Customer Relationship Management:A Database Approach

MARK 7397Spring 2007

James D. HessC.T. Bauer Professor of Marketing Science

375H Melcher Hall jhess@uh.edu713 743-4175

Class 11Discriminate Analysis

GS = location of Goldstar buyerBD = location of Black & Decker buyer

Size ofFamily

10

9 BD BD

8 GS

7 BD

6 BD

5 BD GS GS

4

3 GS GS

2

1

0 10 20 30 40 50 60 70 80 90 100 Taste forSpeed

Discriminant Analysisof Toaster Customers

Location of average Goldstar buyer

Location of average Black & Decker buyer

Size ofFamily

10

9 BD BD

8 GS

7 BD

6 BD

5 BD GS GS

4

3 GS GS

2

1

0 10 20 30 40 50 60 70 80 90 100 Taste forSpeed

Toaster CustomersMeans and Confidence Circles

Size ofFamily

10

9 BD BD

8 GS

7 BD

6 BD

5 BD GS GS

4

3 GS GS

2

1

0 10 20 30 40 50 60 70 80 90 100 Taste forSpeed

Toaster CustomersMeans and Confidence Ellipses

Size ofFamily

10

9 BD BD

8 GS

7 BD

6 BD

5 BD GS GS

4

3 GS GS

2

1

0 10 20 30 40 50 60 70 80 90 100 Taste forSpeed

Discriminant Analysisof Toaster Customers

0=-2.0-.013TS+.456SFor SF=4.2+.03TS

Assignment of Observation to Population

Suppose we have computed discriminant coefficients and have observed a value X for an observation.Suppose that a priori we think the two populations haveprobabilities qBD and qGS and the costs of misclassificationare C(BD|GS) and C(GS|BD). Let the group centroids be XBD and XGS then the observation should be allocated to GS if

X < -------------- + ln --------------------- XBD+XGS

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 BDis 5 times more costly than misclassifying a BD as GS. Then the threshold for allocating to GS is easy since ln(10)=+2.3.