces a plot:

Canonical Discriminant Function Coefficients, Function 1
(constant) -2.154 + .562Party Identification
Unstandardized coefficients

Predicted Group Membership Count of Cases

Vote in 1992

Clinton
Bush
Total

Clinton

40
8
49

Bush

8
30
38

Predicted Group Membership Percentage of Cases

Clinton

82.8
17.2
100

Bush

21.1
78.9
100
81.1% of original grouped cases correctly classified.
Ungrouped cases
32
21
53
Note the treatment of those who didn't vote for either.