These are some of the models in brand loyalty and consumer behaviour. The best part of this subject is that you can actually put a number to your imagination.

1. Quantitative Models in Brand purchase and switching
Models in Consumer Behaviour

2. Quantitative Models
Consumer behaviour models - Elementary understanding
Behavioural Learning
 Under this
theory consumers’
prior experience
is the primary
determinant of
future behaviour
Personality Research
 Consumer
attempts to reconcile
his behaviour,
others’ behaviour,
the state of his
environment etc.
with prior beliefs.
Attitude learning
 Product
attributes are
drivers of the
consumer decision
process
Prior experience
Other people’s personality
and own belief s
Product attributes

3. Brand utility and choice models
Basic approach to decision making ….

4. Brand utility and choice models
In a compensatory model the
weakness of a brand on one
attribute can be
compensated for or by
strength on another, and the
attributes are summed to
determine the favorability or
favorability of the attitude
towards the brand.
In non-compensatory models
usually only three or four
attributes are used to
evaluate a product, and
shortcomings on any one
attribute cannot be
compensated by more
favorable levels on another.
Compensatory Model Non-Compensatory Model

5. Brand utility and choice models
Non-compensatory Models
( Bettman – 1979 )
Conjunctive Model Disjunctive Model Lexicographic Model
In a conjunctive model
a consumer prefers a
brand only if it meets
certain minimum,
acceptable standards
on all of a number of
key dimensions. If any
one attribute is
deficient, the product
is eliminated from
contention.
The conjunctive model is often
called the “AND” model, while
the disjunctive model is called
the “OR” model.
Under the conjunctive model
the consumer may insist on a
product that has lots of memory
and software.
Under disjunctive model the
consumer may want to settle
for either a product with a lot
of memory or a lot of
software.
A lexicographic model
assumes that all attributes
are used, but in a step wise
manner.
Brands are evaluated on
the most important
attributes first; then a
second attribute is used
only if there are ties, and
so forth.

6. Conjunctive form – Brand choice on utility
Computer
Brands
Memory
Capacity
Graphics
Capability
Software
Availability
Price
Apple 10 8 6 8
Compaq 8 9 8 3
Dell 6 8 10 5
IBM 4 3 7 8
Minimum
Requirements
77 66 77 22
Attributes
illustration, Smith family is interested in buying a home computer. The above exhibit gives the attribute ratings
of the four brands of computer on which they have sought information.
Which computer do they buy?
Ratings of four brands of home computer on a 1 – 10 scale, with requirements of various non-compensatory models

7. Disjunctive form – Brand choice on utility
Computer
Brands
Memory
Capacity
Graphics
Capability
Software
Availability
Price
Apple 10 8 6 8
Compaq 8 9 8 3
Dell 6 8 10 5
IBM 4 3 7 8
Minimum
Requirements
9 None 9 None
Attribute
s
Which computer do they buy?

8. Lexicographic Model - Brand utility and choice models
Computer
Brands
Memory
Capacity
Graphics
Capability
Software
Availability
Price
Apple 10 8 6 8
Compaq 8 9 8 3
Dell 6 8 10 5
IBM 4 3 7 8
Minimum
Requirements
3rd
4th
2nd
1st
Attributes
Which computer do they buy?

9. Market share by brand switching

10. One key term used in marketing is “market share” and the other is “market penetration rate”
…
The definition of market share …
Joint
probability
Conditional
probability
Discrete
probability
distribution
Continuous
probability
distribution
1 2
34
Where does market share lie in the above quadrants and why?
Probability
Probability
distribution
How is market
penetration rate
calculated?

11. A basic brand switching model
MARKOV’S MODEL
“It assumes that only the last brand chosen affects the
current purchase”
If market shares are given, then the Markov model can be used to
predict how market shares change overtime.

12. Markov formula for brand switching which determines market share in the next
period…
Formula for predicting the market share is
Mj (t+1) = Σ Pij
i = 1
n
Mit
j = 1,2,3………n
Mit = Market share of brand “i” at time “t”
Pij = Probability of purchasing “j” next, given “i” was
last purchased
Where . . .

13. Markov switching - Problem on market share
1. The initial brand shares are (0.10, 0.40, 0.50) .What is brand A’s expected share next period?
2. What is brand A’s ultimate market share if the switching probabilities remain constant?
3. Using the first -order Markov matrix just shown, just determine the following:
4. The probability that A will be purchased in period t+1, given that C was purchased in period t
5. The probability of At+1, given Bt
6. The probability of Bt+1, and Ct+1, given At
7. The probability of At+1 and At+2, given At
A B C
A
B
C
0.70 0.20 0.10
0.30 0.60 0.10
0.10 0.40 0.50
t-1
t

14. Strategic directions for brands in various market situations . . .
Market
penetration
rate
Market share of
the brand
HighLow
High
Low
Increase advertising
effects to create
switch over from
other brands
Maintain spend and
arrest switch back
rate to competitor
brand
Advertise for
increasing category
usage rate
Missionary
selling

15. Quantitative Models – 2 Factor Euclidean Model

16. Quantitative Models – 2 Factor Euclidean
1) Preference generates choice
2) Choice is inverse of Stress
3) Stress is the “distance” the brand is placed in the mind of the prospect from the ideal brand
(Stress = Deviation)
4) Market share is function of choice (ceteris paribus)
Deviation = ( Rating for the ideal brand – Rating for our brand) 2
Choice = depends on the deviation of our brand from ideal brand , given deviations of other brands to the
ideal brand
Therefore ,
Choice =
k
Total deviation of individual brand
Where . . .
1
∑ (Total deviation of individual brands)
k =

17. Basic Euclidean Model
EXAMPLE:
A group of consumers is asked to rate five different brands of coffee according to 2 characteristics,
strength & aroma. Each brand is rated on a scale from 1 to 7, for each characteristic. Each consumer
is also asked to rate his/her ideal coffee. Average ratings for the 5 brands are given below:
Brand Strength Aroma
A 3 5
B 5 2
C 6 3
D 2 3
E 3 1
I (Ideal) 5 5
Represent these perceptions in Euclidean two-space, and order the different brands according to
consumer preference (which would give us their probable market shares), if the product
characteristics were the only factor counted.

18. Quantitative Models – Luce ratio scaled preference

19. Quantitative Models – Luce ratio scaled preference
• Classical strength theory explains variability in choices by assuming that response strengths
oscillate.
• Luce assumed that response strengths are constant, but that there is variability in the process of
choosing.
– The probability of each response is proportional to the strength of that response.
• Luce is based on the assumption that the relative frequency of choices of “A” brand over “B”
brand should not change with the mere availability of other choices.

20. Quantitative Models – Luce ratio scaled preference
• This model relates the probability of
purchase to a brands perceived utility.
• Luce’s Axiom :
Most high involvement models derive
from Luce’s axioms and models:
Pij(Ci) =
Σk∈ CiVik
Vij
Where…
where
Pij(Ci) = probability that individual
i, chooses brand j
Vij = individuali, has ratio
scaled
preference for brand j
Ci = set of brands in the
individuals consideration
set.
Vik = preference for the kth
attribute by
individual i

21. Quantitative Models – Luce ratio scaled preference
A consumer could select any of the three brands A , B, C.
A consumer whishes to allocate 20 units between the
three by considering them two at a time for comparison.
Luce axiom is based on relative
preference between brands where the
consumer may prefer all the brands but in
varying degrees .
The consumer will prefer brands to each
other on the basis of comparison of
attractiveness (strength of preference) of
the other brands in his consideration set.
The process of comparison will be
“paired” for calculating the ratio of
scaled preferences.
A
B
16
4
A
C
16
4
B
C
10
10
What is the probability that he will buy “A”, “B”
and “C” on the basis of the above data?

22. Quantitative Models – Multinomial Logit

23. Quantitative Models – Multinomial Logit
• Multinomial logit model to represent
“probability of choice.” The individual’s
probability of choosing brand 1 is:
eA1
Pi1 = ––––
∑ eAj
j
where Aj = ∑ wk bijk
k
Aj
Attractiveness of product ‘j” to
individual ‘i”
=
wk
=Importance associated with
attribute “k”
bijk = Individual “i”’s evaluation of
product “j” on attribute “k”
∑ = Sum of all brands

24. Quantitative Models – Multinomial Logit
Parking
Store Variety Quality for Money Value
1 0.7 0.5 0.7 0.7
2 0.3 0.4 0.2 0.2
3 0.6 0.8 0.7 0.4
4 (new) 0.6 0.4 0.8 0.5
Importance
Weight 2.0 1.7 1.3 2.2
Attribute ratings per store

25. Bush Mosteller model on buying behaviour
Acceptor / Rejecter Model
Prediction of buyer probability of purchasing a brand next time given that there is demonstrated
behaviour of purchasing which happened in the previous period

26. Quantitative Models – Bush Mosteller Model
Acceptor / Rejecter model
To understand the model in its simplest form, consider a two – brand market
where
Yt = 1, if the brand of interest is purchased on occasion t
0, otherwise
and
Pt = probability of purchasing the brand on occasion t
[i.e., pt = p(Yt = 1)]
Pt = α1 + λ1 pt-1
Pt = α2 + λ2 pt-1
if brand i is purchased
at t
(Equation 1)
(acceptance operator)
if brand i is not
purchased at t
(Equation 2)
(rejection operator)
ProbabilityofPurchasingBrand
inPeriodt+1,(Pj,t+1)
Probability of Purchasing Brand j in period t
(Pj,t)
0.16 0.60
0.87
1.00
0.78
0.3
1
Purchase Operator
(Slope = λ1)
Rejection
Operator
(Slope = λ2)
45 O
line as a norm
α1
α2

27. Quantitative Models – Bush Mosteller Model
Acceptor / Rejecter model
To understand the model in its simplest form, consider a two – brand market
where
Yt = 1, if the brand of interest is purchased on occasion t
0, otherwise
and
Pt = probability of purchasing the brand on occasion t
[i.e., pt = p(Yt = 1)]
ProbabilityofPurchasingBrand
inPeriodt+1,(Pj,t+1)
Probability of Purchasing Brand j in period t
(Pj,t)
0.16 0.60
0.87
1.00
0.78
0.3
1
Purchase Operator
(Slope = λ1)
Rejection
Operator
(Slope = λ2)
45 O
line as a norm
α1
α2
The incomplete habit formation aspect of this
model is seen by successive substitutions of
equation 1 :
α 1
1 – λ1 upper limit of p
Similarly, when the brand is never bought,
α 2
1 – λ2 lower limit
p pu =
p pL =

28. 28
Quantitative Models – Bush Mosteller Model
Acceptor / Rejecter model
Problem to solve
Given
Acceptor 0.45+0.3λ1
Rejecter 0.23+0.3λ2
A customer wants to buy a brand with a probability of .51 and actually buys it , what is the
estimated probability that he will buy it in the next period ?
And Suppose he does not buy it?
Also assume an interval of 5% on probability in between two purchase events .
Also find the upper and lower limit of acceptance and rejection.

29. Problem in solver
A brand buyer with a 0.60 probability of purchase, actually buys a brand, the
probability that he will purchase the brand the next time becomes 0.77. However
if he does not, then the probability that he will buy the brand next time becomes
0.35.
Determine the constants of the Bush-Mosteller model and the upper and lower
limits of the acceptor of the brand and the rejecter of the brand?

30. Brand loyalty
Colombo Morrison model
“the question of loyalty arises only if the customer had a chance to
be disloyal…”

31. Brand Loyalty
Colombo and Morrison Model
- What brand did you last buy?
- What brand did you buy the time before?
What the Colombo _Morrison model answers are questions such as;
- How many hard-core loyal customers does each brand have?
- How well does each brand do in capturing potential switchers?
Which can be interpreted as;
1) Is the brand retaining its customers effectively?
2) Is the brand capturing more customers from rival brands through efficient marketing?

32. Brand Loyalty
Colombo and Morrison Model
Gravity = Repeat purchase of the brand on two successive occasions
Focus = Ability of the brand to attract buyers of other brand
Let
p ij = the conditional probability that the consumer who purchased brand i will next purchase brand j
(i.e. when i= j, this is repeat probability)
αi = the proportion of Potential switches (regardless of their previous brand or car who will next buy brand i)
These assumptions lead us to calculation of repeat purchase probabilities...

33. Brand Loyalty
Colombo and Morrison Model
Find gravity and focus shares of all the brands ?

34. End