1. Customer Relationship Management: A Database Approach
MARK 7397
Spring 2007
Customer Relationship Management: A Database Approach
Class 11
Discriminate Analysis
Werner Reinartz
James D. Hess
C.T. Bauer Professor of Marketing Science
375H Melcher Hall

2. Discriminant Analysis
of Toaster Customers
Size of
GS = location of Goldstar buyer
Family
BD = location of Black & Decker buyer 10 9 BD BD 8 GS 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1
Taste for 10 20 30 40 50 60 70 80 90
100
Speed

3. Means and Confidence Circles
Toaster Customers
Means and Confidence Circles
Size of
Family
Location of average Black & Decker buyer 10 9 BD BD 8 GS
Location of average Goldstar buyer 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1
Taste for 10 20 30 40 50 60 70 80 90
100
Speed

4. Means and Confidence Ellipses
Toaster Customers
Means and Confidence Ellipses
Size of
Family 10 9 BD BD 8 GS 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1
Taste for 10 20 30 40 50 60 70 80 90
100
Speed

5. Discriminant Analysis
of Toaster Customers
Size of
Family 10 9 BD BD
0= TS+.456SF
or SF= TS 8 GS 7 BD 6 BD 5 BD GS GS 4 3 GS GS 2 1
Taste for 10 20 30 40 50 60 70 80 90
100
Speed

10. Assignment of Observation to Population
Suppose we have computed discriminant coefficients b
and have observed a value X for an observation.
Suppose that a priori we think the two populations have
probabilities qBD and qGS and the costs of misclassification
are C(BD|GS) and C(GS|BD). Let the group centroids be
XBD and XGS then the observation should be allocated to GS if
Xb < ln
XBDb+XGSb
qBDC(GS|BD)
qGSC(BD|GS) 2
Note: if prior probabilities and costs are symmetric then the last term above is ln(1)=0.
However, suppose that qGS=2/3 and misclassifying a GS as BD
is 5 times more costly than misclassifying a BD as GS. Then the
threshold for allocating to GS is easy since ln(10)=+2.3.