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.