A Logit Model of Brand Choice

1
A Logit Model of Brand Choice and Purchase
Incidence
A Real Options Approach
12th ANNUAL INTERNATIONAL CONFERENCE ON REAL
OPTIONS
Takahiro OHNO Waseda Univ. Tokyo, Japan
Hiroto SUZUKI Waseda Univ. Tokyo, Japan
Makoto GOTO Waseda Univ. Tokyo, Japan
2
Backgrounds
Retailers

• Frequently
• Randomly

Price Promotions
The strategy of price promotions
Consumers purchase behavior
Price has strong effect to consumers

• Purchase incidence when
• Brand choice what

(Guadagni and Little(1987), Gupta(1988,1991))
3
Backgrounds
Retailers

• Frequently
• Randomly

Price Promotions
Consumers
The prices Uncertain
Purchase of stockpile products

• Considering uncertainty of the price
• Purchase incidence
• is considered the
  uncertainty

( Sun et al.(2003), Erdem et al.(2003))
4
Backgrounds
Characteristic of Purchase Behavior
( stockpile products )

• Remember the previous prices
• Purchase at lower price
• ( At higher price, postpone the purchase )
• Try to purchase until out of the inventory

( Sun et al.(2003), Erdem et al.(2003) )

• Purchase
• Postpone the Purchase

Remember the previous prices
Purchase during these period
time
t
t1
t2
t3
Decision-making of the Purchase
The Stock0
5
Backgrounds

• Purchase
• Postpone the Purchase

Remember the previous prices
Purchase during these period
time
t
t1
t2
t3
Decision-making of the Purchase
The Stock0

• Decision-making under uncertainty of the prices
• The decision is irreversible
• Considering the value to postpone

Real Options Approach
6
Purpose of our Study
Consumers decision making process
Purchase Incidence
Brand Choice
Modeling by Nested Logit Model
( Bucklin and Gupta (1992))
Modeling the value to postpone the purchase
by using real options
approach
Purpose of our Study
Modeling the consumers purchase incidence and
brand choice considering the uncertainty of the
prices
Retailers Efficient sales promotions
7
Previous Studies
Previous Studies about Purchase Incidence and
Brand Choice
Integrate Purchase Incidence and Brand Choice
Model
Guadagni and Little (1987) Bucklin and Lattin
(1991) Bucklin and Gupta (1992)
Integrate Purchase Quantity Model
Shopping Basket Analysis
The Elaborated Model
Chintagunta(1993) Gupta(1988) Mela, et al.(1998)
Chintagunta(1999) Manchanda, et al.(1999)
8
Previous Studies
The Elaborated Model of Purchase Incidence and
Brand Choice

• The Correlation
• Modeling the correlation between purchase
  incidence and brand choice
• The Reference Point
• Modeling the purchase incidence comparison to
  last purchase

Siddhartha, et al.(2004)
Bell and Bucklin(1999)

• Forward Looking

Sun et al.(2003), Erdem et al.(2003)
Modeling the purchase behavior including
expectations
future prices by dynamic structure model
High cost of computation to estimate parameters
Our model is based on Nested Logit Model
(Bucklin and Gupta (1992))
Low cost
9
Previous Studies
Bucklin and Gupta (1992))
Integrate Purchase Incidence and Brand Choice
Model
(Nested Logit Model)
Purchase Incidence
Brand Choice
The purchase probability of consumer h for brand
i at time t
Brand Choice
Purchase Incidence
10
Previous Studies
Brand Choice
Consumers choice is stochastic
(double exponential distribution)
random variable
stochastic utility
deterministic utility
brand-specific intercept for brand i
vector of response coefficient for variables
vector includes both marketing and
consumer-specific variables
The probability of brand choice ( logit model )
double exponential distribution

without random variable
11
Previous Studies
Purchase Incidence
binomial logit model
Consumer hs deterministic utility for category
purchase at time t
intercept term
vector of response coefficient for variables
vector includes both consumer-specific
variables and category value ( )
highest expected utility to the consumer from
buying a brand in the category at time t
Estimation of parameters Low Cost

• Sequential estimation

brand choice parameters ? purchase incidence
parameters
(maximum likelihood method)
12
Our Suggestion
Cost of Computation
Uncertainty of Price
Previous studies
Nested Logit Model
Low
(Bucklin and Gupta (1992))
Dynamic Structure Model
High
(Sun et al.(2003), Erdem et al.(2003))
Real Options Approach
Our Model
Low
13
Our Model
- Definition of the inventory, and time -
Purchase stockpile products
Consumers try to purchase until out of the
inventory
( Sun et al.(2003), Erdem et al.(2003) )

• The inventory
• Time when the stock gets exhausted

Modeling
Consumer hs inventory of the category at time t
Quantity of the purchase category at t-1
Estimated rate of consumption
( Bucklin and Lattein (1991))
Time when the stock gets exhausted
Th is discrete, so we treat it as cutting off
decimal
14
Our Model
- Modeling consumers purchase behavior -
The purchase probability of consumer h for brand
i at time t
Brand Choice
Purchase Incidence
Brand Choice
Consumer hs deterministic utility for
purchasing brand i at time t
double exponential distribution
brand-specific intercept for brand i
vector of response coefficient for variables
vector includes both marketing and
consumer-specific variables
15
Our Model
- Modeling consumers purchase behavior -
Purchase Incidence
Purchase
No-Purchase
Deterministic utility for no-purchase
Deterministic utility for purchase
parameter
Consumer hs utility for purchase at time t
(double exponential distribution)
Stochastic utility
highest expected utility to the consumer
from purchase at
time t
Consumer hs utility for no-purchase at time t
(double exponential distribution)
Stochastic utility
Option Value (The value to postpone purchase)
16
Our Model
- Modeling the option value -
Price is modeled based on Sun et al. (2003)
discount
Brand
promotion
usual price
Random variable
Transition probability
state vector
17
Our Model
- Modeling the option value -
Option value
transition probability
state
state
expected utility
option value
Expected utility
Time when the stock gets exhausted
state vector
Expected utility
dummy variable (whether to visit)
purchase
no-purchase
no-visit
visit
visit
no-visit
18
Our Model
- Modeling the option value -
Image of calculation the option value
Case)
Brand
state
transition probability
expected utility
option value
19
Simulation
Parameters
Conditions
Consumer goes shopping every time

• Simulation 1 Relation between
• Simulation 2 Relation between
• Simulation 3 Relation between
• Simulation 4 Comparison to rational decision

and
and
and
Choice is not stochastic
20
Simulation 1
and
Relation between
OV
OV
Probability to purchase at lower price
OV
OV
21
Simulation 2
and
Relation between
OV
OV
Probability to continue discounted price
OV
OV
22
Simulation 3
and
Relation between
Discount rate High ? OV High
OV
OV
Probability to purchase at lower price
OV
OV
23
Simulation 4
Comparison to rational decision
rational gt logit
logit probability to choice lower utility
Case of
t ? The difference?
Choice lower utility ? OV Low Accumulation of
the difference
OV
logit
t ? The difference ?
rational
t10 OV0 (stock gets exhausted) logit
probability to choice no-purchase
24
Conclusion
Modeled the consumers purchase incidence and
brand choice considering the uncertainty of the
price
Analyzed the option value (postpone purchase)
Future Studies

• Verification by using POS data
• Considering reference price
• Expand the state of the price

25
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