1. Aaker, Kumar, Day Seventh Edition Instructor’s Presentation Slides
Marketing Research
Aaker, Kumar, Day
Seventh Edition
Instructor’s Presentation Slides

2. Discriminant and Canonical Analysis
Chapter Twenty
Discriminant and Canonical Analysis

3. Discriminant Analysis
Used to classify individuals into one of two or more alternative groups on the basis of a set of measurements
Used to identify which variable contribute to making classification
Major Uses
Prediction
Description
Marketing Research 7th Edition
Aaker, Kumar, Day

4. Objectives
Determining linear composites of the predictor variables to separate groups by measuring between groups variation relative to within-groups variation
Developing procedures for assigning new objects, firms, or individuals, whose profiles, but not group identity, are known, to one of the two groups
Testing whether significant differences exist between the two groups based on the group centroids
Determining which variables account most in explaining inter-group differences
Marketing Research 7th Edition
Aaker, Kumar, Day

5. Discriminant Function
zi = b1 xi1 + b2 xi2 + b3 xi bn xin
Where
z = discriminant score
b = discriminant weights
x = predictor (independent) variables
In a particular group, each individual has a discriminant score (zi)
Σ zi = centroid (group mean)
I = individual
Centroid
Indicates most typical location of an individual from a particular group
Marketing Research 7th Edition
Aaker, Kumar, Day

6. Cut-off Score
Criterion against which each individual’s discriminant score is judged to determine into which group the individual should be classified
For equal group sizes
Z cut-off = ZA + ZB 2
For unequal group size
Z cut-off = NB ZA + NA ZB
Na + nb
Marketing Research 7th Edition
Aaker, Kumar, Day

7. Determination of Significance
Null Hypothesis
In the population, the means of all discriminant function in all groups are equal
Ho : μA = μB
If Ho is rejected, interpret results
Marketing Research 7th Edition
Aaker, Kumar, Day

8. Interpretation
Generally, predictors with relatively large standardized coefficients contribute more to the discriminating power of the function
Canonical or discriminant loadings show the variance that the predictor shares with the function
Marketing Research 7th Edition
Aaker, Kumar, Day

9. Classification and Validation
Holdout Method
Use part of sample to construct classification rule
Other subsample used for validation
Uses classification matrix and hit ratio to evaluate groups classification
Uses discriminant weights to generate discriminant scores for cases in subsample
Marketing Research 7th Edition
Aaker, Kumar, Day

10. Classification and Validation (Contd.)
U-method of Cross Validation
Uses all available data without serious bias in estimating error rates
Estimated classification error rates
P1 = m1 P2 = m2
n1 n2
m1 and m2
Number of sample observations mis-classified in G1 and G2
Marketing Research 7th Edition
Aaker, Kumar, Day

11. Multiple Discriminant Analysis
Number of possible discriminant functions
= Min(p,m-1)
Where
M = number of groups
P = number of predictor variables
Marketing Research 7th Edition
Aaker, Kumar, Day

12. Canonical Correlation Analysis
Focuses on the relationship between one set of dependent variables and one set of independent variables
Application
Concept
Marketing Research 7th Edition
Aaker, Kumar, Day

13. Canonical Correlation Analysis (Contd.)
Inputs
Outputs
Key Terms
Canonical correlation, Canonical loadings, Canonical root, Canonical coefficients, Canonical cross-loadings
Assumptions (least restrictive)
Limitations
From the interpretation
Marketing Research 7th Edition
Aaker, Kumar, Day