MMRCDISCUSSION PAPER SERIES
No. 409

A brand purchase model of consumer goods
incorporating the information search and learning process
Sotaro Katsumata
Nagasaki University
Makoto Abe
The University of Tokyo
May 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 purchase model of consumer goods incorporating theinformation search and learning process
Sotaro Katsumata(Nagasaki University)
Makoto Abe(The University of Tokyo)
Abstract
In this research, we use scanner panel data to construct a stochastic brandchoice model of consumer goods in which consumers repeatedly choose abrand from many alternatives. We thus examine consumers’ repeat purchasebehavior from the perspective of information processing theory. In
particular, we explicitly incorporate the concept of internal 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 purchasedecision. 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 isobservable from purchase records. Because choice subsets are constructedfrom observable data, this concept helps build brand choice models thatincorporate more elaborate information searches and learning processes by
consumers. This, in turn, results in a high predictive validity of the model.
Keywords: Information Search, Discrete Choice Model, Consideration Set,
Markov Chain Monte Carlo Method

11. Introduction
In order to meet the needs of various customers, firms tailor theirproducts to different market segments. Consumers are thus able to choose
the most suitable product from the brands available in the market. As thenumber 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 dothey choose brands through rational decision making. For example, eventhough the shampoo market comprises over 100 brands with each brandproviding different benefits, few consumers can evaluate all these 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” inwhich many alternatives and problems exist in the real world. He also
proposes a decision process whereby consumers do not evaluate allalternatives but review only a subset of them in order to choose the most
preferred option. The imperfection in human cognition is a serious concern inMarketing. 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 brand comprehension 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 level of product knowledge and involvement. These models support thenotion 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 toincorporate them into an empirical analysis 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 whichbrands were evaluated before the customer made his or her actual purchase.
From the previous argument, it is clear that consumers consider only asubset of brand alternatives. However, unless survey research such as direct2

questioning is carried out, it is difficult for firms 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 thatincorporates a brand subset formation process from purchase data alone.

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 field of 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 and Barbour (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 wecannot obtain information on brand subsets except by directly asking
consumers which brands they included. Shocker et al. (1991) and Robert andLattin (1991) propose approaches that allow researchers to infer a brandsubset from behavioral (purchase) data. Andrews and Srinivasan (1995)
extend these models by estimating brand subsets stochastically, and thisconcept has since been followed by other studies, such as Chiang, Chib, andNarashimhan (1999), Gilbride and Allenby (2004), and Nielop et al. (2010).
For practical use, however, these models have serious constraints. As the3number of brands n increases, the possible number of brand subsets
increases exponentially as. In many product categories, n is muchgreater than 10, implying that the number of subsets is unmanageable.
In summary, we cannot observe intermediate brand subsets directlyfrom 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 of brand subsets fromthe perspectives of information searching and brand screening by consumers.

2.2. Steps in Brand Choice from the Perspective of Information
Processing
Information processing models are theoretically based on the S-O-R
model, such as the Nicosia model (Nicosia, 1966), Howard–Sheth model(Howard and Sheth, 1969), and EKB model (Engel, Kollat and Blackwell,1968). These models examine a consumer’s inner purchase decision process.
Further development leads to information processing models of motivatedconsumers, such as that pioneered by Bettman (1979) and followed by otherstudies (e.g., Mitchell, 1981; Howard, Shay and Green, 1988). These models
assume that consumers have some sort of 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 processmodel.
The Bettman and consumer decision process models share two common
structures. First, when consumers have a motive to solve a problem, theyevaluate the available alternatives using knowledge stored in their internal
memories. They resort to searching outside information only when they are
dissatisfied with the alternatives evaluated using their memories. 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 bedivided into the following three steps (e.g., Hoyer and MacInnis, 2008;
Mowen, 1995):
1. Internal search: first, consumers search their internal memories to solve
the problem.

42. External search: if consumers cannot solve the problem through thisinternal search, they refer to outside information.
3. Learning: after consumption, this experiment is stored in consumers’internal memories, and on the next purchase occasion, aninternal search is executed based on this updated memory.
These internal and external search mechanisms are similar to theconcept of bounded rationality. An internal search is conducted within theknowledge of consumers that is “bounded” in comparison to all brands
available in the market. Information processing models further assume thatan external search should be carried out when consumers are unsatisfied
with the results of the internal search. Howard and Sheth (1969) also
assume that the feedback system in that purchase experience affects
satisfaction and brand comprehension.

2.3. A Subset of Experience and Learning from Repeat
Purchase Behavior
In this section, we examine how to incorporate the feedback system intoa brand choice model. Because we cannot observe consumers’ inner
information processing decision from purchase data, we must somehow infer
this search and learning.
Consider the case when consumer purchases brand on the -thpurchase occasion. If brand was purchased previously, consumer musthave knowledge of it. Therefore, previously purchased brands are evaluatedby an internal search. By contrast, if brand has not been purchased before,
this brand is presumably evaluated by an external search. Having purchasedand consumed brand j, the brand is now stored in the memory. Thus, on the(t+1)th purchase occasion, brand j will become an element of the brandsubset that is evaluated by the internal search.
From purchase data, we can obtain the set of brands stored in thememory of each consumer (i.e., those included within the internal search).
This subset is not a set of favorable brands. We name this the “experientialset” and define it as follows. The experiential set is a subset of brands that isformed through repeat purchases and evaluated by an internal search. It
consists of brands that have already been purchased and used by the
consumer. It is conceptually different from the “consideration set” and the5“choice set,” which exist before choice and from which one brand is selected
to be purchased. The “experiential set” is formed after choice as a result oflearning and memory storage feedback. The brand purchased on the next
occasion may not necessarily come from the experiential set.
By introducing this concept of the experiential set, we are able toincorporate the feedback system of consumer information processing
explicitly into the brand choice model using observable data only. Fig. 1
shows the purchase process described above.

Inherited from former
Purchase experiences

Unsatisfied

t-th purchaseoccasion

External
searchInternal
searchExperiential
Set

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

Fig. 1. The model of repetitive search and learning
One advantage of introducing the experiential set is that we can obtainthe 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).

6

3. The Experiential Set Purchase ModelIn this section, we formulate the brand purchase model thatincorporates the concept of the internal search, external search, andexperiential set based on the search and learning model as the extension ofordinary 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 thatincorporates the experiential set.
First, let
be the experiential set of consumer on the -th purchaseoccasion. Because the experiential set changes over time, is attached. The
number of brands within the set is defined as. In the following
sentence, we develop the experiential set along with the relationship withthe observable variables.
When consumer opts to purchase a product on the -th occasion, s/hefirst conducts an internal search. At this time, the consumer retrieves brandinformation from, which was formed after theth purchaseoccasion. If the consumer purchases the brand, which is a member of, at, we see that consumer finds a satisfactory brand from the internal searchand purchases this brand. In this case, the experiential set on the-thoccasion is the same as the set at , that is,. By contrast, if theconsumer remains unsatisfied following the internal search, s/he would findan alternative through the external search. When consumer purchases
brand , which is not in the set, on the -th purchase occasion (),
contains the element ofand brand also becomes a member of theset. In this case, the experiential set expands following the external search.
Let us define the observable variables. First, when consumerpurchases brand on the -th purchase occasion, let the purchase output
variable. In this case, brand is a member of the experiential set() and brandwhich is a member ofand is not purchased, we
define as. The external search is observed when thepurchased brand is not a member of. In other words, the external7search is conducted when
; thus, let the external search variable. In this case, we observe the first purchase of brand ; however,
because brand is not a member of the set, we do not use this occasion toestimate the purchase probability of brand . As described in the definition of
the experiential set, this is the set of brands that have already beenpurchased and used. Therefore, the experiential set
expands not only at
the point of purchase but also after the purchase.
Table 1 shows the constructs of the processes of the internal search,
external search, and experiential set. This table depicts the process of aconsumer who has the experiential set only containing brand at the initialstate (start observation,). The consumer expands his/her experiential
set through the external search. In this table, the first purchase is denotedby, which means that the first purchase occasions cannot be used toestimate brand purchases. In this example, we include the case that theconsumer purchases nothing or purchases more than two brands
simultaneously.

Purchaseoccasiont

Brandpurchaseab

Experiential Externalsetsearch

c

0
1
2
3
4
5
6
7
8

1
1
0
0
0
1
0
1

(1)
0
0
0
0
1
0

(1)
0
0
1

Eit

Zit

{a}

0

{a}
{a}
{a, b}{a, b}{a, b}{a, b, c}{a, b, c}{a, b, c}

0
1
0
0
1
0
0
0

Table 1. The example of search behavior and the experiential set

3.2. Formulation of the ModelIn this section, we assume the constructs in order to explain theobserved variables
and . Because these variables takediscrete8values, we introduce the discrete choice model. In this research, we follow
Albert and Chib (1993) in order to construct a model that has continuous
latent variables. This way of formulation is an application of the data
augmentation proposed by Tanner and Wong (1987) using the Markov Chain
Monte Carlo (MCMC) method. We use this method to estimate parameters.
At first, let introduce the latent variable, which corresponds.
These two variables have following condition:(1){
The latent variable

represents the utility of consumer

for brand

at -th purchase occasion. For brand , in order to be chosen by consumer
at , latent variablemust be exceed a certain threshold and we let thethreshold be 0. In the -th purchase occasion, when all of the latent variablesof brands which are the member of the subset
below 0, no one brands arepurchased at this occasion. On the other hand, when the latent variables ofmore than two brands exceed 0, all of these brands are purchased. This
structure of model is called the multinomial model (e.g. Chib and Greenberg,
1998; Manchanda, Ansari and Gupta, 1999) as contrasted with themultinomial model (e.g. McCulloch and Rossi, 1994, 1996; Allenby and Rossi,
1999; McCulloch, Polson and Rossi, 2000). This model is distinguished what
distribution are assumed on the error term (e.g. Train, 2003). If the
distribution of the error term is the extreme value distribution, the model iscalled the “logit model”, while the error term is normally distributed, themodel called the “probit model”. In this research, since we assume thenormal distribution, the type of model is the “multivariate probit model”.
As same as the observation of brand purchase, we also introduce thecontinuous latent variable, which corresponds

as follows:(2){

Using above latent variables, we assume the construct to explain thesebrand choice and external search behavior. First of all, let
be thedimensional explanatory variable such as the sales promotion reached9consumer at the -th occasion.
includes the intercept. We assume that
degree of the response to these variables are differ from each brand andcustomer, so we assume the coefficient as. The coefficient
includes thedegree of response of the intercept means the brand-dummy. From the above
variables, we assume the following brand choice model:(3)
Additionally, in this research, we assume the correlation among each brand.
Let be the number of brands available in the market (number of wholebrand set), we define
be theparameter of correlation matrix. The
correlation
holds full information of correlation structure of focal market,
however, we assume that each consumer do not know full information of themarket. For consumer , at the -th purchase occasion, the consumer refers
the corresponding subset of . We denote this submatrix as ̃ which
consists of the correlation elements of brands which are member of theexperiential set. In the same manner, we let ̃ is a vector whose
elements are corresponding brands which are member ofextracted from
. Also, ̃ ismatrix which is extracted corresponding elementsfrommatrix. Using these variables, the brandpurchase model is defined as following
regression model:̃̃̃dimensional multivariate

̃

̃

(4)

To construct the external search model, we define following regression
equation using explanatory variable
and its coefficient parameter :(5)
In this research, we assume the hierarchical construct on parameterandto discuss the relation between each parameter and demographic
traits. This is one of reason to use MCMC method. Let
be a demographic
variable vector, a matrix parameter, and an individual parameter. W, we assume the following relation:
10(6)In the equation (6), we need the brand dummy and response parameter for
all brands. However, in brand purchase equation (4), we estimate only forthe brand which is a member of the experiential set. Therefore, theparameters of brands which are not an element of the experiential set of thelast occasion
are missing values. In MCMC method, since we are able toestimate these missing values stochastically, we use the algorism andestimate these values.
In the next section, we will show the explanatory variables in detailafter overview the empirical data. Also, detailed description of priordistribution, posterior distribution, and other settings of the model isprovided in the appendix.

4. Empirical Analysis
4.1. Data Overview
For the empirical analysis, we use the sales records of a drugstore chain
provided by the Joint Association Study Group of Management Science andCustomer Communications. The period of data covers two years fromJanuary 1 2008 to December 31 2009. The studied product category is
shampoo, which is a low price commodity that is generally purchased
repeatedly. Because of these properties, it is suitable to assess our proposedmodel.

4.2. Empirical Analysis Setting
4.2.1.Period of Analysis and Studied Brands
First, to apply the proposed model, we need a period before beginning
the analysis in order to assess the initial state of the experiential set.
Therefore, in this research we use the first 9 months of the 24-month study
period in order to form the initial experiential set. The period of analysis isthus 15 months.
11

The initial experiential set contains the brands that were purchased in
the first 9 months (this is called the formation period). Additionally, to assess
the predictive accuracy of the model, we exclude the last purchase occasion ofeach customer from the analysis (i.e., the validation period). The remaining
period of data is called the calibration period.
We choose the top 10 brands purchased within the whole study period
as our study objects. Although the computation load of the proposed model
does not dramatically increase as the number of studied brands increases,
the reliability of the estimation results will decrease. Table 2 shows the 10
studied brands and their sales.
brand namesales amount

1

Lux

1406

2

Pantane1226

3

TSUBAKI

734

4

merit

710

5

Essential

640

6

Dove

546

7

Super Mild447

8Soft in One

376

9

PB (Private Brand)

420

10

Mod's Hair

389

Table 2. List of Studied Brands

4.2.2.Definition of the Purchase Occasion and Studied
Customers
The proposed model has a multivariate choice structure in which morethan two brands can be chosen on the same purchase occasion and a
consumer can choose nothing at all. We define the purchase occasion basedon this structure. Thus, we set the day when the consumer purchases a
shampoo product as the purchase occasion.
The purchase probability is the conditional probability of a categorypurchase occurring. Although we do not discuss this concept in detail, we areable to obtain the purchase probability on any day in order to estimate thecategory purchase probability and the brand purchase probability obtained12

by our proposed model. Some researchers have proposed a model that divides
purchase probability into store visit, category purchase, and brand purchase(e.g., Chiang, 1991; Chintagunta, 1993; Chib, Seetharaman, and Strijnev,
2004; Van Heerde, and Neslin, 2008). We can extend the proposed model toapply these models.
The number of studied consumers is 400. These are randomly chosenfrom consumers who purchase over three times both in the formation period
and in the calibration period.

4.2.3.Variable Definition
For the explanatory variable, this vector includes the intercept, sale
day dummy, weekend and holiday dummy, and the size of the experiential
set. Because in this drugstore, the first and twentieth day of each month aresale days when all products are discounted, we define a sale day dummy
variable. Furthermore, we use the size of the experiential set as one of the
explanatory variables. For explanatory variable, in this research, we use
the same variables as.

4.2.4.Comparison Model
We construct another model in tandem with the proposed model,
namely the comparison model. For this, we use the logit model, which isestimated using the most likelihood method. The purchase probability of
consumer purchasing brand on the -th purchase occasion is defined asfollows:

(

)

(

(7)

)

where
[

]

[

] [

] [

]

We obtain the parameter for each brand and use this for the prediction.

13.

5. Results
5.1. Parameter Convergence and Prediction
First, we assess the convergence of the parameters of the proposedmodel. To discriminate the convergence, we apply the method proposed by
Geweke (1992). We use the first 10% and the last 50% of the sample
sequence to test the differences between both sample sequences. As a result,
we confirm that all parameters are converged.
Using these parameter samples, we forecast the purchase behavior ofeach customer during the validation period. We obtain the purchaseprobability of the-th purchase and use this score for thepresented predictions.
First, the purchase probability of brand by consumer on the -thpurchase occasion is obtained from the following equation when brand is amember of the experiential set, where the experiential set at
is available using purchase records untilandis the probability
function of the standard normal distribution evaluated as
̂

(̂

)

̂

(8)

We have to consider the relationships between the focal brand and the otherbrands. To obtain ̂, we generate a random sample from
(̂

)

(̃

̃ ) and take the mean of samples where ̃and ̃

are the partial matrices ofand , which contain elements of thecorresponding brands in the experiential set.
The external search probability is obtained from the following equation:
̂

(̂

)

̂

(9)

In the case of the purchase probability of brand , when brand is a memberof the experiential set, we can calculate the probability straightforwardly.
However, when brand is not a member of the set, we cannot obtain thepurchase probability in a precise sense because the proposed model only
estimates the external search probability—it cannot estimate which brand14

will be chosen after the external search. However, in the real world, it isdesirable to forecast the purchase behavior of brands outside the experiential
set.
Therefore, in this research we apply and compare the following two
forecasting methods. The first method sets the probability as 0 for the brands
outside the experiential set in order to obey the theory faithfully and what
the model describes. The second method obtains the probability of the brands
outside the experiential set by multiplying the purchase probability
estimated from the prior structure by the external search probability.
Although this method is slightly different from the rigorous theory of themodel, we are able to obtain the purchase tendency of all brands of some sort.
The purchase probability estimated from the prior structure is obtained
from the demographic variable
and its prior parameter . The predictivescore is obtained from the following equation, where ̆
and ̆
̆
:
̂

̂

̆

(9)

We now compare the predictive accuracy of the two methods above withthe comparison model (logit). To measure the predictive accuracy, we use thehit rate, ROC (receiver operating characteristic) curve, and ROC score. The
hit rate indicates the matching rate between the prediction and theobservation. We set the threshold as 0.5. The ROC score has a value between
0 and 1; as this value approaches 1, it implies that it has an improved
predictive accuracy. A model has a good predictive accuracy when the scoreexceeds 0.5. Detailed descriptions are provided in Blattberg, Kim, and Neslin(2008).
Table 3 shows the forecasting result. In the table, the “number ofbuyers” means the number of consumers who purchase the focal brandduring the validation period. In the external search, the value shows thenumber of consumers who purchase the brand outside the experiential set.
The “non-purchase rate” means the rate of consumers who do not purchasethe focal brand during the validation period. This value is used as thebenchmark of the hit rate. As Table 3 shows, the non-purchase rates of thestudied brands are higher than 0.5. Furthermore, if the forecasting methodsuggests that no consumers will purchase, the hit rate will be equivalent to15

the value. Therefore, we have to compare the hit rate of each method with
the non-purchase rate. The method is said to have a predictive ability only if
the hit rate exceeds the non-purchase rate.
In Table 3, “method 1” sets the purchase probability as 0 if the brand is
not a member of the experiential set, whereas “method 2” estimates thepurchase probability of brands that are outside the experiential set fromprior information and the external search probability. The boldface variables
indicate that the method marks the highest performance of the three (in theexternal search, of the two).

Hit rate
number ofbuyersnon-purchaseratecomparison
modelmethod1

ROC score
method2

comparison
modelmethod1

method2

Lux

73

0.854

0.854

0.952

0.952

0.574

0.965

0.977

Pantane

76

0.848

0.848

0.916

0.916

0.563

0.911

0.936

TSUBAKI

49

0.902

0.902

0.972

0.972

0.627

0.973

0.977

merit

56

0.888

0.888

0.944

0.944

0.620

0.941

0.966

Essential

37

0.926

0.926

0.970

0.970

0.601

0.935

0.947

Dove

39

0.922

0.922

0.968

0.968

0.598

0.920

0.922

Super Mild

23

0.954

0.954

0.970

0.970

0.624

0.911

0.949

Soft in One

29

0.942

0.942

0.984

0.984

0.586

0.928

0.952

PB (Private Brand)

30

0.940

0.940

0.974

0.974

0.611

0.925

0.959

Mod's Hair

13

0.974

0.974

0.992

0.992

0.522

external search

39

0.922

0.922

0.999
0.999
0.926

0.922

0.592

Table 3. Predictive accuracyNote) the results of the external search of methods 1 and 2 are the same.

Table 3 shows that the comparison model has a predictive ability to somedegree because the ROC scores of all brands exceed 0.5. However, the hit
rates of all brands are the same as the non-purchase probability, which
implies that the comparison model cannot discriminate between potential
buyers and non-buyers. By contrast, the hit rates of both methods using theresult of the proposed model of all brands exceed the non-purchaseprobability. Furthermore, the ROC scores of all brands exceed 0.5, and they
are higher than the comparison model. In particular, the predictive
performance of method 2 is higher than method 1 for most brands.
We show in Fig. 2 the ROC curves that were used to obtain the ROC
scores for certain brands. We are able to check visually whether the method
has a predictive ability by viewing the ROC curve. If the area under the ROC
16

curve exceeds 0.5, or the ROC curve exceeds the 45-degree line (dotted line),
we can say that the model (method) has a predictive ability. Compared withthe comparison model, the predictive performances of both two methods ofthe proposed model are fairly high. In particular, method 2 outperforms
method 1 for middle- to low-level consumers. This means that method 2 hasa predictive ability for the purchase tendencies of consumers who do notcontain the focal brands in their experiential sets.
In summary, the proposed model has a high predictive ability and thus
the model is applicable for analyzing the sales data.

0.6

Proposal Method1
Proposal Method2
Comparison

0.0

0.0

Proposal Method1
Proposal Method2
Comparison

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

False Positive Proportion

False Positive Proportion

TsubakiExternal Search

0.8

1.0

0.6
0.4
0.2

0.2

0.4

0.6

True Positive Proportion

0.8

0.8

1.0

1.0

0.0

Proposal Method1,2Comparison

0.0

Proposal Method1
Proposal Method2
Comparison

0.0

True Positive Proportion

0.4

True Positive Proportion

0.2

0.6
0.4
0.2

True Positive Proportion

0.8

0.8

1.0

Pantane

1.0

Lux

0.0

0.2

0.4

0.6

0.8

1.0

0.0

False Positive Proportion

0.2

0.4

0.6

False Positive Proportion

Fig. 2: ROC curves
17

0.8

1.0

5.2. Model Parameters
We next infer the general tendency of consumers in order to assess theparameters of each explanatory variable. Table 4 shows the selected
estimation result of parameter . In the table, “*,” “**,” and “***” indicatethat 0 lies outside the 90%, 95%, and 99% highest posterior density intervalsof the estimate. These highest posterior density intervals are calculatedusing the method proposed by Chen, Shao, and Ibrahim (2000).
We found some differences among each brand. First, from [Intercept Gender], we see that Super Mild is favored by female customers, whereas
Soft in One is favored by older male consumers. Furthermore, from [Sale day- Intercept], the purchase probability of Tsubaki increases on sale days. By
comparing these characteristics of each brand, we can formulate a brandcommunication strategy. For example, Super Mild initiates the concept“Super Mild cheers for fathers who take a bath with their children.1” This
concept is for male customers who have younger children.

TsubakiSuper Mild

Soft inOne

Intercept

GenderAgeIntercept

5.02

0.80

-1.06

Sale day

7.54 **-5.05 ***

-0.40

Weekend and Holiday

3.50

-2.58

-0.11

Size of the experiential set

-0.73

0.64

-0.29

Intercept-2.09-3.59 ***

1.43

Sale day

0.67

0.40

-0.20

Weekend and Holiday

3.76

0.27

-0.98

Size of the experiential set-0.95

1.73 ***-0.31

Intercept-13.53 **-3.30 *

4.43 ***

Sale day-2.65-8.35 **

2.70

Weekend and Holiday

-6.04

2.00

1.26

Size of the experiential set

1.15

1.36 *-0.78

Table 4: Estimated

1 SHISEIDO Co., Ltd., http://www.shiseido.co.jp/sm/concept/index.html, retrieved on May 21, 2012.

18

Table 5 reports the posterior mean of . As in Table 4, “*,” “**,” and“***” indicate that 0 lies outside the 90%, 95%, and 99% highest posterior
density intervals of the estimate. We find that some elements are negatively
significant. This means that when one brand is chosen, another brand tends
not to be. In other words, these two brands are in a competitive relationship.
However, the estimatedshows the brand interrelationships of the wholemarket, implying that no individual consumer has complete information
about the market structure. This matrix is estimated for each consumer andfor the assembled competitive relationships of the whole market.

Pantene
TSUBAKI
Merit
Essential
Dove
Super Mild
Soft in One
PB (Private Brand)
Mod's Hair

Pantene
TSUBAKI
Merit
Essential
Dove
Super Mild
Soft in One
PB (Private Brand)
Mod's Hair

Lux
-0.066 *-0.035-0.036-0.007-0.02-0.01-0.032-0.011-0.007

Pantane

TSUBAKI

Merit

Essential-0.023-0.0330.0033-0.02-0.01-0.018-0.007-0.009-0.026-0.0160.0017-0.013-0.073-0.013-0.024-0.008-0.012-0.043-0.033-0.029-0.05-0.04-0.028-0.03
0.02790.006

Dove

Super Mild Soft in One PB-0.0090.064-0.0390.01050.03-0.027-0.001-0.014-0.023

Table 5: Estimated19-0.013

6. Discussion
6.1. Understanding the Parameters
In this research, we estimate the parameters of brands that are
members of the experiential set. This means that the obtained estimates are
the brand preferences of consumers who have experience of using the brandin question. If a brand is purchased by a consumer through an external
search and it thus becomes a member of the experiential set, its preference
value will be lower if the consumer does not purchase the brand thereafter.
Therefore, parameters are directly affected by the use values of consumers
aside from the expected value derived from sales promotions oradvertisements. In this section, we discuss the application of the parametersand , which have above properties.
First, let us consider the case of the preference of brand by consumer
who has not yet purchased brand yet. If the preference value of brandthat is obtained from the hierarchical structure is high, is the consumer
more likely to choose brand over other brands during the external search?
If consumers have complete information and act rationally, they will choose
brand . However, in the real world, there are many alternatives, and it isdifficult to choose the best brand based on a complete evaluation ofalternatives.
Of the two forecasting methods established in section 5.1, method 1
assumes that the purchase probability of brands that are not members of theexperiential set is 0, while method 2 estimates the probability of brands
outside the set from their hierarchical structures (demographic variables)
and the external search probability. As a result, method 2 outperforms
method 1. This means that when consumers conduct an external search, they
are able to choose their preferred brands to some degree. Because of that, if
their external searches work ineffectively, the predictive accuracy of method
2 would be the same as that of method 1. Although this result also implies
that the brand communication of firms is adequate, we are able to say that
consumers’ external searches work effectively to a certain degree.
From these predictions, we can confirm that the external searches ofconsumers work well. Firms also use the model more actively such as forrecommending preferred brands (e.g., Ansari, Essegaier and Kohli, 2000;
20

Ansari and Mela, 2005). Because many previous recommendation models
have estimated consumer preferences from the purchase records of others,
they risk recommending a brand that is purchased but does not satisfy
consumer needs. By contrast, the proposed model estimates the repeatpurchase intentions of customers for a particular brand and thus reduces theabove risk. The proposed model is therefore theoretically better because
firms can offer brands that will satisfy customers’ needs.

6.2. Size of the Experiential Set
In this research, we use the first 9 months of the overall study period as
the formation period and analyze the purchase behavior and dynamic changeof the experiential set over the following 15 months.
At the end of the observation period, the average size of the experiential
set is 2.25 and the maximum is 8. Although this research focuses on
analyzing the top 10 brands, no one customer purchased all 10 brands. A
total of 108 consumers (27%) purchased only one brand; therefore, the size ofthe experiential set of these consumers is 1. Furthermore, 120 consumers(30%) had two brands in their experiential sets and 76 consumers (19%) had
three brands. In summary, 76% of consumers purchase fewer than or equal
to three brands. We also find that many consumers tend to purchase thesame brand. Hauser and Wernerfelt (1990) report that the size of theconsideration set of the shampoo category is 6.1. Compared with this value,
the size of the experiential set obtained in this research is relatively small.
Thus, it is possible that some brands were considered but never purchased in
the consideration set.
According to the finding that many consumers purchase only a limited
selection of brands, it is difficult to obtain the market competitive structure(variance-covariance matrix)
straightforwardly. However, this researchallows us to obtain the whole structure from the partial choice behavior ofeach consumer using the MCMC method.
Additionally, we have to take account of the upper limit of theexperiential set. The proposed model does not assume that certain brands“drop out” of the long-term memory. This assumption is based on the
proposition of Bettman (1979), who defines long-term memory as“permanent” and an “essentially unlimited store” (p. 151, Proposition 6.4).
21

This means that we do not have to consider the size limit of the set.
Furthermore, most previous papers that have discussed the consideration
set have not assumed that products drop out of this set. For example, Chiang,
Chib, and Nrashimhan (1999) analyze the tomato ketchup market byassuming that the consideration set remains unchanged over 18 months. If
the period of analysis is short, the lack of a so-called “dropout mechanism”
would not cause a serious problem. However, for longer-term analysis weneed to restrict the upper limit of the set or introduce a dropout mechanism.

7. Conclusion
In this research, we use scanner panel data to construct a stochastic
brand choice model of consumer goods in which consumers repeatedly choosea brand from many alternatives. We then reexamine consumers’ repeatpurchase behavior from the perspective of information processing theory.
This research makes three main contributions. First, we construct atheoretical framework to analyze behavioral data such as point-of-sales
records with customer ID numbers. We also reexamine the concepts ofinternal search, external search, and learning proposed in the field ofconsumer studies. Furthermore, we reconstruct consumers’ repeat purchasebehavior 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 thatcan be observed from purchase records, instead of from choice subsets suchas the “consideration set” or “processing set,” we proposed a more practicablemodel. The proposed model is insusceptible to increases in the number ofalternatives and is applicable even for markets comprising dozens ofalternatives.
The second contribution is that we construct a high performing
forecasting model. From the results derived using the validation set, we findthat the proposed model has a high predictive ability. Because the model isdesigned so that the purchase probability of brands that are members of theexperiential set is higher, this result implies that many consumers tend tochoose brands that they have always purchased. This finding is in line withprevious research. The model also predicts external searches with a high22degree of accuracy. This implies that it is able to discriminate between
consumers who tend to conduct external searches (i.e., “variety seekers”) andthose that do not. This model also shows the attitude of each consumer for
the focal product category.
The third contribution is that the proposed model has the potential to
be flexible in terms of application and extension. Because most proposedmodel structures are based on previous brand choice models and are
estimated using the MCMC method, we can easily incorporate the specificmodel structure developed in previous research. We would thus be able toextend the model into, for example, a cross-category or dynamic (time-series)
model.
For future research, we highlight the following two issues. First, futurestudies should examine the proposed model using other product categories.
Although we have found a high level of predictive accuracy by focusing on the
shampoo category, we must confirm that the proposed model has such a
predictive ability in other categories. This research shows the validity of theconcept of the experiential set as a result of predictions; however, we need toreport the existence of the experiential set in other products. The second
issue is the reconsideration of the model’s assumptions. As discussed in
section 6, it is desirable to incorporate a dropout mechanism. When the
period of analysis is extended, such a dropout mechanism will become more
important. Future research should thus reexamine other parts of the modelas the need arises.

23

A. Detailed Description of the ModelIn this section, we will show the detailed description and estimation
procedure of the model. At first, recall the purchase probability of consumer’s -th purchase occasion of brand which is a member of the experiential
set. The proposed model is defined as follows:

{

(A.1)

To consider the interaction of each brand, let ̃

be avector consisting of the elements in} that correspond to thebrands contained in{̃In addition, left

consisting of the elements in{-dimensionalbe amatrix} that correspond to. ̃ is apartial matrix reconstructed from the variance-covariancematrix . With these expressions, the following multivariate regression
model can be formed:
̃

̃

̃

̃

(

̃)

The external search behavior of consumer
occasion is explained by following regression model:

{

(A.2)
on the-th purchase(A.3)

where we assume, in this study, that.

A hierarchical structure to explain(where):andis defined as follows

(A.4)

24

A.1.Prior distributions
At first, we assume the prior distribution ofAnsari, and Gupta (1999):

{

(

)

based on Manchanda,

(

)}

(A.5)

where
is a vector operator, which arranges the upper triangle
elements ofin a vector. Therefore,is a-dimensional
vector. We assume the hyper-parametersandare, respectively, a
and
Since

is a

identity matrix.
matrix, we assume the prior distribution is amatrix normal distribution thatzero matrix and
.

where

is a

We also assume thatis a diagonal matrix and each element is a
Gamma distribution. For stability of the estimate, let,
wherefor each element .
We decompose the equation ofassuming thatis a diagonal
matrix.

( )

(

)

( (

(A.6)

))

A.2. Posterior distributions
The full conditional posterior distribution of the model is defined using
following functions. In this research, we introduce the latent variables basedon Albert and Chib (1990) to solve the discrete choice model. At first, thebrand choice term is defined as follows:|{∏ [∏ (|The external search term is defined as follows:

25

]

̃ |̃

̃

}

(A.7)

|

|

∏

(A.8)

|

Using
and
, the full conditional posterior distribution isdefined as follows (to simplify the expression, let
be the set of parameters,
the set of data, and
.

|

|

[∏

|

|

(A.9)

]

We obtain the conditional posterior distributions from the above equation.

A. 2. 1. The conditional posterior of:

The sample of the latent variable

is drawn from a truncated normal

distribution. There are some methods to obtain the random sample from atruncated normal distribution. Following Geweke (1991), we use different
methods in this research, such as normal rejection sampling and theexponential rejection sampling (Devroye, 1986), depending on the threshold.
Let
be a truncated normal distribution with mean
andstandard deviation

restricted to

|

where
̃.

{

.

(A.10)],

̃

A. 2. 2. The conditional posterior of

̃

,

:

is also drawn from the truncated normal distribution. If
similarto,|.
However,
if
|

]

.

26

,

,
,

A. 2. 3. The conditional posterior of:Since we cannot obtain amatrix parameter, we obtain a-dimensional vector
for alternatives. From the marginal distributionof multivariate normal, an element of multivariate regression is expressed asfollows:(A.11)

̃

̃
where
(̃
),
, and
̃ . In the same manner, we can decompose the prior distribution. In thispaper, we denote the decomposition of

into

(

( (

)

(

)

as follows:(A.12)))

We obtain following equation by marginalizing vector:(A.13)

where(in this paper, since we defined) andas a diagonal,, and. However,.

From equations (A.11) and (A.13), we obtain following posterior
distribution:
|
where
(∑

(A.14)

(∑
(

(
)

))

)) . Additionally,(

indicator function defined as

,

and
is an

.

A. 2. 4. The conditional posterior of:

As mentioned above, amatrix parameter
expresses thecompetitive structure of the whole market. We must obtain the whole matrix
27although in the individual model we use the partial matrix ̃ which
consists of the elements ofthat correspond to the brands contained in.
However, all diagonal elements ofmust be 1, and the matrix needs to bepositive definite (Chib and Greenberg, 1998; Manchanda, Ansari, and Gupta,
1999). Since if
is a positive definite matrix, we can assure that the partial
matrix ̃ is also positive definite, we only need to construct an appropriate
matrix .
We must obtain the posterior distribution of
from the likelihood ofand the prior distribution of . We can express the posterior as a productof these densities:{∏ ∏ ( ̃ |̃

|

̃ )}

(A.15)

However, there is no well-known distribution to satisfy the restriction of .
Authors such as Edwards and Allenby (2003), Chib and Greenberg (1998),
and Manchanda, Ansari, and Gupta (1999) have proposed some methods toconstruct the matrix. In this research, we obtain the candidate sample andthe candidate distribution based on Manchanda, Ansari, and Gupta (1999).
Let the candidate distribution be
and the candidate sample
the acceptance rate is obtained from the following equation:{||

A. 2. 5. The conditional posterior of(A.16)}:(A.17)

|

where
and

(
(

)

,

Then,

(

).
28

),

(

) ,

A. 2. 6. The conditional posterior of:(A.18)

|
where

, and
.
is a sample
matrix normal distribution. Refer to Rowe (2002) and Dawid(1981) for further details of the matrix distribution.

A. 2. 7. The conditional posterior of:(A.19)|
where,is -th column vector of

∑
, and

vectors, the number of elements is

is

(
)
(
),
-th column vector of. In both.

A. 3. Initial values and sample collections
For initial values, we let all latent variables

andbe 0, andparameters , , andbe zero vectors (matrices). In addition, we letbe
an identity matrix and all
be 1.
We ran the chain for 15,000 iterations. The result was reported on asample of 10,000 draws from the posterior distribution, after we discarded
5,000 burn-in draws.

29

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