MARK 7397
Spring 2007
Customer Relationship Management:
A Database Approach
Class 5
James D. Hess
C.T. Bauer Professor of Marketing Science
375H Melcher Hall
jhess@uh.edu
713 743-4175
Brand Choice Models
What Might Have Happened
time
Regular ABB Service, S
ABB Purchases
X X
X X
0
X
X
X
X
X
X X X X
GE Purchases
0.5
X
X
1.0
Year
Brand Choice Models
What You See
Heavyup Service, S+D
Regular ABB Service, S
ABB Purchases
X X
X X
0
X
XX X
X
X
GE Purchases
0.5
XX X X
X
1.0
Year
Brand Choice Models
What You Infer
Heavyup Service, S+D
Regular ABB Service, S
ABB Purchases
X X
XX X
X
XX X X
brand switches
X X
0
X
X
X X X X
GE Purchases
0.5
X
1.0
Year
Regression Model
of Brand Choice
Brand
Choice
?
ABB 1
?
GE
0
Service
?
Logit Model
Of Brand Choice
Brand
Choice
ABB 1
ea+bA
1+ea+bA
GE
0
Service
Explanation: Random Utility Model
Daniel McFadden
2000 Nobel Laureate
UA  a A bA S  e A ABB
UG  a GbG S  e G
GE
The part ai + biS is the “deterministic” part of utility. The terms e i are
aspects of the situation which we are unable to observe, and hence give a
feeling of randomness to the choice. The customers are not really random,
but simply know their situation better than us.
Pr(U A UG) Pr( ε A ε G  aG aA (bG bA )S)
Random Utility Model
(continued)
a
b
Pr(U A UG) Pr( ε A ε G  aG aA (bG bA )S)
If eA-eG has a logistical distribution, then this probability is
a  bS
e
Pr(U A U G ) 
1 e abS
where a=aG-aA and b=bG-bA.
Calibrating the Logit Model
Suppose there were n brand choices and m times
ABB was chosen and n-m times GE was chosen,
each with a different service S. The likelihood of
this is the probability:
L=
ea+bS1

ea+bSm
1
1 + ea+bS1 1 + ea+bSm 1 + ea+bSm+1
ABB

1
1 + ea+bSn
GE
The values of a and b are chosen to “maximize
likelihood” of observing the sample we did.
Interpretation of Logit Coefficients
Logit is not linear like regression, so its coefficients have
a slightly different interpretation.
Odds that ABB is chosen over GE:
Odds = Pr(ABB)/Pr(GE) = ea+bS.
How much do odds of ABB go up if S increases by 1?
New Odds = ea+b(S+1) = ea+bSeb = Odds x exp(b)
Exp(b) tells the factor by which the odds
of ABB rise when S is one unit higher.
Examples: b =2, exp(b)= 2.712 = 7.3, so when b=2,
increasing S by +1 increases the odds of ABB being chosen
by a factor of roughly seven. If they had been 3:1, they are now 22:1.
b = - 1, exp(b)= 2.712-1 = 0.37, so when b= -1,
increasing S by +1 decreases the odds of ABB being chosen
by a factor of roughly one-third. If they had been 3:1, they are now 1:1.
Let’s look at a very simple Excel version of a logit model.
Please download the file “ABB Logit illustration.xls” from
WebCT. It should look like the following.