MMRCDISCUSSION PAPER SERIES
No. 413A Brand Choice Model for Scanner Panel Data
Using the Experiential Set
Sotaro Katsumata
Faculty of Economics, Nagasaki University
Makoto Abe
Graduate School of Economics, The University of Tokyo
August 2012

東京大学ものづくり経営研究センター
Manufacturing Management Research Center (MMRC)
Discussion papers are in draft form distributed for purposes of comment and discussion. Contact the author for
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http://merc.e.u-tokyo.ac.jp/mmrc/dp/index.html

A Brand Choice Model for Scanner Panel Data
Using the Experiential Set

Sotaro Katsumata
Faculty of Economics, Nagasaki University
katsmat@nagasaki-u.ac.jp

Makoto Abe
Graduate School of Economics, The University of Tokyo
abe@e.u-tokyo.ac.jp1Abstract: In this study, we use scanner panel data to construct a stochastic brand choicemodel of consumer goods in which consumers repeatedly choose a brand from many
alternatives. We examine consumers’ repeat purchase behavior from the perspective of
information processing theory. In particular, we explicitly incorporate the concepts ofinternal search, external search, and learning, which have been proposed in behavioral
studies, into the presented brand choice model. Previous research on brand choice hassuggested the existence of choice subsets, such as an “awareness set” or a “consideration set,”in the minds of consumers when they make a purchase decision. These subsets cannot be
observed directly from purchase data, however, because their identification requires either
direct questioning or inference through behavioral modeling. Instead, in this study, we
introduce the concept of an “experiential set” as a means for consumers to process
information and decide on brand choice. Crucially, the experiential set is observable frompurchase records. Because choice subsets are constructed from observable data, this concept
helps build brand choice models that incorporate more elaborate information searches andlearning processes by consumers. This, in turn, results in high predictive validity of themodel.
Keywords: Information Search, Discrete Choice Model, Consideration Set, Markov Chain
Monte Carlo Method21. Introduction
In order to meet the needs of various customers, firms tailor their products to different
market segments. Consumers are thus able to choose the most suitable product from thebrands available in the market. As the number of brands available in the market increases,
theoretically, consumers should be able to obtain higher utility. In practice, however,consumers do not evaluate all the brands that exist in the market nor do they choose brands
through rational decision making. For example, even though the shampoo market comprises
over 100 brands with each brand providing different benefits, few consumers can evaluate allthese brands when deciding what to buy. Thus, in reality, consumers do not exercise rational
choice behavior as assumed by microeconomic theory (Simon, 1947). In mature markets,
most firms and brands face this circumstance.
Simon (1947, 1997) introduces the concept of “bounded rationality” in which many
alternatives and problems exist in the real world. He also proposes a decision process
whereby consumers do not evaluate all alternatives but review only a subset of them in orderto choose the most preferred option. The imperfection in human cognition is a serious
concern in Marketing. Some marketing models assume that consumers allocate cognitive
resources, such as time and effort, differentially across brands when forming their attitude.
For example, the Howard-Sheth model assumes consumers’ inner process of brandcomprehension and attitude formation through environmental stimuli and learning (Howard
and Sheth, 1969). Petty and Cacioppo (1986) propose the Elaboration Likelihood Model(ELM) which posits that consumer’s information process differs according to his or her levelof product knowledge and involvement. These models support the notion that consumers do
not evaluate all brands equally.
Although the theories of bounded rationality and selective information processing
provide ample marketing implications, it is difficult to incorporate them into an empiricalanalysis of consumer purchase behavior because of data limitations. For example, scanner
panel data only tell us what brand was purchased by whom and when. We cannot investigate
which brands were evaluated before the customer made his or her actual purchase. From theprevious argument, it is clear that consumers consider only a subset of brand alternatives.
However, unless survey research such as direct questioning is carried out, it is difficult forfirms to know this “bounded” subset. If we were to incorporate this inner process into a
choice model, we are faced by the issue of inferring consumers’ brand subsets from observedpurchase data. In this paper, we thus construct a brand purchase model that incorporates abrand subset formation process from purchase data alone.

32. The Theory of Brand Choice
2.1. Bounded Rationality in Brand Choice and Brand Subsets
Many of the brand choice models used in marketing are founded on theframework of stochastic utility maximization. Thus, they assume that consumers
have utilities for all brands. When the number of available brands is large,
however, some consumers may not be aware of, or interested in certain brands. For
these brands, therefore, utility does not exist.
While the concept of bounded rationality (Simon, 1947, 1997) was pioneering in
proposing the idea of a brand subset, many conceptual models of subset formation in the fieldof marketing have been proposed based on the cognitive aspects of consumers. For example,
Howard and Sheth (1969) define the “evoked set” as a subset of available brands, and only
these brands are evaluated by consumers. Narayana and Markin (1975) classify brands into
inept and inert types. Some studies have introduced the type of subset, such as the “choice set”
defined by Hauser and Shugan (1989) or the “consideration set” proposed by Wright andBarbour (1977) and Roberts (1989). In addition, others have applied these subsets in a
multi-stage decision process (e.g., Lapersonne, Laurent and Le Goff, 1995; Brisoux andCheron, 1990).
A major difficulty in operationalizing these models is the fact that we cannot obtain
information on brand subsets except by directly asking consumers which brands they
included. Shocker et al. (1991) and Robert and Lattin (1991) propose approaches that allow
researchers to infer a brand subset from behavioral (purchase) data. Andrews and Srinivasan(1995) extend these models by estimating brand subsets stochastically, and this concept has
since been followed by other studies, such as Chiang, Chib, and Narashimhan (1999),
Gilbride and Allenby (2004), and Nielop et al. (2010). For practical use, however, thesemodels have serious constraints. As the number of brands n increases, the possible number of
1. In many product categories, n is muchbrand subsets increases exponentially as 2
greater than 10, implying that the number of subsets is unmanageable.
In summary, we cannot observe intermediate brand subsets directly from behavioral
data. Although some models attempt to estimate these subsets stochastically, their application
is limited to cases that have only a few brands. In section 2.2, we examine the formation ofbrand subsets from the perspectives of information searching and brand screening byconsumers.

42.2. Steps in Brand Choice from the Perspective of Information Processing
Information processing models are theoretically based on the S-O-R(Stimulus-Organism-Response) model, such as the Nicosia model (Nicosia, 1966),
Howard–Sheth model (Howard and Sheth, 1969), and EKB model (Engel, Kollat andBlackwell, 1968). These models examine a consumer’s inner purchase decision process.
Further development leads to information processing models of motivated consumers, such asthat pioneered by Bettman (1970, 1971, 1979) and followed by other studies (e.g., Mitchell,
1981; Howard, Shay and Green, 1988). These models assume that consumers have some sortof goal or need. In addition, Blackwell, Miniard, and Engel (2006) apply information
processing theory to improve the EKB model and thus propose the consumer decision
process model.
The Bettman and consumer decision process models share two common structures.
First, when consumers have a motive to solve a problem, they evaluate the available
alternatives using knowledge stored in their internal memories. They resort to searchingoutside information only when they are dissatisfied with the alternatives evaluated using theirmemories. Second, when consumers purchase a brand, they learn from its usage, and its
experience feeds back to their long-term memories.
Following these structures, search and consumption processes can be divided into thefollowing three steps (e.g., Hoyer and MacInnis, 2008; Mowen, 1995):
1. Internal search: first, consumers search their internal memories to solve the problem.
2. External search: if consumers cannot solve the problem through this internal search, theyrefer to outside information.
3. Learning: after consumption, this experiment is stored in consumers’ internal memories,
and on the next purchase occasion, an internal search is executed based on this updated
memory.
These internal and external search mechanisms are similar to the concept of bounded
rationality. An internal search is conducted within the knowledge of consumers that is“bounded” in comparison to all brands available in the market. Information processing
models further assume that an external search should be carried out when consumers areunsatisfied with the results of the internal search. Howard and Sheth (1969) also assume thatthe feedback system in that purchase experience affects satisfaction and brandcomprehension.

2.3. A Subset of Experience and Learning from Repeat Purchase Behavior
In this section, we examine how to incorporate the feedback system into a brand choicemodel. Because we cannot observe consumers’ inner information processing decision frompurchase data, we must somehow infer this search and learning.
5Consider the case when consumer i purchases brand j on the t-th purchase occasion.
If brand j was purchased previously, consumer i must have knowledge of it. Therefore,
previously purchased brands are evaluated by an internal search. By contrast, if brand j has
not been purchased before, this brand is presumably evaluated by an external search. Having
purchased and consumed brand j, the brand is now stored in the memory. Thus, on the (t+1)thpurchase occasion, brand j will become an element of the brand subset that is evaluated by
the internal search.
From purchase data, we can obtain the set of brands stored in the memory of eachconsumer (i.e., those included within the internal search). This subset is not a set of favorable
brands. We name this the “experiential set” and define it as follows. The experiential set is asubset of brands that is formed through repeat purchases and evaluated by an internal search.
It consists of brands that have already been purchased and used by the consumer. It isconceptually different from the “consideration set” and the “choice set,” which exist before
choice and from which one brand is selected to be purchased. The “experiential set” isformed after choice as a result of learning and memory storage feedback. The brandpurchased on the next occasion may not necessarily come from the experiential set.
By introducing this concept of the experiential set, we are able to incorporate thefeedback system of consumer information processing explicitly into the brand choice modelusing observable data only. Fig. 1 shows the purchase process described above.

6

Fig. 1. The model of repetitive search and learning
Inherited from former
Purchase experiences

Unsatisfied
Internal
searchExperiential
Sett‐th purchaseoccasion

External
search
Choice(Purchase)

Satisfied byInternal search

Purchase intention
Stored in the long‐term memory
and used on the next purchase occasion

Learning(Brand Comprehension)

Unsatisfied

t+1th purchaseoccasion

External
searchInternal
searchExperiential
Set

Purchase intention

Choice(Purchase)
Satisfied byInternal search

Learning
time(Brand Comprehension)
To the next purchase

One advantage of introducing the experiential set is that we can obtain the time-series
formation of brand subsets explicitly from purchase data. The importance of examining
dynamics in brand subsets was raised as early as the late 1970s (Farley and Ring, 1974).

3. The Experiential Set Choice ModelIn this section, we formulate the brand purchase model that incorporates the concept of
the internal search, external search, and experiential set based on the search and learningmodel as the extension of ordinary brand purchase model discussed in section 2.

3.1. The Experiential Set
Consumers store information on specific brands in their long-term memories. This
brand set—the experiential set—is constructed through past purchase behavior. In this section,
we construct the purchase model that incorporates the experiential set.
7

First, let E

be the experiential set of consumer i on the t-th purchase occasion.
Because the experiential set changes over time, t is attached. The number of brands within
the set is defined as n E . In the following sentence, we develop the experiential set alongwith the relationship with the observable variables.
When consumer i opts to purchase a product on the t-th occasion, s/he first conducts
an internal search. At this time, the consumer retrieves brand information from E , which
was formed after the t 1 th purchase occasion. If the consumer purchases the brand,which is a member of E , at t, we see that consumer i finds a satisfactory brand from theinternal search and purchases this brand. In this case, the experiential set on the t 1 -th
occasion is the same as the set at t, that is, E ,E . In contrast, if the consumer remains
unsatisfied following the internal search, s/he would find an alternative through the external
search. When consumer i purchases brand j, which is not in set E , on the t-th purchaseoccasion (j ∉ E ), E ,contains the element of E and brand j also becomes a memberof the set. In this case, the experiential set expands following the external search.
Let us define the observable variables. First, when consumer i purchases brand j on
the t-th purchase occasion, let the purchase output variable be given as y
1. In this case,brand j is a member of the experiential set (j ∈ E ); the purchase output variable of brand k,which is a member of E and is not purchased, is given as y
0 k j, k ∈ E . The
external search is observed when the purchased brand j is not a member of E . In otherwords, the external search is conducted when j ∉ E ; thus, let the external search variable isgiven as y
1. Because brand j is not a member of set E , we do not use this occasion
to estimate the purchase probability of brand j. As described in the definition of E , thisexperiential set is the set of brands that have already been purchased and used. Therefore, E
expands not at the point of purchase but after the purchase.

3.2. The Choice Model for the Multinomial Observations
Before the model formulation, we show the basic framework of the multinomial choicemodel. In it, if there are J alternatives available, the most preferred alternative is chosen. Let
the choice result observation of consumer i at t-th choise occasion be y , ⋯ , y , then any
one element takes 1 (chosen) and other elements take 0 (not chosen). Then, we define thelatent variables of evaluation y ∗ , ⋯ , y ∗ , which have following conditions: if y
1 theny∗

max y ∗ , ⋯ , y ∗ , and if y

0 then y ∗max y ∗ , ⋯ , y ∗ . This means that an

observation will change depending on whether the evaluation is the highest or not. In practice,
we have to set one alternative as the base alternative and fix the evaluation variable as aconstant to satisfy the identification condition. For example, when we fix the evaluation ofJ-th alternative as 0, all of the evaluations of the alternatives other than the J-th alternative
become a relative value, or y ∗y∗ , ⋯ , y∗ ,y ∗ , 0 . Corresponding parameters and8variables that explain the evaluation will also be a relative value (e.g., Train, 2003). We also
have to consider the identification condition of the variance-covariance matrix. We have to
set a constraint to deal with the scale identification problem. We usually, set the 1,1element of variance-covariance matrix Σ as 1 to satisfy the identification.
We now discuss these identification problems. We must first consider which alternative
would be an appropriate base. To construct a hierarchical model that assumes consumer
heterogeneity, the base alternative must be in the experiential set of all consumers for all
periods. Though we have to estimate the parameters relative to the base alternative, wecannot find one. Therefore, we treat the external search y as one of the alternatives and set
this as the base alternative instead of any of the actual alternatives, such as concrete brands.
Thus, the evaluation y ∗ indicates the difference of evaluation between alternative j and theexternal search. For alternative j in the experiential set E , the relation between observationand evaluation is as follows:y

1 if y ∗0 if y ∗max y ∗ |k ∈ E ,0
, if j ∈ E
max y ∗ |k ∈ E ,0

(1)

In a typical multinomial probit model, if there are J available alternatives, we have to
set one as the base alternative and estimate the evaluations of the remaining J 1
alternatives. In this model, however, since we treat the external search as the J 1-th
alternative and set this as the base, we estimate the evaluations of J alternatives.
It is consistent with the above theoretical discussions to set the external search as thebase. When an individual evaluates the alternatives through an internal search, the preferable
alternative will be chosen only if the alternative exceeds a minimum level of satisfaction.
This minimum level of satisfaction is the threshold of the external search that is set as thebase alternative. If an evaluation of all alternatives obtained from the internal search does notachieve the satisfaction level, the individual will find the new alternative through an external
search. In this case, the evaluation of the new alternative will be higher than that of all thealternatives in the experiential set

9

Table 1: Correspondence relationship between observations and evaluations
evaluation(y ∗ )observation(y)choiceExperiential

occasion

y

y

y

ES

y∗

y∗

y∗

ES

set

0

-

-

-

0

-

-

-

0

{1}

1

1

0

0

0

0

-

-

0

{1}

2

1

0

0

0

0

-

-

0

{1}

3

0

1

0

1

0

-

-

0

{1}

4

1

0

0

0

y∗ , 0

y∗

-

0

{1,2}

∗

∗

y ,0

-

0

{1,2}

5

0

1

0

0

y

6

0

0

1

1

0

0

0

{1,2}

∗

y

∗

∗

y ,y ,00{1,2,3}

y∗

∗

7

0

0

1

0

y

8

0

1

0

0

y∗

y∗, y∗ , 0

0{1,2,3}

∗

y

∗

∗

y ,y ,00{1,2,3}y∗, y∗ , 0y∗

0{1,2,3}

9

0

0

1

0

y

10

0

1

0

0

y∗

∗

Note: ES = external Search
Table 1 shows the process of choice subset formulation and brand evaluation. At theinitial state, consumer’s experiential set contains only brand 1. On the first and secondpurchase occasions, the consumer evaluates only brand 1 through internal search. As a result,the subsequent experiential set does not change. On the third purchase occasion, theconsumer chooses brand 2, which is not in the experiential set. It implies that external search
was conducted. The evaluation value of brand 1 for the third occasion is below the value of
external search, which is 0. This means that the consumer is not satisfied with brand 1 andfinds a new brand through external search. Similarly, on the sixth occasion, the consumer is
not satisfied with the brands in the experiential set and chooses a new brand (brand 3)
through external search. Brand 3 is now added to the experiential set, which will be evaluatedthrough internal search at the seventh occasion.
Next, we define the structure of the variance-covariance matrix. This matrix explains
the competitive or complement structure of the whole market. However, since the elements ofthe experiential set differ depending on individual and time, each consumer has only partial
information. In this case, the variance-covariance matrix of a consumer becomes a partial
matrix consisting of the alternatives in the experiential set. We have to estimate the wholematrix from this partial information. Since we need to estimate one matrix parameter for awhole market, we apply the same constraint as in the typical multinomial probit process,which fixes 1,1 element as 1. We cannot obtain a random sample of the matrix parametersatisfying this constraint from any well-known distribution in a straightforward manner.
However, simple approaches have been proposed (e.g., McCulloch and Rossi, 1994; Noible,
10

1998; McCulloch, Polson, and Rossi, 2000; Imai and van Dyk, 2005). For example,
McCulloch, Polson, and Rossi, (2000) decompose the matrix into a vector and a partial
matrix to obtain samples from a multivariate normal distribution and a Wishart distribution,
respectively. Since we cannot apply these methods in this model, however, we obtain samples
from a Gamma distribution for diagonal elements and apply the Metropolis-Hastings (M-H)
method to obtain samples for the non-diagonal elements. Procedures are available forobtaining random samples of the variance-covariance matrix of a multivariate probit modelusing the M-H method, such as those in Chib and Greenberg (1998) and Manchanda, Ansari,and Gupta (1999). We have developed an estimation procedure based on these methods, adetailed description of which is provided in the Appendix.
We define the structure to explain the evaluation using y ∗ and Σ, as defined above. As
is the multivariate probit experiential choice model, this model is constructed from an E -dimensional vector y ∗ extracting a corresponding element from y ∗ and an E
K parameter matrix B , a n E
n E
corresponding element from B and Σ respectively.
y∗B xparameter matrix Σ

ε , ε ∼ N 0, Σ

extracting a(2)

We assume a hierarchical structure for parameter B . This prior structure supplies
information using the customer-specific variable.
vec B

Δw

ξ , ξ ∼ N 0, V

(3)where w is a L-dimensional explanatory variable, Δ is a JK L matrix parameter, and V
is a JK JK variance-covariance matrix. A detailed description of the prior and posterior
distributions is provided in the Appendix.

4. Empirical Analysis
4.1. Data Overview and the Period of Analysis
We now conduct an empirical analysis of the model defined above. This section
provides a data overview. We use the sales records for a drugstore chain’s laundry detergent
provided by the Joint Association Study Group of Management Science and Customer
Communications. The data period covers the two years from January 1, 2008 to December 31,
2009.
11

Since we need the formulation period of the experiential set, we use the first 9 months
as the required period. The initial experiential set consists of the brands chosen during theformulation period, and the period of analysis thus spans the following 15 months. However,
we use each consumer’s last choice occasion for the forecasting set. We set the calibration
period as this 15-month period except for the last purchase.

4.2. Studied Brands and Customers
For our studied brands, we choose the top 10 brands purchased within the study period;
300 customers were studied, as they had purchased these 10 brands more than four times
during the calibration period.

4.3. Explanatory Variables
The proposed model has two kinds of explanatory variable, x and w . In x , we
include the intercept, sale day dummy, and holiday dummy. In this store, all of the goods are
discounted on the first and twentieth days of each month. Therefore, we will include adummy variable for whether or not the day is a sale day. Similarly, we include a dummy
variable for whether or not the day is a holiday. In w , we include the intercept, gender(female = 1), and logarithmic age.

4.4. Forecasting
To examine the forecasting ability of the model, we attempt a choice prediction for eachcustomer’s last choice occasion using the obtained parameter. We use the Hit Ratio and ROC
scores as indicators of prediction performance. The Hit Ratio is the rate of customers who
actually choose the brand predicted to be chosen. It is obtained from theprediction-observation matrix, which compares the forecast and the observation. The ROC
score is usually used in the data mining performed by database marketing to examine theforecasting performance of a model obtained from the ROC curve. An ROC score is obtainedfor each brand. Further details may be found in Blattberg, Kim, and Neslin (2008).

5. Results
5.1. Forecasting PerformancesThis section describes the results of the model’s forecast. First, we see the obtained
ROC scores. We calculate two types of forecasting methods. In Method 1, the choice12

probabilities of the brands in the experiential set are obtained in the usual way, though the
choice probabilities of the brands not in the experiential set are 0. In Method 2, the choiceprobabilities of the brands in the experiential set are the same as in Method 1. However, toobtain the choice probabilities of the brands not in the experiential set, one calculates theprobabilities from estimated parameters and multiplies the external search probability toobtain the complement probabilities. Detailed procedures can be found in the Appendix.
Table 2 shows the obtained ROC scores of each brand. Each score has a value between
0 and 1. As predictive accuracy improves, the value approaches 1. If forecasting iscompletely random, the expectation value will be 0.5. We can thus say that, if the value
exceeds 0.5, the model has some predictive ability. As shown in Table 2, the ROC scores ofall brands exceed 0.5 substantially. We thus find that the predictive accuracy of the proposedmodel is fairly good.
Next, we see the Hit Ratio, defined as the number of consumers who choose the brandas predicted by the model divided by the total number of consumers. As with the ROC score,
the Hit Ratio has a value between 0 and 1, and, as predictive accuracy improves, the value
approaches 1. We calculate the value using the prediction-observation matrix (see Table 3).
Table 3 displays choice forecasting as the column and actual choice as the row. The numberof matching customers is expressed as the diagonal elements. We can obtain the Hit Ratio bydividing the diagonal elements by the total number.

13

Table 2: ROC Score
ROC Score
Ariel

0.88

Attack

0.93

Bold

0.90

New Beads

0.83

Top

0.87

Blue Dia

0.93

PB (Private Brand)

0.91

FaFa

0.86

Liquid Top

NA

Style Fit

0.78

Note: we cannot obtain the result for Liquid Top because
no one chose the brand on the last choice occasion

Table 3: Prediction and Observation Matrix
New
Pred.＼Obs.

Ariel

Attack

Bold

Blue
Top

Beads

PB

Liquid

Style

Top

Fit

FaFa

Dia

ES

Ariel

69

6

4

2

5

4

0

1

0

0

4

Attack

6

31

1

0

3

3

3

0

0

0

2

Bold

2

0

36

0

3

2

0

0

0

0

2

New Beads

2

1

5

12

6

7

0

0

0

0

4

Top

4

2

0

1

14

0

0

0

0

0

1

Blue Dia

1

0

2

1

3

21

0

0

0

0

0

PB (Private Brand)

0

2

1

0

1

4

4

1

0

0

3

FaFa

0

0

0

0

0

1

0

0

0

0

0

Liquid Top

0

0

0

0

0

0

0

0

0

0

0

Style Fit

2

0

0

0

0

1

0

0

0

1

1

External Search

1

0

0

0

0

0

0

0

0

1

0

14

The calculated Hit Ratio is 0.63, which we compare with other forecast values. If theforecasting is completely random, customers will have chosen any 10 brands or conducted an
external search. The expectation value of the Hit Ratio is therefore 1/11 0.09. The
obtained Hit Ratio is substantially higher than this. Moreover, we could forecast that all
customers will choose the brand with the largest share; the largest share brand, Ariel, waschosen by 87 customers, for a Hit Ratio of 87/300 0.29. The Hit Ratio obtained by the
proposed model also exceeds this value.
The proposed model is not only theoretically rigorous but also has high predictive
ability, suggesting that it has practical applicability.

5.2. Parameters
In this section, we examine the model’s parameters. We first show the distributions of
the individual parameter β for each brand. Figure 2 shows the parameters of each brand’sintercept as the boxplot. The intercept of a brand contains each customer’s basic preference.
From this boxplot, we can find the distribution of the individual preferences for each brand.
In the figure, the percentile value in the bracket is the rate of consumers who included thebrand in their experiential set at the end of the calibration period. Note that, although weestimate the parameters of all the brands for all consumers, we include only the parameters of
those consumers who include each brand in the experiential set in the figure.
We find differences within the variances for each brand. For example, few consumers
highly preferred PB (Private Label), and BP’s preference median (the middle line in the box)
is not very high. Moreover, while the medians of Bold and New Beads are roughly equal, thedistribution of Bold is more varied than that of New Beads.

15

of each consumer

0

5

10

Fig. 2: Brand intercept β

Next, we show the parameters Δ and Σ. Table 4 presents the posterior mean of theselected elements of parameter Δ. We see the rough relation between each brand preference
and demographic variable. In the table, “*,” “**,” and “***” indicate that 0 lies outside the90%, 95%, and 99% highest posterior density intervals of the estimate. These highest
posterior density intervals were calculated using the method proposed by Chen, Shao, andIbrahim (2000). Table 5 presents the posterior mean of matrix Σ. In Table 4, we see twobrands, the largest share brands Ariel and PB, and their differences. In the Sales-Genderparameter, Ariel is positive and PB is negative. On sale day, then, Ariel tends to be chosen byfemale consumers, while PB tends to be chosen by males. The table also shows that PB tends
to be chosen by males during the holidays.

16

Table 4: Estimated Δ
Δ
Ariel

PB (Private Brand)

Intercept

GenderAgeIntercept

-4.88

2.56

0.82

Sale

-1.91

2.49 **-0.21

Holiday

-0.04

-0.73

0.23

Intercept

-6.13

-8.14

3.52

Sale

5.19

-7.04 **

0.73

Holiday

8.89-3.95 **

-1.18

Table 5: Estimated Σ
Σ

Ariel

Attack

Bold

New
Beads

Top

Blue Dia

Ariel

1.00

Attack

-0.01

2.93

Bold

0.01

0.02

3.63

New Beads

0.00

0.02

0.02

3.83

Top

0.00

0.02

0.02

0.00

5.05

Blue Dia

0.02

0.01

0.02

-0.01

-0.03

5.79

PB (Private Brand)

0.03

0.02

-0.03

-0.02

-0.11

-0.08

FaFa

0.00

0.07

-0.02

-0.02

-0.04

-0.02

Liquid Top

0.03

-0.04

0.02

-0.12

-0.05

-0.38

Style Fit

-0.01

0.10

0.15

0.23

-0.32

-0.79 *PB

FaFa

LiquidTop

PB (Private Brand)

3.05

FaFa

0.07

3.57

Liquid Top

0.25

0.00

3.58

Style Fit

0.06

-0.32

0.48

17

Style Fit

6.86

6. Discussion
6.1. Reject Brands in the Consideration Stage
Brisoux and Cheron (1990) propose a model in which the size of the consumer choicesubset gradually narrows (known as the “Brisoux and Laroche Conceptualization”); thisallows us to discuss the place of the experiential set in our model. We define the alternatives
in the experiential set as the subset in which elements are evaluated through the internal
search. Therefore, the experiential set is included in the processed set (originally, processedbrands). The processed set, however, also includes the alternatives evaluated and processed
through the external search. Strictly speaking, then, “the experiential set ⊆ processed set.”In addition, the experiential set is defined as the result of user experiences, formed though the
feedback of user memories. This is positioned at the next step of the choice (preference stage)in the Brisoux and Laroche conceptualization. Since the model describes one choice occasion,
the feedback system is not included. However, the experiential set is formed through therepeat choice process. In the processed set, we see that the experiential set contains theevoked, hold, and reject sets at the consideration stage. We will discuss these subsets of theobtained choice probabilities.
We can calculate the choice probabilities of the alternatives in the experiential set fromthe proposed model. Since the probabilities have values between 0 and 1, we cannot classify
these three subsets precisely. However, we can classify them by referring to indicators. For
example, we can obtain the external search probability for each consumer, which will be apreference threshold. If those alternative choice probabilities are lower than the external
search probability, the preference for the alternatives will be very low.
Table 6 presents the choice probabilities for each studied consumer on the last choiceoccasion. Note that the choice probabilities were calculated only from the alternatives in theexperiential set. The average choice probabilities of the first were obtained from the choiceprobabilities of the alternatives with the highest choice probabilities among the alternatives inthe experiential set. The average choice probabilities of the first were obtained from thechoice probabilities of the most preferred alternatives in the experiential set of each consumer.
Likewise, the average choice probabilities of the second were obtained from choiceprobabilities of second preferred alternatives for each consumer. The table below shows the
choice probabilities’ degree of concentration.

18

Table 6: Choice Structure in the Consideration Stage
Average choice probabilities
Size of the

Number ofexperiential set

consumers

1st

2nd

3rd

4th

External

below

search5th

probability

1

38

0.970

-

-

-

-

0.030

2

52

0.788

0.176

-

-

-

0.036

3

62

0.705

0.205

0.058

-

-

0.031

4

54

0.640

0.216

0.074

0.028

-

0.043

5

42

0.552

0.235

0.102

0.050

0.012

0.061

over 6

52

0.520

0.208

0.115

0.058

0.023

0.077

We find that the probabilities of most of the preferred alternatives are very high, while
the probabilities of the second most preferred alternatives are significantly lower. The choiceprobabilities of the third alternatives are even lower, roughly between 5 and 10 percent.
Therefore, many consumers have only one preferred alternative and will not actively choose
others, while the choice probabilities lower than the fourth most preferred alternatives are
smaller than the external search probability. These alternatives may thus be classified as thereject set.
Therefore, consumers therefore have the following general inner structure in theirchoice of laundry detergent: they have one preferred alternative (which may be included in
the evoked set), two or three comparable alternatives (which may be included in the hold set),
and they rarely choose a third (or lower) alternative.

6.2. Customer Satisfaction and Parameters
We can draw implications for firm communication strategies from this experiential
model. Our study divided consumers’ first brand choice from their successive brand choiceoccasions because we wished to analyze the differences in evaluation processes between thefirst choice and subsequent occasions. For their first choice, consumers will evaluate thealternatives based on their expectations, while, after making this choice and having learned,
they will evaluate based on their experience.
The difference between pre- and post-purchase evaluations has been discussed incustomer satisfaction studies such as Oliver (2010). Theoretically, consumer satisfaction isaffected by the disconfirmation between the performance expectations at pre-purchase andthe perceived performance at post-purchase. If the expectation is too high, the consumer feels
unsatisfied. It is not desirable to sell products to consumers who will not be satisfied by themthrough improper marketing communications that raise their expectations. Such a brand may
19not only be classified into the reject set discussed above and never again chosen by the
consumer but may also inspire the consumer to generate negative word-of-mouth. A brandclassified by many consumers into the reject set may present marketing communication
challenges.
In this section, then, we will examine the relationship among three indicators defined
below.
The first indicator, “experienced rate” is defined as the number of consumers who
included the focal brand in their experiential set on the last choice occasion (tby the total number of consumers. We define n∑

1 j∈n E,T ) divided, where we omit thetime subscript (applied hereafter), and the experienced rate of the alternative j is defined asn /N.
Second indicator, “rejected rate” is defined as the rate of experienced consumers whoclassify the focal brand as a reject set. Let us define the external search probability of
consumer i as q and the choice probability of alternative j as p ; the number of rejected∑ , ∈ 1 p
consumers is thus defined as r
q . Using r , we define the rejected rate
as r /n .
Finally, “first choice rate” is defined as the rate of consumers who prefer the focal∑ , ∈brand. The first choice rate is defined as follows: f / , where fp
max pi , pi is a vector of the choice probabilities for the brands in the experiential set.
On the left side of Figure 4, we see that the rejected rates of many brands are roughly
0.3, while the rates of some brands (including PB) are higher than the others. Thus, thoughthese brands were chosen once, they will not be chosen again. Though less than 20% ofconsumers purchased PB, almost half will not purchase it again.
On the right side of Figure 4, we find another aspect of the brands’ relationship.
Although the difference in experienced rates between Ariel and Attack is roughly 5%, thedifference in the first choice rate is over 20%, and PB’s first choice rate is the second highest.
We can thus say that many people do not prefer PB but it has a substantial number of ardentfans.
We can draw useful implications from the result of the experiential set model that could
guide a long-term brand strategy.

20

Fig. 4: Relationships between the experienced rate and the rejected or first choice rate
Experienced Rate and Rejected rate

Experienced Rate and First Choice Rate
Ariel

0.5

0.7

FaFa

0.4

0.6

Liquid Top

0.3

Bold
AttackStyle Fit

Blue Dia
New Beads

0.2

First Choice Rate

0.5
0.4

PB (Private Brand)

Top

Style Fit

0.2

0.1

0.3

Rejected Rate

PB (Private Brand)

AttackAriel
0.0

New Beads
Bold
Top
Blue Dia
0.1

0.2

0.3

0.4

0.5

0.6

Liquid Top

0.1

Experienced Rate

FaFa

0.2

0.3

0.4

0.5

0.6

Experienced Rate

7. Conclusion
In this research, we use scanner panel data to construct a stochastic brand choice modelof consumer goods in which consumers repeatedly choose a brand from many alternatives.
We then reexamine consumers’ repeat purchase behavior from the perspective of information
processing theory.
This research makes three main contributions. First, we construct a theoreticalframework to analyze behavioral data such as point-of-sales records with customer ID
numbers. We also reexamine the concepts of internal search, external search, and learning
proposed in the field of consumer studies. Furthermore, we reconstruct consumers’ repeatpurchase behavior from the perspective of information processing theory. By introducing
these concepts into the quantitative model, the proposed model is more theoretically valid.
Furthermore, to define the experiential set that can be observed from purchase records,
instead of from choice subsets such as the “consideration set” or “processing set,” weproposed a more practicable model. The proposed model is insusceptible to increases in thenumber of alternatives and is applicable even for markets comprising dozens of alternatives.
The second contribution is that we construct a high performing forecasting model. From
the results derived using the validation set, we find that the proposed model has a highpredictive ability. Because the model is designed so that the purchase probability of brands
that are members of the experiential set is higher, this result implies that many consumers
tend to choose brands that they have always purchased.

21

The third contribution is that the proposed model has the potential to be flexible interms of application and extension. Because most proposed model structures are based on
previous brand choice models and are estimated using the MCMC method, we can easily
incorporate the specific model structure developed in previous research. We would thus beable to extend the model into, for example, a cross-category or dynamic (time-series) model.
For future research, we highlight the following two issues. First, future studies should
examine the proposed model using other product categories. Although we have found a highlevel of predictive accuracy by focusing on the laundry detergent category, we must confirm
that the proposed model has such a predictive ability in other categories. This research shows
the validity of the concept of the experiential set as a result of predictions; however, we needto report the existence of the experiential set in other products. The second issue is toincorporate a dropout mechanism of brands from an experiential set. When the duration ofanalysis is long, such a dropout mechanism will become more important. Future researchshould thus reexamine other parts of the model as the need arises.

22

A. Appendix
A.1.

Prior Distributions and a Full Conditional Posterior Distribution
Recall the model proposed in this research. Let y ∗ be an n E -dimensional vector

extracting corresponding elements from y ∗ . Let B
consisting of a J K matrix B and Σ
a J J matrix Σ.

y1 if y ∗0 if y ∗an n Ebe an n E

n E

matrix parameter consisting ofmax y ∗ |k ∈ E ,0
, if j ∈ E
max y ∗ |k ∈ E ,0y∗ B xε , ε ∼ N 0, Σ
Δw ξ , ξ ∼ N 0, V
vec B
We assume prior distributions for Σ, Δ, and V

K partial matrix

(A.1)
(A.2)
(A.3)

diag v , ⋯ , v. Let Δ~N Δ , V, S

and v ~G ν /2, V /2 . To estimate Σ, we generate samples of its diagonal and off-diagonal
elements separately. We define the diagonal elements of Σ as d, hence d diag Σ . We
define the off-diagonal lower triangle elements of Σ as s. To introduce the operator vec ∗ ⋅that vectorizes the lower triangle elements of the objective matrices, we can denote thatsvec ∗ Σ . The prior distributions are then defined as follows:d ∼ IGs ∝ exp

q Q
,
,j
2 2

2, ⋯ , J

0.5 s

G

s

s

(A.4)
s

(A.5)

where, IG a, b is an Inverse-Gamma distribution with parameter a, b . We define a priordistribution of Σ from the above two distributions. To be a variance-covariance matrix of thediscrete choice model, we need to introduce some restrictions for Σ. First, all diagonal
elements of Σ have to be positive, and Σ needs to be a positive-definite matrix.
Additionally, in MNP, we need a scale restriction that fixes the 1,1 element as 1. In thisresearch, we set the region satisfying the above restrictions as set C. Using set C, we define
the prior distribution as follows:

π Σ ∝

π d

π s

23

1 Σ∈C

(A.6)

where 1 ⋅ is an indicator function. This expression is from Chib and Greenberg (1998),
who propose an MVP estimation method.
From the above settings, the full conditional posterior distribution is defined as follows:
π θ|D
π y |y ∗ π y ∗ B , Σ∝

π B |Δ, V(A.7)

π Δ|V π V π Σ

where, θ is a set of parameters and D is a set of inputs. Moreover, π y |y ∗is defined asfollows (Albert and Chib, 1993):
π y |y ∗1 y

1 ∧ y∗

max y ∗ , 0
(A.8)

∈

1 y

A.2.

0 ∧ y∗

max y ∗ , 0

Posterior Distributions

A.2.1. Conditional Posterior of∗

The sample of the posterior distribution of y ∗ is obtained by following truncatednormal distributions:1y∗ | ⋅ ~where, am

TN , μ, s
TN , μ, s

max y ∗ |k ∈ E ,0 , μ

B x , and e

m

m

if y
if y
S, S

1
,
0
,

if

e , s

j∈E

Σ

(A.9)

S, S

,

S

,,

S

Σ ,

y ∗ . Note that subscript j is not a j-th element of the partial

matrix/vector but aj-th element of the full matrix/vector.

1

In practice, to stabilize the simulation, we introduced a restriction that sets the thresholdmaximum/minimum value. To introduce the threshold, let the interval of the TN be a, C
andC, a . Since this threshold C is attached to the prior distribution (A.8), the restriction

will not cause any theoretical problems. In this research, we set C

24

10.

A.2.2. Conditional Posterior of
The posterior sample of Σ is separately obtained from d and s, since we apply the
random walk M-H to obtain s the same way as MVP; see Chib and Greenberg (1998) for
further details. In this section, we will show a method of obtaining d .
The conditional posterior distribution of d is as follows:
π d|⋅ ∝

Σ

exp

1 ∗
y
2

B x

y∗

Σ

B x

(A.10)

π d
We show the decomposition for the whole matrix Σ as a general case. First, using LDU
decomposition, let us decompose the matrix into a lower triangle matrix L and a diagonal
matrix D, where D diag d . From Σ LDL , we can decompose the determinant into|Σ||L | |D| |L| . Additionally, since D is a diagonal matrix, we obtain |D|

|d |

⋯ d

. Similarly, using the relation Σ

rewrite the quadratic form. Let L

y∗

LDL

L

e , we obtain y ∗Bx

D L , we can
Bx

Σ

y∗

Bixit e′D 1e. Since D is a diagonal matrix, e′D 1e e1d1 1e1 ⋯ eJdJ 1eJ. Fromthese relations, we can obtain the following equation:

π d|⋅ ∝

d

exp

1
ed e
2

∈

π d

(A.11)

Note that, in the t-th choice occasion of consumer i, e would not exist if j-th alternative
would not be a member of E . Then, we operate this case introducing an indicator function
1 j ∈ E . From this equation, we find that the posterior distribution of d follows a gamma
distribution:d | ⋅∼ IG

where, q∑∑ 1 j∈E

q Q
,
,j
2 2

q and Q25

2, ⋯ , J∑∑(A.12)

1 j∈E eQ.

A.2.3. Conditional Posterior ofSince we cannot obtain a J K matrix parameter B from a well-known distribution,
we split up B into vectors and obtain a K-dimensional vector β for J alternatives.
From the marginal distribution of multivariate normal, an element of multivariate
regression is expressed as follows:
where μ

S , S

,

y∗

β x

y∗ ,

B , x

e , e ~N μ , σ, σ

S(A.13)

S , S

,

S

, , andS

Σ . Inthe same manner, we can decompose the prior distribution. In this paper, we denote thedecomposition of b into β as follows:
b

Δ
⋮
Δ

β
⋮
β

V
ξ , ξ ~N 0, ⋮
V

v

⋯ V
⋱
⋮
⋯ V

(A.14)

whereV
diag v , ⋯ v;
therefore,
for
the
j
diagonal
block,V
diag v, ⋯ , v . Since we defined V as a diagonal, we obtain the following
equation from the partial vector β :βΔzζ , ζ ~N 0, V

(A.15)

From equations (A.11) and (A.13), we obtain following posterior distribution:β | ⋅ ~N m , V(A.16)

m

V

∑

∑

V

where
I σ x

function defined as Iy∗μ

I σ x x
L

Δz

L
c

Δz

c

. Additionally, I

andis an indicatorj∈E .

A.2.4. The Conditional Posterior ofandThe posterior sample of Δ is obtained from following matrix normal distribution.
Δ| ⋅ ~Δ , ,(A.17)

where SS
WW
, and Δ
vec B W Δ S S , W
w ,⋯,w .
Δ follows JK L matrix normal distribution. Refer to Rowe (2002) and Dawid (1981) for
further details of the matrix normal distribution.
The posterior sample of v , k
distribution.

1, ⋯ , JK is obtained from following gamma

v |⋅~

/2,

/2

(A.18)∑
where ν
ν
N, V
V
b
δ ⋅v
δ ⋅ δ , ⋅ Ω δ ⋅ δ , ⋅ , v is
k-th element of vectorilized parameter vec B , δ ⋅ is k-th column vector of Δ, and δ , ⋅is k-th column vector of Δ . In both vectors, the number of elements is L.
26

A.3. Initial Values and Sample Collections
For initial values, we let all latent variables y ∗ be 0 and parameters B and Δ bezero vectors or zeros matrix. In addition, we let Σ be an identity matrix.
We ran the chain for 15,000 iterations. The result was reported on a sample of 10,000
draws from the posterior distribution after we discarded 5,000 burn-in draws.

A.4.

Choice Probabilities

In this section, we will show the detailed discussion of choice probabilities.
First, the choice probability of an alternative in an experiential set is obtained from thefollowing equation:
Pr y

1j∈E

⋯

ϕ z B x , Σ dz∗

where J∗an E

. We set the region a , j∞, max z , 0 if k1, ⋯ , J∗ as a

(A.19)

max z , 0 , ∞andj if to obtain the choice probability of j -th alternatives,∞, 0 , k 1, ⋯ , J ∗ if to obtain the external search probability. Let the
besides a
choice probabilities of alternatives in the experiential set be p , ⋯ , p ∗ respectively and theexternal search probability be q. Thus, p⋯ p ∗ q 1.
Since this model has no information about the alternative choice after the external
search, we theoretically cannot forecast which will be chosen after the external search. Note
that, as mentioned in Simon (1947), individual search and choice are not a completely
random. Consumers tend to choose the alternative they will prefer and can predict what thiswill be to some extent. We then fill the choice probabilities of the alternatives after theexternal search from the hierarchical structure. We will now describe the procedure we used
to fill the probabilities.
Since we have the preference parameter β , even if the alternative is not in theexperiential set, we use that parameter. Let the number of alternatives not in the experiential
set be J and the corresponding extracted parameters be B and Σ . From theseparameters, we obtain the choice probability of these alternatives from the following
equation:
Pr y

1j∉E

⋯
27

ϕ z B x , Σ dz

(A.20)

where amax z , ∞ and a∞, max z if k j if to obtain the choiceprobability of j-th alternatives. Let the obtained probability be p . Note that the sum
Pp⋯ p will not be 1. Then, divide by the sum P , and define p /P as theconditional choice probability of the j-th alternative. We define the choice probability of thej-th alternative not in the experiential set by multiplying the external search probability q.
We can then obtain the set of choice probabilities whose sum is 1:

p
∈

q
∉

p
P

1

(A.21)

The first term on the left hand side is the summary of the choice probabilities of thealternatives in the experiential set. The second term is the summary of the choiceprobabilities of the alternatives not in the experiential set. In the second term, all choiceprobabilities are multiplied by the external search probability.

28

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