Annals of Business Administrative Science 7 (2008) 19–32
Available at www.gbrc.jp

Online ISSN 1347-4456 Print ISSN 1347-4464©2008 Global Business Research Center

Estimating Individual Preferences in theMusic CD Market

Sotaro KATSUMATA
Graduate School of Economics, the University of Tokyo
E-mail: ee077021@mail.ecc.u-tokyo.ac.jp

Abstract: This research proposes a model to analyze individual customer preferences usingpurchase records such as Point-of-Sales (POS) data. To some extent, we can identify theinterests of customers from their demographics. Consumers are, however, essentiallyheterogeneous. It is difficult to determine individual customer behavior in detail throughaggregate-level estimation. In this paper, we use a Markov chain Monte Carlo (MCMC)
method to construct a hierarchical model for tackling this problem. The model encompasses
both “commonality” and “heterogeneity.” We apply this MCMC method to the music CD
market, where customers have some commonalities although they are heterogeneous. Thisempirical analysis shows that a hierarchical Bayes (HB) model has a high predictive
performance as compared to the naïve forecasting and aggregate-level models.
Keywords: customer relationship management, customer heterogeneity, hierarchical Bayes
model

1. Introduction

data along with customer profiles, and firms can now
record the individual time-series purchase data of

In classical economics, the individual heterogeneity

their customers. At the same time, this has led to aof preferences is treated as an “error term” or aneed for new methods to analyze the vast amounts of“disturbance.” In marketing, on the other hand, it is

POS data. Although firms collect massive amounts

assumed that consumers are heterogeneous. Theof data, ironically, a problem they often face is thatrecent developments in information technology havethe individual figures of purchases are not sufficientfacilitated the collection of Point-of-Sales (POS)

for analysis. For example, an ordinary household

19Katsumata

does not purchase detergents numerous times in a

These records are collected over a period of twoyear. When we construct a model using classicalyears.

regression, we need to aggregate the data because of

demographics such as age and gender.

Additionally,

weobtaincustomerthe scarcity of the number of individual samples.
However, when using this method, the customer

2.2. Modeling procedure

identification information of the data gets ignored.

We need to consider the following three factors

In cases where it is not possible to estimate thewhen analyzing the music CD retail selling database.

individual parameters of the model, a BayesianFirst, we must consider the complexity of customer

estimation through the use of a Markov chain Montepreferences as customers never purchase music CDs

Carlo (MCMC) method can be utilized to obtainthat do not interest them. Although we can estimateparameters. In an MCMC method, we suppose that

their preferences on the basis of age and gender toallprobability

some extent, there is significant variability even

distributions and derive estimates from the random

within the same demographic group. Hence, it isnumbers generated from these distributions. Using adifficult to construct a practicable model without

MCMC method, we can easily expand models andconsidering customer heterogeneity. Second, weconstruct complex models that are difficult toneed to consider the number of purchases by aestimate through the most likelihood method. Therecustomer; the number of customers who purchaseare many existing application researches in the fieldmusic CDs over twenty times in a year is remarkably

of marketing (e.g., Abe, in press; Rossi and Allenby,

low. Therefore, it is difficult to accurately estimate

2003).

choice behavior using custom-made (individual)

parametersare

distributed

In this paper, we analyze a vast amount of data

models. Third, the number of products needs to beusing an MCMC method and investigate the process

considered. There are several hundreds to thousands

for the application of hierarchical Bayes (HB)of artists in the music CD market. Hence, it ismodels for database analysis.

difficult to apply ordinary discrete choice models(e.g., logit and probit models).
In this paper, we consider the three issues

2. Data and modeling procedure

mentioned above. At first, we adopt a hierarchical2.1. Data overview

model using an MCMC method to tackle the first

We use POS data with customer identificationand second problems. The hierarchical structure

information in a music CD retail store provided bysuccessfully solves the abovementioned problems as

the 2005 Data Analysis Competition hosted by Jointit

Association Study Group of Management Science.

demographic variables for an individual model. It is
20

can

add

the

aggregate-level

tendencyofEstimating individual preferences in the music CD market

especially effective for analyzing markets like thegood accuracy of artist score estimation. Therefore,

music CD market, which has few samples and

we use the sales of the top 500 artists for estimation.

individual

variations.

However,inpreviousIn the first year, 161,805 customers purchased

researches involving hierarchical modeling, models

the music CDs of these top 500 artists. However,using discrete choice methods have been used. Thesemost of the customers make purchases only once ormodels cannot be applied to this case without

twice (74,276 customers buy once and 32,410

modification. Therefore, we adopt a dimension

customers buy twice). In this paper, we only

reduction method that is used for perceptual

consider the 55,119 customers who purchased CDs

mapping (e.g., Churchill, 1999) and a joint spaceover three times in our analysis. In addition, later inmap (e.g., DeSarbo and Wu, 2001; DeSarbo,

this paper, we will discuss the follow-up estimation

Ramaswamy, Wedel, and Bijmolt, 1996). Using thisfor the excluded samples.

method, we assign each artist multidimensional
continuous values of attribution in order to deal with

3.2. Data division

the third problem.

We divide the above-mentioned 55,119 customers
into two datasets, namely, A and B. We derive artist
attributes using dataset A and construct models to

3. Model construction

estimate individual preferences using dataset B. This

Purchase records are collected over a period of two

procedure aims to avoid a loop of analysis caused by

years. We use the first half of the data collected (thethe derivation of artist attributes for dependent andfirst year) as a learning period to estimate theexplanatory variables from the same data source. We

parameters of models, and the latter half of the data

separate datasets A and B completely and treat artist(the second year) as a calibration period to validate

attributes as an exogenous variable.

the predictive performance of the model. In otherwords, we predict the purchases of the coming year

3.3. Derivation of artist attributes

using the history of the preceding one.

In this section, we describe the process of thederivation of artist attributes. From dataset A,

3.1. Objective customers and artists

attributes characterizing artists are extracted and

The total number of purchases recorded in the firsteach artist is rated according to these attributes.

year is 605,593 and the number of artists whose

At first, we prepare a matrix of the size 27,559

music is purchased in this period is 8,545. However,× 500. The number of artist k’s CDs purchased by

the top 500 artists account for 81% of the total sales.

customer j is contained in the (j, k) element of the

If the sales figures are too low, we cannot assure

matrix. The rows of this matrix signify customers’21

Katsumata

co-purchases. By assuming that the artists whoseWeassume

that

there

is

individual

music CDs are purchased by a particular customer

heterogeneity of variance. It is appropriate to makehave similar attributes, we can obtain artist attributes

this assumption since some people may depict

reflecting customer preferences from this co-variety-seeking behavior, while others may show

purchase matrix.

loyalty to a particular artist(s).

Artist attributes are obtained from this co-

In addition, since individual purchase samples

purchase matrix by reducing dimensions. Although

are scarce, we supplement our information using the

reducing data gives rise to some errors, it is difficult

demographic variables rn and their parameters Q. We

to use a co-purchase matrix to obtain attributes

can describe this relation as follows:

without modification. We use factor analysis (using

yn = Qrn + un ,the most likelihood and varimax rotation methods(refer Harman, 1976)) and obtain 11 factors whose

un ~ N (0, Γ)(2).

rn contains (1) number of purchases in learning

eigenvalues exceed 2.

period (Tn), (2) age, and (3) gender (male = 0, female

In general, dimension reducing methods such

= 1). We exclude individuals whose genderas factor analysis are used for mapping in order toinformation is missing. The percentage of exclusioncompare the relative position of each brand or

is less than 0.1%.

product. Although we do not use mapping in this

⎛ 1
⎞
⎜
⎟
⎜ log(Tn ) ⎟rn = ⎜
Age n ⎟⎜⎟⎜ Gender ⎟n ⎠⎝paper, we adopt a similar technique—namely, factor
analysis—to treat reduced variables as brand andproduct value attributes.

(3)

We denote the factor loadings of artist k as fk.
Figure 1 shows attributes of representative artists.

We can obtain a model by assembling the above
two equations as follows:

3.4. Construction of the hierarchical Bayes⎧ xnt = yn + ε nt , ε nt ~ N (0, Σ n )⎨⎩ yn = Qrn + un , un ~ N (0, Γ)(HB) Model
When an individual n chooses an artist k’s CD as(4)

his/her t-th purchase, let xnt = fk, where xnt is a j-

Customer preference y is a vector variable that

dimensional continuous variable. Assuming that xnt

supplements individual purchase behavior withis a revealed variable of his/her latent preference yn

aggregate attitude from demographic variables.

with error term εnt, we get,xnt = yn + ε nt , ε nt ~ N (0, Σ n )We estimate the parameters of this hierarchicalmodel using an MCMC method. For more
(1).
information on prior distributions, posterior distributions,22

Estimating individual preferences in the music CD market

Figure 1. Attributes of representative artists

Sound Track (Foreign Movies)
0.5

Morning Musume
0.9

Mr. Children
0.15

0.8
0.4

0.1

0.7
0.6

0.3

0.05

0.5
0.2

0.4

0
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

0.3
0.1

-0.05

0.2
0.1

0
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14
-0.1

-0.1

0
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14-0.1

Sound Track (Japanese Movies)
0.35

Aya Matsuura

Ayumi Hamasaki
0.35

0.7

0.3

-0.15

0.3

0.6

0.25

0.25
0.5

0.2

0.2
0.4

0.15
0.1

0.15
0.1

0.3

0.05

0.05

0.2

0
-0.05

0
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

0.1
-0.05
0

-0.1

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

-0.15

-0.1

-0.15

Pornograffitti
0.2

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14-0.1

Animation

Orange Range
0.25

0.25
0.2

0.2

0.15
0.15

0.15
0.1

0.1
0.1

0.05
0.05
0

0.05
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

0

-0.05
0

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

-0.1
-0.05

-0.05

-0.15
-0.1

-0.2

Ken Hirai-0.1

Mika Nakashima

ASIAN KUNG-FU GENERATION

0.4

0.25

0.35
0.35

0.2

0.3
0.3

0.15

0.25

0.25
0.1

0.2

0.2

0.15

0.15

0.05

0.1

0.1

0
f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

0.05

0.05

-0.05

0

0
-0.1
-0.15

-0.05

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

-0.1

-0.05
-0.1

23

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10f11f12f13f14

Katsumata

Figure 2. Modeling procedure

Obtain attributes
from separated
datasetCalculate artist
attributes f

Dataset A
3 or morepurchases

Estimation using
HB modelDatabase
top 500
artists

Dataset B
3 or morepurchases

Parameter

Q, G

5,000 customers

Follow-up
estimation

Less than
3 purchases

and hyper parameters, please refer to the appendix.

In the simulation, we burn-in these proceduresfor 1,000 iterations, and then save 10,000 samples.

3.5. Sampling

Figure 2 shows the modeling procedures at this

We choose 5,000 customers from dataset B,

point.

consisting of 27,559 customers (N = 5,000), in ordertoestimate

parameters.

However,we

3.6. Comparison models

cansubsequently estimate excluded customers by using

We also estimate the following two models

these parameters. The sampling procedure is as

collaterally

follows:

performances with the HB model.

tocomparetheir

forecasting

1. Q | Γ, ynNaïve forecasting model: The artist whom the

2. Γ| Q, yn

customer purchased most frequently during the first

3.1. yn | Q, Γ, Σnyear will be purchased again by him/her in the

3.2. Σn | yn

second year.
However, this forecasting model cannot rank

1–2 are samplings of upper layers. 3.1–3.2 aresamplings

for

each

individual.

The

detailed

people who purchase artist k’s CDs the same number

explanations of posterior distributions can be foundof times or those who do not purchase them at all.

in the appendix.

Aggregate
24

model:

An

aggregatemodel

Estimating individual preferences in the music CD market

estimates y directly from the second layer of the HB

closeness to an artist’s attributes, the higher is themodel using ordinary least squares (OLS). This

likelihood of purchasing the artist’s CD. Next, we

model cannot estimate parameters for individuals or

obtain the squared differences between the attributes

classify customers on the basis of their demographicofvariables (number of purchases, age, and gender).

individual preferences. We can derive ênk —squared

Since the same parameters Q and Γ are common

differences between customer n and artist k—fromacrossthe following equation.

customers,

customers

with

the

same

demographic profile have the same preferences.

y j = Qr j + u j ,ASIAN

KUNG-FU

GENERATIONeˆnk = ( f k − yn )′( f k − yn )

and

(7)

N

j = 1, L , ∑ Tn

(5)

In the aggregate model, substitute the OLS

n =1

estimator of the equation and calculate the squared
differences.

4. Results

Figure 3 is the cumulative gain chart (Berry and
Linoff, 1997, 2000) that arranges customers in the

4.1. Predictive performanceascending order of their squared differences on the

4.1.1. Predicting individual preferences

horizontal axis and the cumulative sales rate on the
In

this

section,wecomparethepredictive
vertical axis. In naïve forecasting, customers who

performances of the HB and comparison models.
purchase CDs the same number of times are
Initially, we determine the customers who have aarranged in a random order.
high likelihood of purchasing the music CDs of theSince all models exceed a center line, theserock band “ASIAN KUNG-FU GENERATION” inthree models possess predictive power to a certain
the validation period (the latter year of data
degree. The naïve forecasting model shows goodcollection).
performance on the left side. This means that the
We use the mean of the samples of yn as thecustomers who purchase the music CDs of “ASIAN
predictive values of the HB model.
KUNG-FU GENERATION” in the first year alsoyn =1 M (m)∑ y n , (6)M m =1purchase its CDs in the next year. However, thenaïve forecasting model cannot predict customers
who do not purchase the band’s CDs in the first year.

where M is number of samples (in this paper, M =Unfortunately, this category of people forms the majority.
10,000). Value m in the bracket on the top-right ofyn(m) denotes the value obtained at m-th sampling.

yn is a vector variable that is of the same sizeas the artist attributes. The greater the approximate
25

Katsumata

Figure 3. Cumulative gain chart of

ASIAN KUNG-FU GENERATION

4.1.2. Predictive performances compared by

Table 1 shows the summations that indicate thegain area

ranks of the predictive performances for all the
We obtain the predictive performance of anotherartists. The HB model shows the best performance ofartist and calculate the area between the cumulative
230 artists, while the naïve forecasting model shows
gain chart and center line. Let this area be S. Thisthe best performance for 159 artists. The HB model
indicator may take a negative value if the prediction
shows “N/A” for 83 artists and this figure is theis worse than random guessing.
lowest among the three models. On the whole, it can
We obtain S for all artists. Since this indicator
be concluded that the HB model shows the bestshows the relative predictive performance of a model,
performance, followed by the naïve forecasting
we compare these models by rank. We compare the S
model. Since the aggregate model discriminatesof the three models and rank these models for eachindividual heterogeneity only on the basis ofartist. When S takes a negative value, we classify the
demographic variables, it cannot describe theartist as “N/A (not applicable)” Furthermore, we
diversity of the music CD market.
exclude artists whose CDs are not purchased in thevalidation period.

26

Estimating individual preferences in the music CD market

Table 1. Rank of predictive performance

Figure 4. Area S

1

se
sa
h
cr
u
p
fo
%

1st
2nd
3rd
N/A

S

HB
230
125
17
83

Naïve
159
101
82
113

Aggregate
29
129
127
170

Table 2. Comparison of HB Model and naïve

forecasting0% of population

1st
2nd
N/A

1

Table 2 shows the comparison of the HB model

HB
252
120
83

Naïve
163
179
113

Table 3. Comparison of HB Model and naïve

and the naïve forecasting model. This table also

forecasting (prospects)

indicates that the performance of the HB model isbetter than that of the naïve forecasting model.

1st
2nd
N/A

Table 3 shows the comparison of the predictive

HB
174
21
260

Naïve
41
45
269

performances for artists that were not purchased
during the first year (learning period). With the naïve
forecasting model, the rule becomes equivalent to

the impact of the d-th explanatory variable on the j-random guess. Note that the performance of theth factor.

naïve

forecasting

model

deteriorates

Table 4 shows the sample mean of parameter Q.

severely,

It allows us to observe which variables affect which

whereas that of the HB model stays the same.

particular factors. In this table, “**” denotes

As described above, the HB model can maintainsignificance at 99% level. We calculate thesea better quality of forecasting among prospects.

indicators from the MCMC samples. Significance at
4.2. Application

the 99% level implies that 0.99% of the highest

4.2.1. Application of second layer

posterior density interval (HPD/HPDI) does not

Parameter Q of the second layer of the HB model iscross 0. “*” indicates 95% and “・,” 90%. We cana matrix whose size is the dimension of factors

view the aggregate level tendency of customer(dependent variables) × the number of demographic

preference. Further, using this information, we canvariables. The (j, d) element of the parameter shows

perform any actions for prospects.
Q and Γ can also be applied to customers
27Katsumata

excluded from the estimation and to new customers

customer preferences to identify target customers.

who purchase a CD for the first time. For example, if

For example, we can define target customers who

we obtain the sample mean Q , Γ of Q and Γ

haveestimated by N customers and use this sample mean

Nakashima” in the following manner.

like“Ayumi

Hamasaki”

and

“Mika

as a hyper parameter for the first layer, then we can
Let the new artist’s attributes, f{New Artist}, beestimate a single-layer Bayes model for customer iand obtain i’s preferences. The sampling procedureis the same as that of the HB model. The difference1( f{Mika Nakashima}+ f{Ayumi Hamasaki}) (8).
2in the case of the aggregate model is that while theThus, we can obtain a customer set whoseparameters of the aggregate model are the same

preferences approximate the new artist’s attributes

among individuals, a single-layer Bayes modeland promote the new artist to these customers.

estimates parameters individually.

However, it should be noted that this procedure mayf{New Artist} =1. yn | Q , Γ ,Σnbe futile when averaging too many artists.

2. Σn | yn
4.2.3.

Applications

forrecommendation

4.2.2. Promotion of new artists and targetingsystems

customers

In the music CD market, the top 500 artists accountIn cases of target segments that are already defined,

for 80% of the total sales. However, it is unlikely

we can use the information on artist attributes andthat ordinary customers know all these 500 artists. It
is possible that there are some unknown artists that

Table 4. Parameters Q

approximate their preference. Recommendations areespecially effective in stimulating these latent needs.

NumberInterceptofPurchases
f1
10.3
f2 −291.6**
f3
61.3
−12.4
f4
f5
75.4・
−47.1
f6
f7
55.0
f8
164.0**
f9
42.5
f10
53.7
f11
2.7

8.6・
−3.9
3.1
2.6
6.0
−3.4
1.0
−1.2
−1.7
2.3
1.6

Age

When firms estimate the preferences of their

Gendercustomers, they can rank artists for each customer−3.3
118.5**
5.7
12.8
−17.9
26.4・
−7.8
−43.4
−9.0
−18.9
−1.1

−11.6
9.6
9.6
7.4
−12.4
−6.1
−1.6
−7.0
−4.4
7.1
−1.2

and

developpreference

information

into

recommendation systems. This system is not of the
type

that

recommendsaproduct

whosecharacteristics correspond to those of another—for
example, recommending B to customers whopurchased product A. Instead, this model also
considers customers’ purchase records in the past

Note: For simplify to show, multiple 103

year and compliments this information using
28

Estimating individual preferences in the music CD market

demographic variables such as age and gender.

and estimation methods of factor analysis, and otherAnsari, Essegaier, and Kohli (2000) applied a model

dimension

using

component analysis, fuzzy clustering, and MDS for

an

MCMC

methodforInternetrecommendation systems.

reducing

methods

likeprincipal

elaboration. Moreover, we have to determine amethod of modeling using non-condensed data.
In addition, we need to expand the model to

5. Conclusion

contain a time series variation of artist attributes and

It is difficult to develop a model that considers bothcustomer preferences. Although the proposal model

the aggregate tendency of demographics and theassumes that these variables are stable over a span ofheterogeneity of customers using the classicaltwo years, it is possible for them to change over time.

framework of econometric methods. Furthermore,Hence, it is desirable to exclude the assumption ofwhile POS data records a vast amount of data, manystability when analyzing more long term data.

researchers face the problem of scarcity of data when
they try to analyze the data on an individual basis.

Acknowledgement

The HB model is a breakthrough model as it deals
with both the “heterogeneity” and “commonality” of

The author would like to thank Professor Makoto

customers.

Abe for advice and feedback, Joint Association
Study Group of Management Science for providing

The useful feature of the model is that it has

the data.

predictive power for purchases by prospective
customers (customers who do not purchase in thefirst one year) that cannot be predicted by the naïve

This paper was first published as Katsumata, S.

forecasting model. There is no effective technique(2007) "Ongaku CD koubai ni okeru kojin shiko nofor taking into account a large number of prospects

suitei," Communications of the Operations Research

only through the naïve forecasting model. However,Society of Japan, Vol. 52, pp. 725–731. (Inthe HB model can estimate the latent needs of both

Japanese).

prospective and new customers.
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we

use

condensed

attributes

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⎜ ⎟R=⎜ M ⎟
⎜ r′ ⎟⎝ N⎠

Estimating individual preferences in the music CD market

Σn-1 | yn ~ W (sn1, Sn1)

Likelihood function and prior distributions
xnt ~ NJ (yn, Σn)sn1 = s0 + Tn

Q ~ NJ × D (Q0, Γ, Λ0)

S n1 = S 0 + ∑ ( xnt − yn )( xnt − yn )′Tn

Γ-1 ~ W (g0, G0)

t =1

yn ~ NJ (Q rn, Γ)
A.2. Generation of random numbers

Σn-1 ~ W (J, 100IJ)

We can generate random numbers from matrix
Q0 = OJ × D

normal distribution (matrix distribution) and Wishart

Λ0 = ID

distribution by following these procedures, for which

g0 = J

Gamerman (1997), Rossi and Allenby (2003) and

G0 = 100 IJ

Rowe (2002) provide detailed explanations.

s0 = J
Matrix normal distribution: NM × N (M, A, B)

S0 = 100 IJ(1) Generate the M × N matrix Z, where zij ~ N(0, 1).

Starting values
Q(0) = OJ × D(2) Calculate lower triangle matrices LA and LB

Γ(0) = IJ

that satisfy L'A LA = A, L'B LB = B, then X = L'A

yn(0) = 0, n = 1,…, N

ZLB + M ~ NM × N (M, A, B).

Σn(0) = IJ, n = 1,…, N
Wishart distribution: W (ν, V)(1) Generate a lower triangle matrix T, where

Posterior distributions
Q | Γ, Y ~ NJ × D (Q1, Λ1)()
Q = (Y ′Σ R + Λ Q )Λ−1

Λ1 = R′Σ −n1 R + Λ 0−1
n1

its diagonal elements Tii ~ Χ2 (ν) and non-

−1
0

0

diagonal elements, Tij ~ N (0, 1) (where, i > j ).
(2) TT' ~ W (ν, I).

1-1

Γ | Q, Y ~ W (g1, G1)(3) Decompose V and obtain U, where V = U'U.

g1 = g 0 + N(4) We get X = U'TT'U ~ W (ν, V).

N

G1 = G0 + ∑ ( yi − Qri )( yi − Qri )′i =1[Received September 30, 2008; accepted October 7, 2008]yn | Q, Γ, Σn ~ NJ (yn1, Σn1)(

Σ n1 = Γ −1 + Tn Σ −n1

)

−1

Tn
⎛
⎞
yn1 = Γn1 ⎜⎜ Γ −1Qrn + ∑ Σ −n1 xnt ⎟⎟
t =1
⎝
⎠

31

Katsumata

32

ABAS: Annals of Business Administrative ScienceVol. 7 December 2008

CHIEF EDITOR

Junjiro Shintaku, the University of TokyoEDITORIAL BOARD

Makoto Abe, the University of Tokyo
Takahiro Fujimoto, the University of Tokyo
Makoto Kasuya, the University of Tokyo
Nobuo Takahashi, the University of Tokyo
Technical Editor: Maki Nishida, Global Business Research Center

ABAS: Annals of Business Administrative Science is published annually by Global
Business Research Center, Marunouchi, Chiyoda-ku, Tokyo, JAPAN. http://www.gbrc.jp