MARK 7397
Spring 2007
Customer Relationship Management:
A Database Approach
Class 11
Discriminate Analysis
James D. Hess
C.T. Bauer Professor of Marketing Science
375H Melcher Hall
jhess@uh.edu
713 743-4175
Discriminant Analysis
of Toaster Customers
GS = location of Goldstar buyer
BD = location of Black & Decker buyer
Size of
Family
10
BD
9
BD
GS
8
BD
7
BD
6
BD
5
GS
GS
4
GS
3
GS
2
1
0
10
20
30
40
50
60
70
80
90
100
Taste for
Speed
Toaster Customers
Means and Confidence Circles
Size of
Family
Location of average Black & Decker buyer
10
BD
9
BD
GS
8
Location of average Goldstar buyer
BD
7
BD
6
BD
5
GS
GS
4
GS
3
GS
2
1
0
10
20
30
40
50
60
70
80
90
100
Taste for
Speed
Toaster Customers
Means and Confidence Ellipses
Size of
Family
10
BD
9
BD
GS
8
BD
7
BD
6
BD
5
GS
GS
4
GS
3
GS
2
1
0
10
20
30
40
50
60
70
80
90
100
Taste for
Speed
Discriminant Analysis
of Toaster Customers
Size of
Family
10
BD
9
BD
0=-2.0-.013TS+.456SF
or SF=4.2+.03TS
GS
8
BD
7
BD
6
BD
5
GS
GS
4
GS
3
GS
2
1
0
10
20
30
40
50
60
70
80
90
100
Taste for
Speed
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
qGSC(BD|GS)
XBDb+XGSb
Xb < -------------- + ln --------------------2
qBDC(GS|BD)
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.