Applications of Data Sciencein Social Sciencein honor of Prof. Nobuhiko Teruisupported by JSPS KAKENHI

Program and Abstracts
Feb. 17-18th, 2022
Graduate School of Economics and Management
Tohoku University
financially supported by
Grant-in-Aid for Scientific Research(A) 20H00576, (B) 21H03400

Feb 17, 2022
9:30-11:00 ࠙Session 1ࠚChair: Masataka Ban (University of Tsukuba)
࣭Sotaro Katsumata (Osaka University)
Online Review Text Analysis Incorporating Valence and Vote: Extending the Topic Modelto Include Performance Measures࣭Mirai Igarashi (University of Tsukuba)
Finding Influential Users by Topic in Unstructured User-generated Content
࣭Hiroshi Onishi (Tokyo University of Science)
Does Deregulation of Health Claims on Functional Food Package Design Change
Consumers' Purchase Behaviors?
11:10-12:10 ࠙Session 2ࠚChair: Shohei Hasegawa (Hosei University)࣭Junji Nakano (Chuo University)
Statistical model for article citation network in Web of Science
࣭Manabu Asai (Soka University)
High-Dimensional VAR Models via Sparse Precision Matrix
Lunch 12:10-13:10
13:10-14:10 ࠙Session 3ࠚChair: Wirawan Dony Dahana㸦Osaka University㸧
࣭Naoto Kunitomo (The Institute of Statistical Mathematics)
Local SIML Estimation of Some Brownian and Jump Functionals under Market
Microstructure Noise࣭Nobuaki Hoshino (Kanazawa University)ࣅࢵࢢ࣑ࢡࣟࢹ࣮ࢱࡢࣉࣛ࢖ࣂࢩ࣮ಖㆤ
14:20-15:20࠙Session 4ࠚChair: Tsukasa Ishigaki (Tohoku University)
࣭Takemi Yanagimoto (The Institute of Statistical Mathematics)↓᝟ሗ஦๓ศᕸࡢ⌮ゎ㸸බᖹ࡞ศ㓄࡜ᮍ▱ẕᩘ࠿ࡽ
࣭Hiroshi Itosu (Tokyo University of Science)ࣃ࣓࣮ࣛࢱ㆑ูྍ⬟࡞ࢢࣛࣇ࢕࢝ࣝࣔࢹࣝ࡟ࡼࡿḞࢆྵࢇࡔ 22 ศ๭⾲ࡢᑐ⛠ᛶࡢ᳨ᐃ

15:30-16:30 ࠙Session 5ࠚChair: Yasumasa Matsuda (Tohoku University)
࣭Makoto Abe (The University of Tokyo)
Deriving Lifetime Value of a Customer Who Exhibits Non-Poisson Purchase Behavior:

Application to Marketing Intervention for Customer Retention
Thomas Otter (Goethe University)
࣭T
Discrete Choice in Marketing through the Lens of Rational Inattention
16:40-17:40 ࠙Session 6ࠚChair: Wirawan Dony Dahana㸦Osaka University㸧࣭Nobuhiko Terui (Tohoku University)
Service Economy and Data ScienceFeb 18, 2022
9:30-11:00࠙Session 7ࠚChair: Shohei Hasegawa (Hosei University)
࣭Greg Allenby (Ohio State University)
A Choice Model of Utility Maximization and Regret Minimization
࣭Jaehwan Kim (Korea University)
The Impact of Gig Economy on the Product Quality through the Labor Market: Evidence
from Ride-sharing and Restaurant Quality
࣭Takuya Satomura (Keio University)
A Multiple Duration Choice Model for Service Data
11:10-12:10 ࠙Session 8ࠚChair: Masataka Ban (University of Tsukuba)
࣭Yoshimasa Uematsu (Tohoku University)
Robust False Discovery Rate Control via Debiased Rank Lasso
࣭Junichi Hirukawa (Niigata University)
Innovation algorithm of fractionally integrated ($I(d)$) process and applications on theestimation of parameters
Lunch 12:10-13:10
13:10-14:10 ࠙Session 9ࠚChair: Tsukasa Ishigaki (Tohoku University)
࣭Qingfeng Liu (Otaru University of Commerce)
Machine Collaboration
࣭Takaki Sato (Tohoku University)ࢥࣟࢼ⚝࡟࠾ࡅࡿឤᰁᣑ኱㜵Ṇᑐ⟇ࡢேὶᢚไຠᯝ࡟㛵ࡍࡿᐇドศᯒ
14:20-15:20 ࠙Session 10ࠚChair: Yasumasa Matsuda (Tohoku University)

࣭M
Masataka Ban (University of Tsukuba)㉎ධᆺࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࡢ㈨㔠ㄪ㐩ࣃࢱ࣮ࣥศᯒ
࣭Shohei Hasegawa (Hosei University)
BTYD ࣔࢹࣝ࡟ࡼࡿ Q&A ࢧ࢖ࢺࡢᢞ✏⾜ືࡢศᯒ15:30-16:30 ࠙Session 11ࠚChair: Wirawan Dony Dahana㸦Osaka University㸧࣭Li Yinxing (Tohoku University)
Product Embedding For The Large-scale Disaggregated Sales Data
࣭Shogo Takedomi (Tohoku University, BRIDGESTONE )ᚅࡕ᫬㛫ணࣔࢹࣝࢆ฼⏝ࡋࡓ pMP ࣔࢹࣜࣥࢢ࡟ࡼࡿ⥭ᛴ࣮ࣟࢻࢧ࣮ࣅࢫ᪋タ㓄⨨᭱㐺໬2Introduction•

CGM (consumer generated media) influence firms’ financial
performance– e.g., Chevalier and Mayzlin (2006), Dellarocas, Zhang, Awad (2007), Liu(2006)

Online Review Text Analysis Incorporating Valence and Vote:
Extending the Topic Model to Include Performance Measures•

GGMs for consumers and firms– Spread their product information without additional financial costs (Tirunillai
and Tellis, 2014)– Effective source of information for firms to obtain external evaluations of
their products (Dellarocas 2003).

Applications of Data Science in Social Science
Symposium in honor of Prof. Nobuhiko Terui, supported by JSPS KAKENHI@Tohoku University
Feb. 17, 2022•

Consumer reviews are written in natural language– Some analytical frameworks are presented recently (Berger et al. 2020;
Humphreys and Wang 2017; Balducci and Marinova 2018)

Sotaro Katsumata
Graduate School of Economics, Osaka University
katsumata@econ.osaka-u.ac.jp•

P. K. Kannan
Robert H. Smith School of Business, University of Maryland
pkannan@umd.edu

It is necessary to understand some other characteristics of consumer
reviews– Polarity and Importance



3

4

Polarity (Valence) and Importance (Vote)•

Collective Evaluation for CGM“Polarity” of online review•– Some reviews have a negative impact on firm performances– Positive reviews have a positive impact on market outcomes and vice versa• Chevalier and Mayzlin (2006), Liu (2006), Moe and Trusov (2011), Moe and Schweidel(2012)– Review polarity depends on the products•

Vote is an indicator to examine the quality of reviews
–
–
–
–
–

• Burns and Hou, (2017), Schoenmueller, Netzer, and Stahl (2020)•

Valence reflects the sentiment of reviews– (e.g., Blei and McAuliffe 2010; Tirunillai and Tellis 2014)– Difficult to accurately determine the impact on financial outcomes (e.g.,
Chevalier & Mayzlin 2006; 2006; Moe and Trusov 2011).

• Volume, Variance, and Valence need to be considered (Dellarocas et al. 2003)“Importance” of online review– Viewers can vote and see how many votes have been cast
• Mudambi and Schuff (2010), Lu, Wu, and Tseng (2018)– Viewers prefer posts attract many votes• Egebark and Ekstrom (2018)(Mudambi and Schuff 2010).
This “double voting” mechanism: a fair indicator(Mayzlin, Dover, and Chevalier 2014).
Collect vote from others also increases trust(Egebark and Ekstrom 2018; Ding, et al. 2017).

– Associated with actual corporate financial performance• Ding, et al. (2017)••

Necessary to consider both valence and vote together

Impact of review on the market is different– Interactivity (sociality) of UGC as one of the open issues for digital marketing (Kannan
and Li, 2017)– Several studies have presented models to analyze valence and text simultaneously(e.g., Büschken and Allenby 2016, 2020)– Necessary to separate important topics from less important ones (Mimno etal. 2011)– Incorporating this valence/vote in the topic model, we can select important
topics

5

6

Model

Review Text

• Three Components of the model
1. Text
2. Valence, the rating score• ‫ݓ‬௜ : ݅-th observed token (word)1,– ‫ݓ‬௜௩ = ቊ0,– used as useful information to examine market trends even before thedevelopment of text analysis methods (e.g., Ansari, Essagaier and Kohli
2000).

if the word ‫ ݒ‬is observed in token ݅else‫ݓ‬௜ ‫݈ܽܿ݅ݎ݋݃݁ݐܽܥ ׽‬௏ ߰෨ ௜௄௭߰෨ ௜௩ = ෑ ߰௞௩೔ೖ ,3. Vote, the number of “helpful” votes– The reviews by viewers (Mudambi and Schuff 2010)௞ୀଵ• ‫ݖ‬௜ : ‫ܭ‬-dimensional parameter• Index– ܰ: The total number of tokens (individual words) observed in all
documents– ‫ܦ‬: the total number of documents (reviews)– ‫ܭ‬: the number of potential topics needs to be determined by the analyst– ‫ݖ‬௜௞ = ቊ

1,
0,

if token ݅ belongs to topic ݇else• ߰௞௩ : a parameter which obtained for each topic.

7

Writers’ Valence• ‫ݕ‬ௗ௝ : Rating of perspective ݆ of review ݀– if the data is collected on a 5-point scale in item ݆, define ܳ௝ = 4 and‫ݕ‬ௗ௝ ‫{ א‬0,1,2,3,4}‫ݕ‬ௗ௝ ‫ܳ ݈ܽ݅݉݋݊݅ܤ ׽‬௝ , ߶෨ ௗ௝ ,௄௖߶෨ ௗ௝ = ෑ ߶௞௝೏ೖ ,௞ୀଵ• ܿௗ : the ‫ܭ‬-dimensional parameter1,– ܿௗ௞ = ቊ0,

if document ݀ belongs to topic ݇else• ߶௞௝ : parameter that influences the height of item ݆’s score obtainedfor each topic.
• Expected value of the score of item ݆ of the review belonging to topic
݇ is ܳ௝ ߶௞௝ .

8

Viewers’ Vote• ‫ݎ‬ௗ : The number of “helpful” ratings by viewers– a natural number greater than or equal to zero– assume a negative-binomial distribution ܰ݁݃‫)ڄ(݊݅ܤ‬.

‫ݎ‬ௗ ‫߬(݊݅ܤ݃݁ܰ ׽‬ǁ ௗ , ߩ෤ௗ )
௄

௄
௖

௖

ߩ෤ௗ = ෑ ߩ௞೏ೖ , ߬ǁ ௗ = ෑ ߬௞೏ೖ
௞ୀଵ

௞ୀଵ

• ܿௗ௞ : a parameter that indicates the topic assignment of document ݀,• Note: The negative binomial distribution of ߬௞ = 1 is equivalent to
the geometric distribution.

910Model (Directed Acyclic Graph)

Data Description••

Categorical

Categorical

Dirichlet

‫ݖ‬

‫ݓ‬

߰

Data: collected from Kakaku.com (https://kakaku.com/)
A consumer review site mainly written in Japanese with a long history– The website launched in 2000
– The global No. 1 in the “E-commerce and Shopping > price comparison”
category in September 2021 (Similarweb, https://www.similarweb.com/),– The ranking of all websites, ranks 328th in the world, and 33rd in Japan.
– Tanked 441st in the world and 36th in Japan (Alexa ranking,https://www.alexa.com/).

ߚ

݊ௗ
ߙ

ߠ

‫ݕ‬

Dirichlet߶Binomial

Beta

ܿ

ߛ
‫ܬ‬

ߩ

Categorical

Reliability of the Source– A market survey has shown that online review platforms have fewer
manipulated posts than shopping platforms– Trustworthiness of reviews is one of the major issues, such as fake reviews
and manipulated reviews

ߜ

Beta

‫ݎ‬
Negative
Binomial

•

‫ܦ‬

߬

• (e.g., Chen, Guo and Huang 2021; Mayzlin, Dover, and Chevalier 2014)

ߟ

Beta-Prime

11

12

Review Texts

Apple iPhone Reviews (‫ܦ‬௜௉௛௢௡௘ = 6922)

Writer’s name

iPhone3G
iPhone6
iPhone8Plus
iPhone11ProMax

180

160

iPhone3GS
iPhone6Plus
iPhoneX
iPhone12iPhone4
iPhone6s
iPhoneXR
iPhone12mini

iPhone4S
iPhone6sPlus
iPhoneXS
iPhone12Pro

iPhone5iPhone7iPhoneXSMax
iPhone12ProMax

iPhone5c
iPhone7Plus
iPhone11
iPhoneSEg1

iPhone5s
iPhone8
iPhone11Pro
iPhoneSEg2

140

Title and Main Text

120

100

80

60

40

20

Writer’s Valence0

2008-072008-10
2009-01
2009-04
2009-072009-10
2010-01
2010-04
2010-072010-10
2011-01
2011-04
2011-072011-10
2012-01
2012-04
2012-072012-10
2013-012013-04
2013-072013-10
2014-01
2014-04
2014-072014-10
2015-01
2015-04
2015-072015-10
2016-01
2016-04
2016-072016-10
2017-012017-04
2017-072017-10
2018-012018-04
2018-072018-10
2019-01
2019-04
2019-07
2019-102020-01
2020-04
2020-07
2020-102021-01
2021-04

Viewers’ vote

Five star scores by perspective
Design/Potability/Response/Screen/
Battery/(Camera)

Number of vote by viewers who
evaluate the review was “helpful.”

13

14

Topic Summaryy (example)(pRegression for Salient Topics••

Examine the factors affecting ߠௗProblems in assuming– Constraint and Efficiency of Estimation

߰௞ : Top 12 frequently
observed words• ߠௗ௞ is the probability of topic affiliation, so there is a constraint that σ௄௞ୀଵ ߠௗ௞ = 1.
– Mimno and McCallum (2008), Blei and Lafferty (2006) Büschken and Allenby (2016),
Liu and Toubia (2018), Toubia, et al. (2019)

Expected Vote߬௞ ߩ௞ /(1 െ ߩ௞ )Wordclouds ->– Compatibility• Cannot not determine in advance which words will be classified into which topics– Quality of topics• A certain percentage of topics are considered poor and have low informational
value (Mimno, 2011)•

Observed probability
for each model: ߠ௠ߠ௠ =Focus only on the helpful Salient Topics• Based on the aggregate demand model (Berry 1994)

–
–
–
–

1
෍ ߠௗ
# ‫ܦ‬௠
௧‫א‬஽೘

where, ‫ܦ‬௠ is a set ofreviews evaluatedfor model ݉.

ܵ: set of helpful salient topics,ܵ ௖ : set of other topics,ߠௗ଴ = σ௞‫א‬ௌ ೎ ߠௗ௞ : the base topics
log ߠௗ௞ െ log ߠௗ଴ : Dependent variable

Expected Valence߶௞

15

Regression for Salient Topics• Explanatory variables– LatestModel: 1 if the model to be reviewed is the latest and 0 otherwise,the– Writers’Experience: the number of submissions within the past three
years by review writers (add 1 and take the logarithm)– LatestModel: 1 if the review is about a new model– #ofWords, #ofWords2 : the number of words in the review, curve linearly
related to helpfulness for readability (Agnihotri and Bhattacharya 2016)– In addition to these variables, incorporate the dummy variables of themodels (products) as a random effects• Model:ெlog ߠௗ௞ െ log ߠௗ଴ =ߣ଴଴௞ + ෍ ‫ݕ݉݉ݑܦ݈݁݀݋ܯ‬ௗ௠ ߣଶ௠௞௠ୀଵ+‫݈݁݀݋ܯݐݏ݁ݐܽܮ‬ௗ ߣଷ௞ + ܹ‫ ݏݎ݁ݐ݅ݎ‬ᇱ ‫݁ܿ݊݁݅ݎ݁݌ݔܧ‬ௗ ߣସ௞+#‫ݏ݀ݎ݋ܹ݂݋‬ௗ ߣସ௞ + #‫ݏ݀ݎ݋ܹ݂݋‬ௗଶ ߣହ௞ + ߝௗ௞ , ݇ ‫ܵ א‬

16Result of Regression: Apple iPhone Series
topic iPhone series: Frequent words
No.
Negative-Helpfulnothing, say, anything, should, wrong, opinion, useless,
92 bad,special, else, particularly, think(-1)
support, replacement, store, tell, care, break, say, ask,
53 apple,repair, replace, again
start, end, moment, freeze, seem, then, happen,
29 sometimes,
issue, frequently, fix, stop
price, late, series, cheap, camera, high, enough,57 performance,
spec, expensive, low, size
image, mode, lens, wide, night, angle, video, digital,
18 camera,shoot, even, canPositive-Helpful
shape, much, become, well, folder, fast, design, ios5, make,8 3gs,
flat, ios4
level, excellent, resolution, term, texture, especially,
91 high,perfection, complete, ease, performance, functionality
docomo, decide, mnp, get, lose, worry, decision, glad,
72 switch,
end, family, factor
ipod, use, panel, compare, convenient, own, nano, 4th,
77 touch,dock, 5th, intuitive
apps, app, also, lot, own, many, fun, enjoy, useful, make,95 can,customize

LatestModel

Writers'
Experience#ofWords#ofWords2-0.001(-0.076 )0.028 ***
(4.086 )0.022 **
(3.206 )0.040 ***
(5.872 )-0.007(-1.016 )-0.048 *(-2.016 )-0.042 †(-1.781 )-0.049 *(-2.069 )0.227 ***
(9.624 )0.040 †
(1.695 )0.015(0.183 )0.057(0.687 )-0.114(-1.365 )-0.182 *(-2.180 )-0.673 ***(-8.058 )-0.030 **(-3.061 )-0.042 ***(-4.210 )-0.016(-1.599 )-0.009(-0.960 )0.067 ***
(6.748 )-0.060 ***(-8.738 )0.001(0.215 )0.005(0.800 )-0.011(-1.579 )0.016 *
(2.309 )0.061 *
(2.562 )0.037(1.549 )-0.084 ***(-3.554 )-0.046 †(-1.955 )-0.081 ***(-3.413 )0.175 *
(2.090 )-0.454 ***(-5.434 )0.396 ***
(4.743 )-0.288 ***(-3.443 )0.166 *
(1.987 )-0.073 ***(-7.412 )0.030 **
(3.036 )-0.091 ***(-9.174 )0.008(0.797 )-0.045 ***(-4.558 )Note)
The model incorporating the intercept, and model (device) random effects.
†: p<10%, *: p<5%, **: p<1%, ***: p<0.1%.
Model summary statistics: R2 = 0.170, Adj. R2 = 0.166, and F-value = 44.15 (p<0.001).

Finding Inﬂuential Users by Topic in Unstructured
User-generated Content
Mirai Igarashi∗

Kunpeng Zhang†

P.K. Kannan‡

Nobuhiko Terui§February 17, 2022

1

Introduction

This study addresses two critical limitations in the extant research on social inﬂuence, whichis the concept that consumers eﬀect each other’s behavior. First, despite a vast amountof literature on social inﬂuence, few studies have developed models for unstructured usergenerated content (UGC), such as text and images, inﬂuenced by others’ contents. Most of
the research has examined the structure of consumer behavior inﬂuenced by social interactionin terms of the numerical aspects of consumer behavior, such as the volume or binary of the
focal behavior. However, since people get a lot of information from nonnumerical content
in social media, analyzing how the generated unstructured content inﬂuences on other users
and how the generated content changes while being inﬂuenced by other users are importantresearch topics. Second, in this study, social inﬂuence is estimated heterogeneously for eachedge and topic of content. Previous studies have examined various moderators that couldchange the level of inﬂuence such as types of connections (Iyengar et al., 2011) and consumer
attributes (Wang et al., 2013). However, assuming diﬀerent social inﬂuence for each edge isthe strongest assumption and includes all the possible moderators in the previous studies.
In addition, we consider that the inﬂuence on the behavior generating content varies withthe topic of the content, just as the inﬂuence on purchasing products varies with the productcharacteristics (Park et al., 2018). These assumptions allow us to determine who has a strong
inﬂuence on the network at the level of edges and by topic.
∗

Faculty of Business Science, University of Tsukuba
Decision, Operations and Information Technologies, Robert H. Smith School of Business, University of
Maryland‡Marketing, Robert H. Smith School of Business, University of Maryland§
Graduate School of Economics and Management, Tohoku University
†

1

2

Model

The observed UGC data is assumed to be decomposed into multisets of the smallest unit
constructs (e.g., words in a text and objects in an image) disregarding the order of the unit
but keeping multiplicity. In the following, we denote the UGC data as W = {wut }, where
u and t refer user and time points, respectively, and wut = (wut1 , . . . , wutNut ) (Nut denotes
the number of constructs). We also observe the following relationships among social media
users, and the set of users that user u follows is represented by Fu .
First, we introduce the generative model for the elements of UGC following the conventional topic model. The proportion of topics included in the contents generated by theuser u at time t is represented by a topic distribution, θut . The latent topic behind wuti
is thought to be determined from a categorical distribution, zuti ∼ categorical(θut ). Whenthe topic assignment is given, the corresponding wuti is also generated from a categorical
distribution, wuti | zuti = k ∼ categorical(φk ). φk is a element distribution, which represents
the generative probability of elements in the context of topic k.
Next, we incorporate the dynamic changes in users’ interests and the inﬂuence of friendgenerated contents on these interest levels. The topic distribution, θut , has the following
hierarchical structure.
exp(ηutk )θutk = ,ηutk ∼ N (λutk , 1)k exp(ηutk )βuf k · ηf t−1k + γtk + δuk
λutk = αk · ηut−1k +

(1)
(2)

f ∈Fu

βuf k represents the lagged social inﬂuence of friend f whom user u follows on the interest ofuser u in topic k, and it varies depending on the topic as well as the network edge. γtk andδuk are time-topic and user-topic ﬁxed eﬀects controlling for common shocks at a speciﬁctime and each user’s intrinsic preference for a speciﬁc topic, respectively.

References
Iyengar, R., Van den Bulte, C., and Valente, T. W. Opinion leadership and social contagion
in new product diﬀusion. Marketing Science, 30(2):195–212, 2011.
Park, E., Rishika, R., Janakiraman, R., Houston, M. B., and Yoo, B. Social dollars inonline communities: The eﬀect of product, user, and network characteristics. Journal ofMarketing, 82(1):93–114, 2018.
Wang, J., Aribarg, A., and Atchadé, Y. F. Modeling choice interdependence in a social
network. Marketing Science, 32(6):977–997, 2013.
2

Does Deregulation of Health Claims on Functional Food
Package Design Change Consumers' Purchase Behaviors?

Hiroshi Onishi1, Tokyo University of Science
Masakazu Ishihara, New York University

Abstract
Japanese government deregulated health claim legislation for functional food products in
April 2015. A new healthy food category, called “Kinousei (Functional-food)” brands, wasintroduced in addition to the incumbent category of “Tokuho (Special-health)” brands which
requires more rigid scientific evidences of health effects for an official approval. This research
investigates the effects of the health claim deregulation for the functional food products to
consumers' purchase behaviors, for example, whether people have bought more volumes andswitched to the healthy claimed products, or they have not changed their purchase behaviors,
and which types of consumers are vulnerable to the health claims of food products. In addition,
this study also examines what kinds of product package designs are perceived as healthy
image by consumers.
We use a purchase panel dataset of functional yogurt products in Japanese market toinvestigate our research questions. We apply the deep learning framework of theBrandImageNet model (Liu et al. 2020) in order to evaluate the health image of productpackages among more than one thousand of the yogurt items. Then, we estimate thedifference-in-difference regression with cluster-robust inference by Cameron & Miller (2010)
to investigate the effect of the health claim deregulation for the Kinousei brands and theconsumers’ healthy image perception to the product package designs on consumers’
1 All correspondence may be addressed to the first author at hohnishi@rs.tus.ac.jp.

functional yogurt purchase behaviors by comparing the Tokuho brands as a control groupbetween pre and post periods when the deregulation was in force in Japanese market.
We find the positive impacts of the health claim deregulation and healthy package
design images among only consumers whose wellness consciousness is low, which results inswitching their purchase products from normal brands to health claimed the Kinousei brands.
Whereas, consumers with high wellness consciousness have not changed their purchasebehaviors to keep buying the Tokuho brands. We then also discuss managerial implications
for functional food manufacturers.

Keywords: Health Claims; Package Design; Functional Foods; Deep Learning; Difference-inDifference (DiD); Error Correction Models

Statistical model for article citation
network in Web of Science
Yuichiro Yasui
The Graduate University for Advanced Studies, SOKENDAI, Tokyo, Japan

Junji Nakano
Chuo University, Tokyo, Japan

Abstract
We propose a stochastic generative model to represent a directed
graph constructed by citations among academic papers, where nodes
and directed edges represent papers with discrete publication timeand citations respectively. The proposed model assumes that a citation between two papers occurs with a probability based on the typeof the paper, importance of cited paper, and diﬀerence between their
publication times. We consider that the importance and type of apaper are approximated by the in- and out-degrees of the node. In
our model, we adopt three functions: a logistic function for illustrating the numbers of papers published in discrete time, a generalized
Pareto distribution for describing the out-degree distribution, andan inverse Gaussian probability distribution function to express theaging eﬀect based on the diﬀerence between publication times. The
model is initiated by analyzing statistics papers assembled from the
Web of Science database. By using the proposed model, we can generate graphs and demonstrate that they are similar to the original
data concerning the in-degree, out-degree, and triangular distributions. In addition, we analyze two other citation networks derived
from physics papers in the arXiv database and verify the eﬀectivenessof the model.

Estimation of High Dimensional Vector
Autoregression via Sparse Precision Matrix
Benjamin Poignard∗
Graduate School of Economics, Osaka University and Riken-AIP, Japan
Manabu Asai†
Faculty of Economics, Soka University, Japan

Abstract

We consider the problem of estimating sparse vector autoregression (VAR) processes via penalized precision
matrix. Such matrix is the output of the underlying directed acyclic graph of an indirect form of the VAR
process, whose zero components correspond to zero coeﬃcients in the indirect form. The precision matrix
estimators are deduced from the class of Bregman divergences and regularized by the SCAD, MCP and
LASSO penalties. Under suitable regularity conditions, we derive error bounds for the regularized precision
matrix for each Bregman divergence. Moreover, we establish the support recovery property, including thecase when the penalty is non-convex. These theoretical results are supported by empirical studies.

∗ E-mail address: bpoignard@econ.osaka-u.ac.jp (corresponding author)† E-mail address: m-asai@soka.ac.jp1ࢢ৔ϊΠζΛ‫ؚ‬Ή৔߹ͷδϟϯϓɾϒϥ΢ϯӡಈͷ൚ؔ਺ͷ‫ ॴہ‬SIML ਪఆ(Local SIML Estimation of Some Brownian and Jump
Functionals Under Market Microstructure Noise)
January 2022ࠃ༑௚ਓ (Naoto Kunitomo, Institute of Statistical Mathematics)andࠤ౻੔ঘ (Seisho Sato, University of Tokyo)

Abstract
To estimate some Brownian and jump functionals from high-frequency ﬁnancial data under market microstructure noise, we introduce a new local estimation method of the integrated volatility and higher-order variation of Ito’s
semi-martingale processes. Although it is straight-forward to extend the realized volatility (RV) estimation to more general cases without micro-market
noise, it may not be straight-forward to estimate Brownian and Jump functionals in the presence of micro-market noise. We develop the local SIML (LSIML)
method, which is an extension of the separating information maximum likelihood(SIML) method proposed by Kunitomo, Sato and Kurisu (2018) and Kunitomo
and Kurisu (2021). The new method is simple and the LSIML estimator has somedesirable asymptotic properties as well as reasonable ﬁnite sample properties.
Key Words
High-Frequency Data Analysis, Integrated Volatility, Separating Information Maximum Likelihood (SIML), Higher-Order Brownian and Jump Functionals, Stable
Convergence, Local SIML Estimation

References[1] Ait-Sahalia, Y. and J. Jacod (2014), High-Frequency Financial Econometrics, Princeton University Press.
[2] Barndorﬀ-Nielsen, O., P. Hansen, A. Lunde, and N. Shephard (2008), ”Designig Realized Kernels to Measure the Ex Post Variation of Equity Prices
in the Presence of Noise,” Econometrica, 76-6 (2008) 1481-1536.
[3] Hausler, E. and Luschgy, H. (2015), Stable Convergence and Stable Limit
Theorems, Springer.
[4] Jacod, J., Y. L., Per A. Mykland, M. Podolskijc, and M. Vetter (2009),”Microstructure noise in the continuous case: The pre-averaging approach,”
Stochastic Processes and their Applications, 119 (2009) 2249?2276.
1

[5] Ikeda, N. and S. Watanabe (1989), Stochastic Diﬀerential Equations andDiﬀusion Processes, 2nd Edition, North-Holland.
[6] Jacod, J. and P. Protter (2012), Discretization of Processes, Springer.
[7] Kunitomo, N. and Kurisu, D. (2017), ”Eﬀects of Jump and Noise in
High-Frequency Financial Econometrics,” Asia-Paciﬁc Financial Markets,
Springer.
[8] Kunitomo, N., S. Sato and D. Kurisu (2018), Separating Information Maximum Likelihood Method for High-Frequency Financial Data, Springer.
[9] Kunitomo, N. and Sato, S. (2021), ”Local SIML Estimation of Some Brownian and Jump Functionals Market Microstructure Noise,” MIMS-RBP Statistics & Data Science Series (SDS-21),
http://www.mims.meiji.ac.jp/publications/datascience.html[10] Kunitomo, N. and Kurisu, D. (2021), ”Detecting Factors of Quadratic Variation in the Presence of Market Microstructure Noise,” Japanese Journal of
Statistics and Data Science (JJSD), 4(1), 601-641, Springer.
[11] Malliavin, P. and M. E. Mancino (2009), “A Fourier Transform Method
for Nonparametric Estimation of Multivariate Volatility,” Ann. Statist., 37,
1993-2010.
[12] Mancino, Maria Elvira, Recchioni, Maria Cristina, and Sanfelici, Simona(2017), ”Fourier-Malliavin Volatility Estimation Theory and Practice,”
Springer.

2

ビッグミクロデータのプライバシー保護
星野伸明 ∗

2022 年 2 月 17 日

「ミクロデータ」とは、特定個体の属性変数の実現値の組で、これを一行（レコード）として扱うのがミクロデータセットと考えられる。社会科学において方法論的個人主義を採用するなら
ば、ミクロデータの分析によって得られる知見は一義的な価値を持つ。特に経済学では方法論的個人主義が席巻し、一昔前は集計表の分析にとどまっていた社会科学者たちは、ミクロデータを分析するようになった。
松田 (2000) によれば 1940 年代から社会科学者のミクロデータ分析は始まっており、労働経済学など一部の分野では 1960 年代までに定着している。当時は簡単な手続きでミクロデータが利用出来たと言われている。しかし 1960 年代後半から、欧米諸国においてプライバシーが意識されるようになった。宇賀 (2012) によれば、プライバシーを「自己情報をコントロールする権利として理解する立場が有力」である。また「この考えの影響を受けた個人情報保護立法は 1970 年代からみられるようになった」。この時期以降、ミクロデータの情報保護研究は本格化する。
実は集計表の情報保護は遅くとも 1940 年代には米国センサス局で始まっており (Cox, 2001)、統
計学的なミクロデータの保護は、集計表保護概念の影響を強く受けている。集計表は magnitudeの集計結果の場合もあるが、ミクロデータの保護と強く関係するのは度数の集計表、すなわち分割表である。
分割表の保護における目標は、度数が小さいセルにおいて真の度数を隠す1 こと、と考えられてきた。例えば小売業の事業所が一つしか存在しない地方の二元分割表で（小売業, 売上一千万円）のセル度数が 1 と分かれば、この事業所の売上は露見する。もし小売業の事業所が多くある地方だったとしても、売上が高い事業所は限られるだろう。つまり分割表においてセル度数が小さければ、そこに所属する個体群を絞り込めることはあり得る。
営業秘密が暴露されるような統計調査に協力は期待できないので、データ主体の秘密保護については真剣に研究されている。研究の蓄積により分野として確立しており、統計的開示制限 (statistical
disclosure limitation) ないし管理 (control) と呼ばれる。なお厳密にはプライバシーは個人の権利である。法人も含めて秘密を保護する概念は “conﬁdentiality” と呼ばれる。
さて、ミクロデータは集計表とは別物と理解されているかもしれないが、（離散観測の）ミクロ
データセットは分割表と一対一に対応させることが出来る。つまりミクロデータの属性実現値の組は、分割表のセルを一意に示す。目視のための分割表は低次元にならざるを得ないが、分割表とは個体の属性空間を分割して各セルに所属する個体数を示すものであり、目視の制約を外せば属性空間の次元は高くても問題ない。実際、計算機による処理が前提のデータベースでは、多次元分割表（データキューブ）を処理の高速化に用いる。
従って度数が小さいセルを隠すということは、同一属性の個体数が少ないレコードを隠すということと同値である。集計表の秘匿と同様に考えればレコードを削除することになるが、ミクロ∗
1

金沢大学経済学経営学系
例えば平成 28 年経済センサスでは度数が 2 以下のセルに x を代入している。太田・北原 (2019) を見よ。

1

データセットには周辺度数がないこともあり、好まれない。最もよく使われるのは「再符号化」な
いし「一般化」である。この方法は属性の分類を粗くし、セルを併合することで小さい度数のセルを減らす。例えば 1 歳刻みで記録されている年齢を 5 歳刻みに再符号化すれば、セルの度数は単調非減少である。全てのレコードについて同じ（大域的）符号化をするなら結果は “grouped data”
であり、これを社会科学者は扱いなれているので受容されたと考えられる。
ところが再符号化は、いわゆるビッグデータの保護において主役ではあり得ない。ビッグデー
タという言葉が 2010 年代に流行した背景には、多くの人がインターネット上で活動履歴を膨大なデータとして残すようになった社会状況が存在する。そのようなミクロデータセットの属性変数の種類（フィールド数）は桁違いに多いものがある。例えば通販サイトではユーザーの各時点の挙動がそれぞれ変数（フィールド）である。フィールドが増えれば、分割表のセル度数はほとん
ど 0、正でも 1 ばかりということになる。このような状況で再符号化をすると、度数が非ゼロの遠いセル同士を併合することになり、データに分析する価値が残らない。
ビッグミクロデータの場合、度数を不確実にすることによっても度数が小さいセルが隠れると考えるべきである。非確率的な方法も存在するが、ランダムネスによる情報保護が「疑似データ」の生成や情報学的なプライバシー保護では主流である。例えばデータ（経験分布）をそのまま公開するのではなく、経験分布からの iid（ブートストラップ）標本を公開すれば、度数は不確実になる。
しかし iid 標本はビッグミクロデータの保護に向かない。iid の場合、標本サイズに比例してフィッシャー情報量が増えるため、ビッグデータでは母集団（ブートストラップでは経験分布）が正確に推定出来てしまう。従って Fienberg(1994) の言うように経験分布を平滑化した母集団モデルからの標本を公開することが考えられるが、情報保護目的と母集団記述目的のモデリングが混交し最適化を妨げる。あくまで母集団モデリングは母集団記述を目的とし、情報保護はサンプリングで行うべきである。Hoshino (2009) の条件付き複合ポアソン分布族のメンバーは、性質が良い非iid 標本を生成する。また母数によってフィッシャー情報量のオーダーを管理可能である。

参考文献[1] Cox, L. (2001) Disclosure risk for tabular economic data, Conﬁdentiality, disclosure, anddata access, Doyle, P. et al. eds., pp.167–184, Elsevier, Amsterdam.
[2] Fienberg, S.E. (1994). A radical proposal for the provision of micro-data samples and thepreservation of conﬁdentiality. Technical report, Department of Statistics, Carnegie Mellon
University.
[3] Hoshino, N. (2009). The quasi-multinomial distribution as a tool for disclosure risk assessment. Journal of Oﬃcial Statistics, 25, 269–291.
[4] 松田 芳郎 (2000) 『統計調査制度とミクロ統計の開示』, 松田 芳郎他編, pp.19–23, 日本評論社.
[5] 太田 将彰・北原 昌嗣 (2019) 『平成 28 年経済センサス‐活動調査における秘匿処理について』, 統計研究彙報, 第 76 号, pp.115–134.
[6] 宇賀 克也 (2012) 『情報法』, 宇賀 克也・長谷部 恭男編，chapter 6, 有斐閣.

ແ৘ใࣄલ෼෍ͷཧղɿެฏͳ෼഑ͱະ஌฼਺͔Β༄ ຊ ෢ ඒ: ౷‫਺ܭ‬ཧ‫ॴڀݚ‬

1. ಈ‫ػ‬ϕΠε๏͸‫ج‬ຊతʹ‫ط‬ଘͷࣄલ৘ใΛ༗ޮʹऔΓࠐΉख๏Ͱ͋Δɻ͔͠͠ɺղੳ݁Ռ͸ར༻ͨ͠‫ط‬ଘͷࣄલ৘ใʹґଘ͢ΔɻैͬͯɺҟͳΔ৘ใ͕ਖ਼͍͠ͱ৴͡Δਓͱ͸ղੳ݁ՌΛ‫ڞ‬༗ग़དྷͳ͍ɻ
‫ݧܦ‬తͳ‫؍‬ଌʹ΋‫͍ͨͮج‬ਪ࿦Λॏࢹ͢Δɺ࿦ཧ࣮ূओٛͷ‫͔఺؍‬Β͸ड͚ೖΕΒΕͳ͍ɻ͜ͷ໰୊Λղܾ͢ΔࢼΈ͕ɺແ৘ใࣄલ෼෍͋Δ͍͸٬‫؍‬తࣄલ෼෍ͷར༻Ͱ͋Δɻจࣈ௨Γແ৘ใࣄલ෼෍
Ͱ͋Ε͹ɺͦΕΛར༻ͯ͠΋ղੳ݁Ռ͸‫ڞ‬༗ग़དྷΔ͸ͣͰ͋ΔɻҰ༷෼෍ɾJeﬀreys priorɾreference

prior ͳͲ͕ఏҊ͞Εɺଞʹ΋༷ʑͳ۩ମతͳࣄલ෼෍͕ఏҊ͞Ε͍ͯΔɻ๬·͍͠ແ৘ใࣄલ෼෍Λߟ࡯͢Δͱɺ‫͚͓ʹֶࡁܦ‬Δެฏͳ෼഑ͱͷؔ࿈ʹ‫͘෇ؾ‬ɻ΋͠ɺଟ͘ͷਓ͕ड͚ೖΕΔແ৘ใࣄલ෼෍͕ఆٛग़དྷΔͳΒ͹ɺެฏͳ෼഑ʹରͯ͠৽͍͠ࢹ఺͕ಘΒΕΔͱ‫ظ‬଴ग़དྷͦ͏Ͱ͋Δɻ‫͑ݴʹٯ‬͹ɺແ৘ใࣄલ෼෍ͷఆٛ͸೉͍͠໰୊Ͱ͋Δ͜ͱΛҙຯͯ͠
͍Δɻ͜ͷ໰୊ʹ͍ͭͯվΊͯߟ࡯ͨ͠ͷͰใࠂ͢Δɻ

2. ແ৘ใࣄલ෼෍
ඪຊϞσϧΛ P = {p(y|θ); y ∈ X (⊂ Rn ), θ ∈ Θ(⊂ Rp )} ͱ͢Δɻ฼਺ۭؒ Θ ্ͷҰ༷෼෍͕࠷΋ૉ๿ͳແ৘ใࣄલ෼෍Ͱ͋Δɻ͔͠͠ɺ͜ͷఆٛͰ͸฼਺ͷม਺ม‫ʹ׵‬ґଘ͢ΔͷͰෆมʹͳ
Δ Jeﬀreys prior ͕ఏҊ͞ΕͨɻΑΓચ࿅͞ΕͨఏҊ͕ Bernardo (1979, JRSS B) ʹΑΔ reference

prior Ͱ͋Δɻ͔͠͠ɺఆٛ͸‫͋Ͱີݫ‬Δ͕ద༻ൣғʹ੍໿͕͋Γɺ࣮ࡍతͳϞσϧͰ͸઴ۙతੑ࣭Λద༻͢Δ͔͠ͳ͍ɻ
ແ৘ใࣄલ෼෍Λཧղ͢ΔͨΊʹɺc ∈ Θ, d(·, ·) Λ Θ ্ͷ (ٖ) ‫ͯ͠ͱ཭ڑ‬ɺࣄલີ౓

π(θ) = C exp{−δ0 d(θ.c)}b(θ)(1)ୠ͠ C ͸‫֨ن‬Խఆ਺ɺδ0 ͸ॴ༩ͷਖ਼਺ɺΛߟ͑Δɻ͜ͷఆࣜԽͰ͸ɺb(θ) ͕ແ৘ใࣄલؔ਺ͱ‫ݟ‬ͳ͞ΕΔɻ࣮ࡍɺδ0 ͕ඇৗʹখ͍͞ͱɺਪ࿦্͸ b(θ) ΛԾఆͨ͠৔߹ͱຆͲมΘΒͳ͍ɻ

3. ެฏͳ෼഑ͱະ஌฼਺
ެฏͳ෼഑͸ޮ཰తͳ؅ཧɾӡӦͱฒΜͰ‫ֶࡁܦ‬ͷॏཁͳ֓೦Ͱ͋Δɻ·ͨࣾձֶతʹ‫ͯݟ‬΋‫ج‬ຊతͰ͋Δɻެฏͳ෼഑ʹؔͯ͠ҟ࿦͕গͳ͍ͷ͸࣍ͷೋͭͷ৔߹Ͱ͋Δɻ1) ෼഑͢Δର৅ͷ (গ) ਓ਺ʹԠͯ͡‫ۉ‬౳ׂʹ͢Δ2) ಛఆͷҰਓ͕ಠΓ઎Ί͢Δ

Ͱ͋Δɻ1) ͕ૉ๿ͳެฏͳ෼഑Ͱ͋Γ 2) ͸ͦͷ൓ର֓೦Ͱ͋Δɻ͜ΕΒ͸֤ʑɺཁૉ͕༗‫ݸݶ‬ͷۭؒ Θ ͷ౳֬཰෼෍ɺc ∈ Θ ʹର͢ΔҰ఺෼෍ π(θ) = δD (θ − c) Ͱද‫ݱ‬ग़དྷΔɻ
͔͠͠ɺૉ๿ͳ֓೦Ͱ͸‫ۉ‬౳෼഑Ͱ͸ެฏ‫ײ‬͸‫ݶ‬ΒΕΔɻଟ਺ͷ‫ۈ‬࿑ऀ΁ͷ഑෼Ͱ͋Ε͹ɺ࿑ಇ࣌ؒɾೳྗɾٕೳͳͲʹ͕ࠩ͋Δ͔Βෆެฏ‫͕ײ‬ੜ͡Δɻࣄ‫ۀ‬ͷ੒Ռͷ഑෼Ͱ͸ɺ౤ࢿֹɾ౤ࢿϦεΫͳͲʹҧ͍͕͋Δ͔Β΍͸Γෆެฏ‫͕ײ‬ੜ͡Δɻෆެฏ‫ײ‬Λআͨ͘Ίʹ͸ɺ͜͜ͷঢ়‫ʹگ‬Ԡͯ͡ରԠ͢Δɻͦͷख๏Λࣄલ෼෍ͷࢹ఺͔Β‫ݟ‬Ε͹ɺࣄલ৘ใΛ࠷େ‫ʹݶ‬ར༻͢Δ͜ͱʹରԠ͢Δɻ
࿑ಇٕೳͱ͔౤ࢿϦεΫΛఆྔԽ͢Δ͜ͱ͸೉͍͕͠ɺࣄલͷ৘ใʹԠܾͯ͡ΊΔ͜ͱʹͳΔɻཁ
͢ΔʹɺϕΠζతࢹ఺Ͱ͸ࣄલ৘ใͷੵ‫ۃ‬తར༻ʹରԠ͢Δɻ
ެฏͳ෼഑Λͦͷ࿮಺Ͱٞ࿦ΛਐΊͯ΋ํ޲‫͚ܽʹײ‬ΔɻΑΓ‫࣮ݱ‬తʹ͸ࣾձͷਓʑ͕ड͚ೖΕΔ͔Ͳ͏͔ͱ͍ͬͨҕͶΔ͔͠ͳ͍ɻ݁Ռͱͯ͠ਓʑͷՁ஋‫ʹ؍‬ґଘ͢Δɻ
໬౓࿦ͱ͔ස౓࿦Ͱଟ༻͞ΕΔɺະ஌฼਺ɾ‫ط‬஌฼਺ͷ֓೦͸಺༰͕ബऑͰ͋Δɻ‫ط‬஌฼਺ͷ֓೦͸ 2) ͷಠΓ઎ΊʹରԠ͢Δɻ͔͠͠ɺະ஌฼਺ͷ֓೦͸Ͳ͏͠Α͏΋ͳ͘ҙຯ͕ෆ໌Ͱ͋ΔɻϕΠζ๏ʹ͓͚Δɺແ৘ใ/٬‫؍‬తࣄલ෼෍ͷ֓೦͸ະ஌฼਺ͷ֓೦ͷҰͭͷද‫ݟͱݱ‬ΒΕΔɻ‫ʹٯ‬ɺະ஌฼਺ͷ֓೦͕ެฏͳ෼഑ͱແ৘ใࣄલ෼෍ͷཧղΛॿ͚Δࢹ఺͸‫ݟ‬౰ͨΒͳ͍ɻ

4. ౷‫ͯ͠ͱྔܭ‬ͷϕΠζਪఆྔೋͭͷແ৘ใࣄલ෼෍ π1 (θ), π2 (θ) ͕͋ͬͨͱ͖ʹɺͲͪΒ͕ΑΓແ৘ใͰ͋Δ͔Λٞ࿦͢Δ͜ͱ͸೉͍͠ɻ΋͠ೋͭͷࣄલ෼෍͕༠ಋ͢Δਪଌ๏ɺྫ͑͹ਪఆྔɺͷͲͪΒ͕༏Ε͍ͯΔ͔Ͱ͋
Ε͹ɺٞ࿦͕ਐΈಘΔɻස౓࿦Ͱ͸ਪఆྔ͸ϦεΫʹΑΓධՁ͞ΕΔɻ
΋͠Ϟσϧ P ͱ‫؍‬ଌ஋ x ͷΈ͔Βߏ੒͞ΕΔࣄલؔ਺Λ༻͍ͯਪఆྔΛಋग़͢Ε͹ɺͦͷࣄ‫ޙ‬ฏ‫ۉ‬ɾࣄ‫ޙ‬Ϟʔυ͸౷‫ͳʹྔܭ‬Δɻ‫͑׵͍ݴ‬ΔͱਪఆྔͰ͋Δɻͦͷਪఆྔͷੑೳ͕ྑ͚Ε͹ྑ͍ਪఆྔͰ͋Δɻࣄલີ౓ (1) ΛԾఆͨ͠৔߹ʹ͸ɺc ʹґଘ͢ΔͷͰ౷‫Ͱྔܭ‬͸ͳ͘ͳΔɻਪఆྔ͕ྑ͘ͳͬͨͷ͸औΓ΋௚ͣ͞ʹࣄલؔ਺͕๬·͍͔͠Βͱ͔͠ߟ͑Α͏͕ͳ͍ɻ͜͏ͨ͠Ұൠతͳࣄલؔ਺͕ແ৘ใࣄલ෼෍͔Ͳ͏͔ͷٞ࿦͸೉͍͠ɻ͔͠͠ɺϞσϧͱ‫؍‬ଌ஋͔ΒͷΈߏ੒͔ͨ͠Βɺղੳऀͷओ‫ͱ؍‬Ձ஋͸ೖΔ༨஍͕ͳ͍ɻ͜ͷࢹ఺Ͱ͸‫੍͍ڧ‬໿͕ͳ͍ͷͰɺ෯޿͍ࣄલؔ਺
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[ຊઅͷٞ࿦͸‫ాٶ‬༱Ұࢯ (ߴ࡚‫ࡁܦ‬େֶ)ɺখໆಁࢯ (ࡾॏେֶපӃ) ͱͷ‫ڞ‬ಉ‫͋Ͱڀݚ‬Δ]

パラメータ識別可能なグラフィカルモデルによる欠測を含んだ 2 × 2 分割
表の対称性の検定
糸洲弘 1 ，中川智之 2 ，田畑耕治 2
1

東京理科大学大学院理工学研究科，2 東京理科大学理工学部

1. はじめに縦断研究やケース・コントロール研究，前後テスト分析等で発生するデータは正方分
割表にまとめられる．これらの分割表においては，行の周辺分布と列の周辺分布が同等かどうかに関心がある．特に，2 × 2 分割表においては，対称性の検定によってこれを調べる（McNemar, 1947）．しかし，調査データには様々な理由から欠測が生じる．通常，欠測値を含むデータを分析するとき，欠測メカニズムを仮定する．欠測メカニズム
は MCAR，MAR，NMAR の３つに分類され (Little and Rubin, 2020)，NMAR の場合には完全に観測された部分のみで解析を行うとパラメータ推定値にバイアスが生じる．
そのため，無視不可能な欠測と呼ばれている．Ma et al. (2003) は，無視不可能な欠測を含む 2 × 2 分割表の欠測メカニズムをグラフィカルモデルを用いて示し，パラメータの識別可能性について議論した．
本報告では，無視不可能な欠測を含む 2 × 2 分割表の対称性の検定について議論する．
Ma et al. (2003) で提案されたパラメータ識別可能なグラフィカルモデルに対して，対称性の制約を導入した仮説検定を提案する．適合度検定に対数尤度比統計量を用いることから，最尤推定値の計算には EM アルゴリズムを用いた．また，提案法の第 1 種の誤り確率と検出力をモンテカルロ・シミュレーションにより評価した．

2. 提案手法
行変数と列変数をそれぞれ Y1 と Y2 とし，対応する変数の欠測指標を R1 と R2 とする．
欠測値を含んだ分割表に対して，同時分布 P (Y1 = y1 , Y2 = y2 , R1 = r1 , R2 = r2 )（以後，簡単のため P (y1 , y2 , r1 , r2 ) と記す）を考える. ただし，yt = j (t = 1, 2; j = 1, 2)，rt = k(t = 1, 2; k = 0, 1) であり，0 を観測，1 を欠測とする．Ma et al. (2003) は，パラメータ
識別可能なモデルの一つとして，図 1 のモデル (d) を提案した．
図 1: パラメータ識別可能なグラフィカルモデルの例（モデル (d) ）欠測値を含んだ分割表に対して，対称性はP (1, 2, r1 , r2 ) =P (2, 1, r1 , r2 )
r1

r2

r1

r2

と表される．モデル (d) において，同時分布は

P (y1 , y2 , r1 , r2 ) = P (y1 , y2 )P (r2 |y1 )P (r1 |r2 ) = πy1 y2 αr2 |y1 P (r1 |r2 )と表せるから，対称性の制約は π12 = π21 となることに注意する．図 1 のモデル (d) に対称性（π12 = π21 ）の制約を加えたもとでの最大対数尤度を求めるために EM アルゴリ
ズムを用いる．求めたいパラメータは θ = (π11 , π12 , π21 , π22 , α0|1 , α1|1 , α0|2 , α1|2 ) である．
E-step における Q 関数はQ(θ|θ (t) ) ∝

2
1 


nα(t)l|i log αl|i +l=0 i=1

2
2 


n(t)
πij log πij

i=1 j=1

で与えられる．ただし，⎧
(t) (t)α0|i πij⎪⎪(t)⎪nα0|i =
n00,ij + n10,+j  (t) (t) ,
⎪
⎪
⎪
⎪
j
i α0|i πij
⎪
⎪
⎪

⎪
(t) (t)(t)⎨α1|i πij
πij(t)nα1|i =
n01,i+  (t) + n11,++ ,(t) (t)
⎪
π
α
π
⎪
ij
ij
j
j
i,j
1|i
⎪
⎪
⎪
⎪
(t) (t)(t) (t)(t)⎪α0|i πij
α1|i πij
⎪
πij
⎪
(t)
⎪
,
⎪
⎩ nπij = n00,ij + n01,i+  (t) + n10,+j  (t) (t) + n11,++ (t) (t)j πij
i α0|i πij
i,j α1|i πijであり，n00,ij は完全観測部分のセル度数，n10,+j と n01,i+ は一方のみ観測できたセル度
数，n11,++ は両方観測できなかったセル度数である．M-step の最大化点は，陽に求められ
(t)

πij =

(t)

nπij + nπji
,
2N

(t)

αl|i =

nαl|i
(t)

(t)

nα0|i + nα1|i(t)で与えられる．ただし，N = i,j nπij である．これらの結果を用いた検定方式，モデル(d) 以外のパラメータ識別可能なグラフィカルモデルを用いた場合の結果，シミュレー
ションによる性能評価については当日報告する予定である．
参考文献
Little, J. A. and Rubin, D. B. (2020). Statistical Analysis with Missing Data, 3rd ed., Wiley,
Hoboken, New Jersey.
Ma, WQ., Geng, Z. and Li, XT. (2003). Identiﬁcation of nonresponse mechanisms for two-way
contingency tables. Behaviormetrika 30, 125–144.
McNemar, Q. (1947). Note on the sampling error of the diﬀerence between correlated proportions or percentages. Psychometrika 12, 153–157.
連絡先: 糸洲弘・中川智之・田畑耕治 ∗〒 278-8510 千葉県野田市山崎 2641
東京理科大学理工学部情報科学科∗ E-mail: kouji tahata@rs.tus.ac.jp

Deriving Lifetime Value of a Customer Who Exhibits Non-Poisson Purchase
Behavior㸸㸸 Application to Marketing Intervention for Customer Retention
Makoto Abe
The University of Tokyo

In non-contractual CRM where customer withdrawal cannot be observed, thewithdrawal is inferred by using BTYD (Buy Till You Die) models, such as Pareto/NBD.
One advantage of a Pareto/NBD model --- the benchmark for customer-base analysis--- is that it requires minimal purchasing data from customers, namely recency andfrequency. The tradeoff is the model posits strong assumptions on consumer behavior.
Of those, the most restricting assumption is the Poisson purchase, which imposes amemoryless purchase process, implying that purchase occurs independent of theprevious interpurchase time. The assumption is appropriate when purchases involvea wide variety of categories, such as purchases at a department store or an online
shopping mall, since transactions tend to occur randomly. However, whentransactions occur cyclically, for example, by focusing on a narrower product category,
this assumption may not be satisfied. Furthermore, Pareto/NBD assumes that the two
gamma distributions for the purchase rate and the withdrawal rate are independent.
This ignores the association between the purchase behavior and the withdrawal
behavior.
This research proposes a general purchase model that can accommodate either
memoryless or cyclic pattern, which is then applied to customer-base analysis. Similar
to the Pareto / NBD model, which has abundant previous research, it is assumed thatthe withdrawal is random and the amount per transaction follows a lognormal
distribution within a customer, while a logistic threshold model captures the purchaseperiodicity. The proposed model (1) provides customer-specific measures fortransaction cyclicity and lifetime value, (2) permits more accurate estimation ofindividual probabilities of being active, (3) results in a more reliable estimate forcustomer-base.
In the empirical analysis, customer transaction data from a hair salon was used tocompare the individual model assuming random purchase and the aggregate model(Pareto / NBD) based on the mixture distribution. The proposed model was superior tothese two models in terms of prediction and parameter stability. Furthermore, as anapplication to customer retention strategies, the optimal intervention level thatmaximizes the increase in lifetime value was calculated for each customer.
Keywords: Customer Lifetime Value (CLV), BDTY Model, Random Purchasing,
Periodicity, Pareto / NBD, Poisson

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, 3HUVRQDOL]DWLRQKHWHURJHQHLW\PRGHOLQJ,, /DUJHVFDOHGDWDKLJKGLPHQVLRQDOVSDUVHPRGHOLQJ
,,, 1HWZRUNDQG8*&GDWDFRPPXQLW\GHWHFWLRQXVLQJQHWZRUNDQGXVHUJHQHUDWHG
FRQWHQWVLQVRFLDOPHGLD,H[SODLQWKHVWDWLVWLFDODQGPDUNHWLQJPRGHOVRQWKHVHWRSLFVE\WKHUHWURVSHFWLYHUHYLHZRIRXUZRUNVDQGFRQFOXGHE\VWDWLQJFXUUHQWDQGIXWXUHUHVHDUFKA Choice Model of Utility Maximization
and Regret Minimization

Abstract
Consumers often try to achieve multiple goals when purchasing products and services, wherechoices are sought that maximize utility and other objectives such as to minimize regret. If
the choice outcomes are associated with high level of uncertainty at the time of purchase,
consumers worry that the alternative of interest may turn out to be not optimal and theywant to avoid this when making a purchase. We ﬁrst propose a new regret function andexplore its properties. Then we propose a generalized framework of multiple goal pursuitand apply it to a utility maximization and regret minimization problem. Pareto optimal sets
are an outcome of multiple goal optimization problems where there exists multiple alternatives that are non-dominated. Our proposed framework allows us to generalize a dual-goalproblem as a constrained optimization problem where either utility is maximized subject toconstraints on regret, or regret is minimized subject to utility constraints. The proposedmodel ﬁts the data better, provides improved predictions and oﬀers a tractable solution toa problem of utility maximization and regret minimization.

Keywords: Multiple Goal Pursuit, Performance Uncertainty, Consideration Sets

The Impact of Gig Economy on Product Quality through the Labor Market:
Evidence from Ride-sharing and Restaurant Quality
Minkyu Shinѽ Jiwoong Shin† Soheil Ghili†

Jaehwan Kim‡

City University of Hong Kongѽ, Yale School of Management†, Korea University Business School‡

The rapid growth of the gig economy in recent years has transformed many sectors of theeconomy. Airbnb has challenged the hotel industry; Uber and Lyft have challenged traditional
taxi companies and curtailed ridership on public transportation. And while these effects of gig
work on direct competitors is very important, more indirect effects also merit attention.
This paper seeks to demonstrate the impact of the gig economy on the local economy beyond
directly related incumbent industries through the labor market. We look at the restaurant
industry as a case study for service sector. We design our analysis around a natural experiment
where, due to regulatory shifts, Uber and Lyft exited the market in Austin, Texas, in May 2016
and returned in May 2017. Leveraging this exogenous exit and reentry, we conduct a series ofanalyses to study the relationship between rideshare and restaurant quality. Specifically, we areinterested in examining the following hypothesis: The presence of Uber and Lyft in a city
provides individuals with gig-work opportunities.
We first establish the relationship between the presence of ride-sharing companies andrestaurant quality by analyzing how the quality of restaurant service in Austin responds to thepresence of Uber and Lyft. We employ text analysis and difference-in-difference(DiD
henceforth) approach to determine whether the entry and exit of Uber and Lyft influenced
customer satisfaction with local restaurants. Dallas serves as a control group. We use every
Yelp review of restaurants in Austin and Dallas from 2014 to 2019 to measure quality. Thisentails text analysis of each review to capture restaurant quality along two dimensions: service
and food. First, leveraging a difference-in-difference setting, we find that the quality of service
decreases in Austin relative to Dallas with the presence of Uber and Lyft.
Secondly, we carry out our main analysis a second time looking at customer satisfaction withfood quality, rather than service quality, as our dependent variable. We hypothesize that
customer experience with the food quality would be less influenced by the presence of Uberand Lyft than is the service quality. Employees in charge of the food quality such as chefs
working in the kitchen are not much attracted by the opportunity to drive for Uber and Lyft,
relative to workers such as wait-staff mostly dealing with the service for customers. We
demonstrate that the customer evaluation of food quality does not change before and after Uberand Lyft’s re-entry to Austin.
Third, we divide restaurants into two tiers based on pricing labels provided by Yelp. One groupconsists of restaurants that are assigned a single dollar sign($) in Yelp, meaning they are cheaper.
The rest of the restaurants, those with two or three dollar signs($$-$$$), comprise the second
group. Workers in low-tier restaurants would be paid less, either because their base hourly wage
is lower or their tipped income is lower. Therefore, we expect Uber and Lyft’s impact to bemore pronounced for a single dollar sign restaurants whose service workers are more likely to
be lured by gig-work opportunities. Our empirical analysis confirms this expectation. We findthat the effect of Uber and Lyft in Austin on service quality is significant for single-dollar sign
restaurants. In contrast, we do not find any significant effect for high-tier restaurants.
Next, we directly test our mechanism by examining turnover rates of staff at restaurants byleveraging a unique worker-level dataset of restaurants in Austin and Dallas from 2014 to 2019.
We examine how the turnover rate of staff in Austin’s restaurants changes with the local activityof Uber and Lyft relative to Dallas. We find that the turnover rate increases in Austin relative
to Dallas after Uber and Lyft return. Additionally, in the same spirit as the dollar-sign analysis
in Yelp Data, we use the restaurant category information in the dataset to examine whether we
see a similar pattern in the turnover rates for different restaurant tiers. In our hypothesis, we
expect the effect of Uber and Lyft on turnover rates to be stronger for low-end restaurant
categories than relatively high-end restaurants. We conduct separate DiD analyses for eachcategory and indeed find an increase in turnover only for low-end restaurants. In contrast, we
do not see such a pattern for middle-end or high-end restaurants.
We then delve deeper into the analysis by decomposing the turnover rates into those for “backof-house” staff and “front-of-house” staff. The latter group represents those who directly deal
with customers and consists mainly of service staff, whereas the former includes higher-paid
positions such as managers and chefs. The results are consistent with the Yelp review data
analysis: the increase in turnover is observed only for front-of-house workers, while there is no
significant effect for back-of-house staff.
Finally, we check our results by conducting several robustness checks and discuss otheralternative explanations based on demand-side channels. One would expect some otherchannels through which the rideshare companies could have impacted the local economy, suchas the demand changes due to the easier mobilization. While we cannot completely rule out all
possible explanations, we show that these alternative accounts cannot fully explain the patterns
observed in our data. We present other evidence suggesting that our findings are more likely toarise from the supply-side channel through the labor market rather than the demand-side
channels.
Our paper also contributes to marketing literature, especially in service marketing and the roleof employee for customer satisfaction, making a connection between employee turnover andcustomer satisfaction about a restaurant’s service quality. This work shows that the expansionof the gig economy, by providing new work opportunities for low-wage, low-skilled workers,
has far-reaching and significant ramifications on broader industries through the labor market.
As the gig economy expands, as it is predicted to do, understanding these second-order effects
will be critical for the development of effective regulatory policy. Our work focuses on thehospitality sector, but we consider it a telling case study for the service economy as a wholeand hope it serves as a starting point for deeper study of how the gig work may shape the future
economy.

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Kazuma Sawaya and Yoshimasa Uematsu
Department of Economics and Management, Tohoku University

1

Model and the Rank Lasso

We consider the high-dimensional linear modely = Xβ 0 + ε,(1)where y = (y1 , . . . , yn ) is the vector of n independent responses, β 0 ∈ Rp is the sparse coeﬃcient
vector, X = (X1 , . . . , Xn ) is the empirically centered n independent observations of p features,and ε = (ε1 , . . . , εn ) is the i.i.d. error vector with density function f (·). Let S ⊂ {1, . . . , p} denote the set of important variables; i.e., S = {j : βj0 = 0}. Our goal is to propose a robust method
to yield “discoveries” S of S with controlling the false discovery rate (FDR), E |S c ∩ S|/|S| ,below predetermined level.
Wang et al. (2020) propose the rank Lasso estimator
⎧
⎫
⎨
⎬

1
(2)
(yi − yj ) − (Xi − Xj ) β + λβ1 ,β = arg min⎭β∈Rp ⎩ n(n − 1)i=jwhich is robust to heavy-tailed error distribution such as Cauchy distribution. Using this estimator, we propose a new method for variable selection.

2

New Methodology

We start with removing the bias of β to make it asymptotically normal in a similar way of thedebiased Lasso estimator(Javanmard and Montanari, 2014). Deﬁne
β d := β + 11

f 2 (u)du 2n(n + 1)

ΘX  (2r(ε) − (n + 1)),(3)where Θ is a consistent estimator of the precision matrix Θ = E[X1 X1 ]−1 , ε = y − X β, andr(·) is the rank. Thanks to the asymptotic normality of βjd as shown below, some selection
algorithms with this estimator work well. Speciﬁcally we employ the data-splitting method of(Dai et al., 2020); see Algorithm 1.

3

Theoretical Results

We justify that our Algorithm 1 controls the FDR under the preassigned level.
Theorem 1 Under regularity conditions, we have for any j ∈ {1, . . . , p},√n(βjd − βj0 ) = Zj + Δj ,√where Z = [ 12n f 2 (u)du]−1 Θ S(ε) and Δ is some remainder such that


1
d

Θ
Δ∞ = op (1).
Zj → N 0,
jj ,12[ f 2 (u)du]2
1(5)

Algorithm 1 FDR control via a single data split with the debiased rank Lasso
1. Split the data into two groups (y (1) , X (1) ) and (y (2) , X (2) ), independent to the response
vector y.
2. Estimate (3) for each group as impact coeﬃcients β d(1) and β d(2) with some Θ(1) , Θ(2) oneach part of the data.
3. Calculate the mirror statistics 
Mj = sign β d(1) β d(2) g |β d(1) |, |β d(2) | ,where function g(u, v) is non-negative, symmetric about u and v, and monotonically increasing in both u and v.
4. Given a designated FDR level q ∈ (0, 1), calculate the cutoﬀ τq as:#{j : Mj < −t}≤q .
=τq = min t > 0 : FDP(t)#{j : Mj > t} ∨ 1(4)

5. Select the features {j : Mj > τq }.
√Theorem 2 For any designated FDR level q ∈ (0, 1), assume that s log pn and that there
exists a constant tq > 0 such that 2(FDP(tq ) ≤ q) → 1 as p → ∞. Then, under regularity
conditions, we have
lim sup FDR(τq ) ≤ q.
n,p→∞In the presentation, we will conﬁrm the validity and robustness of our procedure throughnumerical experiments.

References
Dai, C., B. Lin, X. Xing, and J. S. Liu (2020). False discovery rate control via data splitting.
arXiv preprint arXiv:2002.08542 .
Javanmard, A. and A. Montanari (2014). Conﬁdence intervals and hypothesis testing for highdimensional regression. The Journal of Machine Learning Research 15 (1), 2869–2909.
Wang, L., B. Peng, J. Bradic, R. Li, and Y. Wu (2020). A tuning-free robust and eﬃcientapproach to high-dimensional regression. Journal of the American Statistical Association,
1–44.

2

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Machine Collaboration∗
Qingfeng Liu† and Yang Feng‡
February 5, 2022
Ensemble learning has emerged and been extensively studied by many in the past few decades(e.g., Dasarathy and Sheela (1979), Schapire (1990), Ho (1995), and Breiman (1996)), with its
popularity recently skyrocketing (e.g., Lu and Van Roy (2017), Yu et al. (2018), Qi et al. (2019),
and Tian and Feng (2021)). Mendes-Moreira et al. (2012), Sagi and Rokach (2018), and Dong et al.
(2020) are some recent comprehensive surveys. The general idea of ensemble learning is to combine
the predictions obtained from diﬀerent learning methods (hereafter, base machines), or predictions
based on diﬀerent subsamples or diﬀerent feature spaces, in order to improve prediction performance.
Bagging, stacking, and boosting are three prominent examples. In bagging (Breiman, 1996) andstacking, base machines are ﬁrst run in parallel and independently, and then the ﬁnal prediction isconstructed as a simple/weighted average of the predictions from these base machines. In boosting(Schapire et al., 1998), the base machines work jointly in a top-down manner. In all three algorithms,
the output from each base machine is ﬁxed after being calculated. Like human collaboration, anidea that may yield potential improvement is to let diﬀerent kinds of base machines communicate
with each other and update their outputs after observing the predictions of the other base machines.
Based on this idea, we propose the Machine Collaboration (MaC) ensemble learning framework withheterogeneous base machines, where the word heterogeneous stands for that the base machines are ofdiﬀerent types (e.g. DT, DNN, Ridge Regression). Compared with bagging, stacking, and boosting,
MaC has the following desirable features. Figure 1 provides the schematic for bagging, stacking,boosting, and MaC. As illustrated, bagging and stacking are parallel & independent, boosting issequential & top-down, while MaC is circular & recursive. In the framework of MaC, base machines
work in a circular manner. Further, the circulation goes multiple rounds. Valuable information ispassed recursively through base machines around a “round table", but not top-down. In this process,the base machines update their structures and/or parameters once in each round, according to theinformation received from the other machines. We demonstrate that MaC can deliver competitive
performance when compared with the base machines or other ensemble methods.
∗ The authors gratefully acknowledge the support of the Japan Society for the Promotion of Science through
KAKENHI Grant No. JP19K01582 (Liu), the Nomura Foundation for Social Science Grant No. N21-3-E30-010 (Liu)and a National Science Foundation CA-REER Grant No. DMS-1554804 (Feng).
† Corresponding author. Department of Economics, Otaru University of Commerce, Otaru City, Hokkaido, Japan.
Email: qliu@res.otaru-uc.ac.jp.
‡ School of Global Public Health at New York University, NY, NY, USA. Email: yang.feng@nyu.edu.

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1hReferences
Breiman, L., 1996. Bagging predictors. Machine learning 24, 123–140.
Dasarathy, B.V., Sheela, B.V., 1979. A composite classiﬁer system design: Concepts and methodology. Proceedings of the IEEE 67, 708–713.
Dong, X., Yu, Z., Cao, W., Shi, Y., Ma, Q., 2020. A survey on ensemble learning. Frontiers ofComputer Science 14, 241–258.
Ho, T.K., 1995. Random decision forests, in: Proceedings of 3rd international conference on document analysis and recognition, IEEE. pp. 278–282.
Lu, X., Van Roy, B., 2017. Ensemble sampling, in: Guyon, I., Luxburg, U.V., Bengio, S., Wallach,
H., Fergus, R., Vishwanathan, S., Garnett, R. (Eds.), Advances in Neural Information Processing
Systems, Curran Associates, Inc.. pp. 3259–3267.
Mendes-Moreira, J., Soares, C., Jorge, A.M., Sousa, J.F.D., 2012. Ensemble approaches for regression: A survey. Acm computing surveys (csur) 45, 1–40.
Qi, Y., Liu, B., Wang, Y., Pan, G., 2019. Dynamic ensemble modeling approach to nonstationary
neural decoding in brain-computer interfaces, in: Wallach, H., Larochelle, H., Beygelzimer, A.,d'Alché-Buc, F., Fox, E., Garnett, R. (Eds.), Advances in Neural Information Processing Systems,
Curran Associates, Inc.. pp. 6087–6096.
Sagi, O., Rokach, L., 2018. Ensemble learning: A survey. Wiley Interdisciplinary Reviews: Data
Mining and Knowledge Discovery 8, e1249.
Schapire, R.E., 1990. The strength of weak learnability. Machine Learning 5, 197–227.
Schapire, R.E., Freund, Y., Bartlett, P., Lee, W.S., 1998. Boosting the margin: A new explanation
for the eﬀectiveness of voting methods. The annals of statistics 26, 1651–1686.
Tian, Y., Feng, Y., 2021. Rase: Random subspace ensemble classiﬁcation. Journal of Machine
Learning Research .
Yu, Z., Luo, P., Liu, J., Wong, H.S., You, J., Han, G., Zhang, J., 2018. Semi-supervised ensemble
clustering based on selected constraint projection. IEEE Transactions on Knowledge and Data
Engineering 30, 2394–2407.

2ίϩφՒʹ͓͚Δ‫ײ‬છ֦େ๷ࢭରࡦͷਓྲྀ཈੍ޮՌʹؔ͢Δ࣮ূ෼ੳ౦๺େֶ ࠤ౻ Ӊथେࡕࢢཱେֶ ࠇా ༤ଠ౦๺େֶ দా ҆ণຊ‫ڀݚ‬ͷ໨త͸ɺ৽‫ܕ‬ίϩφ΢Πϧε‫ײ‬છ঱ͷ‫ײ‬છ֦େ๷ࢭΛ໨తͱͨ͠ਓྲྀ཈੍੓ࡦͷޮՌΛ࣮ূతʹ໌Β͔ʹ͢Δ͜ͱͰ͋Δɻ2020 ೥ 1 ݄Ҏ߱ɺ৽‫ܕ‬ίϩφ΢Πϧε‫ײ‬છ঱ͷ‫ײ‬છ֦େ͸ੈք‫ن‬໛Ͱ‫ى‬͓ͬͯ͜Γɺͦͷ‫ײ‬છ֦େΛ཈੍͢Δ͜ͱ͸ۙ೥ͷॏཁͳ՝୊ͷҰͭͱͳ͍ͬͯΔɻ೔ຊʹ͓͍ͯ΋ɺ੓෎΍஍ํ࣏ࣗମ͕த৺ͱͳΓɺ͜Ε·Ͱʹ‫ࣄٸۓ‬ଶએ‫ݴ‬΍·ΜԆ๷ࢭ౳ॏ఺ાஔͳͲͷ੓ࡦ͕ਓྲྀͷ཈੍Λ໨తʹߦΘΕ͖ͯͨɻએ‫ݴ‬Λߦ͏͜ͱͰਓʑͷҠಈ΍ߦಈΛ੍‫͢ݶ‬Δ͜ͱ͕ՄೳʹͳΓɺ৽‫ܕ‬ίϩφ΢Πϧεͷ‫ײ‬છ֦େ๷ࢭʹޮՌ͕͋Δͱߟ͑ΒΕ͍ͯΔɻ͔͠͠ɺએ‫ʹ࣌ݴ‬͸֎ग़੍‫ݶ‬΍ࣗॗʹΑ
Δ‫ࡁܦ‬ͷఀ଺΍ɺҿ৯ళ΁ͷิॿۚͷࢧ‫Ͳͳڅ‬ͷ‫ࡁܦ‬ίετ͕ൃੜ͍ͯ͠Δɻ೔ຊશࠃͷਓྲྀσʔλΛ༻͍ͯ੓ࡦͷਓྲྀ཈੍ޮՌΛσʔλ͔Βఆྔతʹ໌Β͔ʹ͢Δ͜ͱ͸ɺ‫ߦࡏݱ‬ΘΕ͍ͯΔิॿۚʹΑΔ
ॴಘͷ࠶෼഑͕ద੾Ͱ͋Δ͔൱͔Λ‫͢ূݕ‬ΔͨΊʹ΋ॏཁͰ͋Δɻຊ‫ڀݚ‬ͷಛ௃͸ҎԼͷ 3 ఺Ͱ͋Δɻ1 ఺໨͸ԤถͰ͸ͳ͘೔ຊͷਓྲྀσʔλΛ࢖༻͍ͯ͠Δ఺Ͱ͋Δɻσʔλ΁ͷΞΫηεͷ༰қ͞ͳͲ͔Βɺ‫ط‬ଘ‫ڀݚ‬ͷଟ͘͸ԤถͷਓྲྀσʔλΛ༻͍ͯਓྲྀ཈੍੓ࡦͷޮՌΛ‫͍ͯ͠ূݕ‬Δɻຊ‫Ͱڀݚ‬͸೔ຊͷਓྲྀσʔλΛ࢖༻͢Δ͜ͱͰɺਓྲྀ཈੍੓ࡦͷޮՌ͕Ԥถͷࠃʑͱ೔ຊͰ͸ͲͷΑ͏ʹҟͳΔͷ͔ʹ͍ͭͯ໌Β͔ʹ͢Δɻ2 ఺໨͸ 2021 ೥Ҏ߱ͷ৽‫ܕ‬ίϩφ΢Πϧε‫ײ‬છ঱ͷ‫ײ‬છ֦େͷୈ 2 ೾Ҏ߱ͷ੓ࡦͷޮՌ΋ධՁ͍ͯ͠Δ఺Ͱ͋Δɻ‫ط‬ଘ‫Ͱڀݚ‬͸‫ײ‬છ֦େॳ‫ظ‬ͷ 2020೥લ൒ʹߦΘΕͨ੓ࡦͷධՁΛߦ͍ͬͯΔ΋ͷ͕ଟ͍ɻຊ‫Ͱڀݚ‬͸ 2020 ೥݄͔̍Β 2021 ೥ 9 ݄·ͰͷσʔλΛ༻͍ͯ෼ੳΛߦ͏͜ͱͰɺ2021 ೥Ҏ߱ʹ࣮ࢪ͞Εͨ 2 ճ໨Ҏ߱ͷ‫ࣄٸۓ‬ଶએ‫ݴ‬ͷޮՌ΋‫͠ূݕ‬ɺ੓ࡦͷճ਺͕૿͑ΔʹͭΕͯɺ੓ࡦͷޮՌ͕ͲͷΑ͏ʹมԽ͢Δͷ͔ʹ͍ͭͯ໌Β͔ʹ͢Δɻ3 ఺໨͸஍ҬͷಛੑΛද͢ࢢຽࢿຊͱ͍͏֓೦Λ༻͍ͯɺ੓ࡦޮՌͷ஍Ҭࠩʹؔͯ͠෼ੳ͍ͯ͠Δ఺Ͱ͋Δɻઌߦ‫Ͱڀݚ‬͸ͦͷ஍Ҭͷਓʑͷརଞੑ΍ެ‫ڞ‬ੑΛਤΔࢦඪͰ͋ΔࢢຽࢿຊΛ༻͍ͯɺ੓ࡦޮՌͷ஍ҬࠩΛ໌Β͔ʹ͍ͯ͠Δɻຊ‫͍͓ͯʹڀݚ‬΋ɺ౤ථ཰͔Β࡞੒͞Ε֤ͨ஍ҬͷࢢຽࢿຊΛ༻͍Δ͜ͱͰɺ೔ຊ
ʹ͓͍ͯ΋ࢢຽࢿຊͷ஝ੵʹԠͯ͡ɺ੓ࡦޮՌͷ஍Ҭ͕ࠩଘࡏ͢Δ͜ͱΛ໌Β͔ʹ͢Δɻ
ຊ‫Ͱڀݚ‬͸ NTT υίϞ͕ఏ‫͍ͯ͠ڙ‬ΔϞόΠϧۭؒ౷‫ܭ‬σʔλΛ༻͍ͯ࡞੒ͨ͠ਓྲྀσʔλʹɺ‫ݻ‬ఆޮՌύωϧσʔλϞσϧΛԠ༻͢Δ͜ͱͰɺҎԼͷ࣮ূ෼ੳ݁ՌΛಘͨɻ·ͣɺ‫ࣄٸۓ‬ଶએ‫ݴ‬΍·ΜԆ๷ࢭ౳ાஔͷ੓ࡦ͕ߦΘΕ͍ͯΔ‫ʹؒظ‬͸੓ࡦ͕ߦΘΕ͍ͯͳ͍‫ͱؒظ‬ൺֱͯ͠ɺਓྲྀ͕཈੍͞Εͯ
͍Δ͜ͱ͕໌Β͔ʹͳͬͨɻ·ͨɺએ‫࣌ݴ‬Ҏ֎ͷฏ࣌Ͱ΋ਓྲྀ͸ 2020 ೥લ൒ͷ৽‫ܕ‬ίϩφ΢Πϧε‫ײ‬છ঱ͷ‫ײ‬છ֦େҎલͷਫ४ʹ͸໭͍ͬͯͳ͍͜ͱ΋ࣔ͞Εͨɻ࣍ʹɺࢢຽࢿຊΛ༻͍ͨ੓ࡦޮՌͷ஍Ҭࠩͷൺֱ͔Βɺ1 ճ໨΍̎ճ໨ͳͲͷ‫ࣄٸۓ‬ଶએ‫ݴ‬ͷճ਺͕গͳ͍࣌‫ʹظ‬͸Ͳͷ஍ҬͰ΋੓ࡦͷޮՌ͸΄΅ಉ͕ͩ͡ɺ̏ճ໨΍̐ճ໨ͱએ‫ݴ‬ͷճ਺͕ଟ͘ͳΔʹͭΕͯɺࢢຽࢿຊͷߴ͍஍ҬΑΓ΋௿͍஍Ҭͷਓʑͷྲྀग़Λ཈੍͢ΔޮՌ͕௿͘ͳ͖͍ͬͯͯΔ͜ͱ͕໌Β͔ʹͳͬͨɻ·ͨɺҿञʹؔ͢Δ੓ࡦͷҧ͍Λ༻͍ͨ෼ੳ͔Βɺࢢຽࢿຊͷߴ͍஍ҬͰ͸੍‫ݶ‬ͷ‫͍ڧ‬੓ࡦΛͱΔ΄Ͳͦͷ஍Ҭͷਓʑͷଞ஍Ҭ΁ͷྲྀग़Λ཈੍͢ΔޮՌ͕‫ͳ͘ڧ‬Δ͕ɺࢢຽࢿຊͷ௿͍஍Ҭͷਓʑʹؔͯ͠͸੍‫ݶ‬Λ‫ͯ͘͠ڧ‬΋ޮՌ͕มΘΒͳ͍͜ͱ͕ࣔ͞Εͨɻ࣮ূ෼ੳ݁Ռ͔ΒಘΒΕΔߟ࡯͸࣍ͷ̎఺Ͱ͋Δɻ̍఺໨ͱͯ͠ɺࢢຽࢿຊͷ௿͍஍Ҭͷਓʑͷྲྀग़Λ཈੍͢Δʹ͸ҿञͷ‫ࢭې‬΍ఏ‫ؒ࣌ڙ‬ͷ୹ॖ͚͚ͩͩͰͳ͘ɺҿ৯ళͷӦ‫Ͳͳࢭېۀ‬ɺΑΓ‫͍ڧ‬੓ࡦ͕ඞཁͰ͋Δͱߟ͑ΕΔɻ2 ఺໨ͱͯ͠ɺਓྲྀ཈੍੓ࡦΛߦ͏ͱɺࢢຽࢿຊͷߴ͍஍Ҭͷਓʑͷྲྀग़͸཈͑ΒΕΔ͕ɺͦͷ஍Ҭ΁ଞͷ஍Ҭͷਓʑ͕Ҡಈ͢Δྲྀೖ͸཈͑Δ͜ͱ͕Ͱ͖ͳ͍ɻͦͷͨΊɺྲྀೖΛ‫ݮ‬Βͨ͢Ίʹ͸ɺࢢຽࢿຊͷ௿͍஍Ҭ͚ͩͰͳ͘ɺߴ͍஍Ҭʹؔͯ͠΋͜Ε·ͰҎ্ʹ੍‫ݶ‬ͷ‫͍ڧ‬੓ࡦΛಉ࣌ʹߦ͏ඞཁ͕͋Δͱߟ͑ΒΕΔɻ

㉎ධᆺࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࡢ㈨㔠ㄪ㐩ࣃࢱ࣮ࣥศᯒ
ෆ⏣ᙯᾈ㸦⟃Ἴ኱Ꮫ኱Ꮫ㝔㸧࣭కṇ㝯㸦⟃Ἴ኱Ꮫ㸧 ㏆ᖺࠊ㉎ධᆺࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࡢᕷሙつᶍࡀᣑ኱ࡋ࡚࠾ࡾࠊྠᕷሙࡢ࣓࢝ࢽࢬ࣒ࡢ⌮ゎࡀᚲせ࡜ࡉࢀ࡚࠸ࡿࡀࠊ᪂⯆ศ㔝࡛࠶ࡿࡓࡵᏛ⾡࣭ᐇົ࡜ࡶ࡟ࡑࡢ⌮ゎࡣ㐍ࢇ࡛࠸࡞࠸ࠋ
ෆ⏣࣭క㸦2022, ᪥ᮏ࣋ࣥࢳ࣮ࣕᏛ఍ㄅ㸧࡛ࡣ㉎ධᆺࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࣉࣟࢪ࢙ࢡࢺ
㸦௨ୗࠊPJ㸧ࡢ᭱⤊ⓗ࡞㉎㈙௳ᩘ࡜ࠊPJ ࡀᥖࡆࡿ┠ᶆ㔠㢠ࢆ㉸࠼ࡿ㈨㔠ࢆㄪ㐩ฟ᮶ࡓ࠿ྰ
࠿ࡢ PJ ᡂྰ࡟ࡘ࠸࡚ࠊ₯ᅾࢡࣛࢫᅇᖐࣔࢹࣝ࡟ࡼࡗ࡚⌮ゎࢆ῝ࡵࡓࠋᮏ◊✲࡛ࡣ PJ ࡢ㈨㔠ㄪ㐩ࣃࢱ࣮ࣥ࡟ࡘ࠸࡚ࠊBass ࣔࢹࣝ࡬ࡢ㐺⏝࡟ࡼࡗ࡚⌮ゎࢆ῝ࡵࡿࠋBass ࣔࢹࣝࡀᑐ㇟࡜ࡍࡿ⌧㇟ࡣࠊ㢖⦾࡟ࡣ㉎ධࡉࢀ࡞࠸〇ရ࡟࠾ࡅࡿึᅇ㉎㈙࡟ࡼࡿ
〇ရᬑཬ࡛࠶ࡿࠋ㉎ධᆺࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢ࡛ᢅ࠺ฟ㈨࡬ࡢᑐ౯㸦ࣜࢱ࣮ࣥ㸧ࡣࠊ୍⯡ⓗ࡞ᑠ኎ᗑ࡛ࡣ㉎ධ࡛ࡁ࡞࠸〇ရࡸࠊᕷ㈍ࡉࢀࡿ๓ࡢ〇ရ࡛࠶ࡾࠊࡉࡽ࡟ PJ ⤊஢ࡲ࡛ࣜࢱ
࣮ࣥࢆᡭ࡟ྲྀࡿࡇ࡜ࡣฟ᮶ࡎࠊPJ ᮇ㛫ෆ࡟ࣜࣆ࣮ࢺ㉎㈙ࡀฟ᮶࡞࠸ࡶࡢ࡛࠶ࡾࠊBass ࣔࢹࣝࡀᑐ㇟࡜ࡍࡿ⌧㇟࡜ࡢ㢮ఝⅬࡀ࠶ࡿ࡜⪃࠼ࡿࠋࡲࡓࠊBass ࣔࢹࣝࡀ᝿ᐃࡍࡿ࢖ࣀ࣮࣋ࢱ
࣮࡜࢖࣑ࢸ࣮ࢱ࣮࡟ࡘ࠸࡚ࡶࠊPJ 㜀ぴ᫬ࡢ㈨㔠ㄪ㐩ලྜࢆ⪃៖ࡏࡎ࡟ពᛮỴᐃࡍࡿฟ㈨⪅࡜ࠊࡑ࠺࡛ࡣ࡞࠸ฟ㈨⪅ࡢᏑᅾ࡜ࡋ࡚ࡑࢀࡒࢀ᥼⏝ࡍࡿࡇ࡜ࡀฟ᮶ࡿ࡜⪃࠼ࡿࠋࡋ࠿ࡋࠊ୍⯡ⓗ࡞〇ရࡢᬑཬ࡜␗࡞ࡾࠊPJ ࡢᐇ᪋ᮇ㛫ࡀ᭷㝈࡛࠶ࡿࡏ࠸࠿ࠊBass ࣔࢹ࡛ࣝࡣ᝿ᐃࡉࢀ
࡞࠸ PJ ᐇ᪋ᮇ㛫ᮎᮇ࡛ࡢฟ㈨㸦㉎㈙㸧ࡢ㞟୰ࡀ࠶ࡾࠊ㉎ධᆺࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢ㈨㔠
ㄪ㐩ࣃࢱ࣮ࣥࢆศᯒࡍࡿࡢ࡟㐺ࡋࡓࣔࢹࣝࡀᚲせ࡛࠶ࡾࠊᮏ◊✲࡛ᥦ᱌ࡍࡿࠋ
 PJ ࡢ㈨㔠ㄪ㐩᫬⣔ิࢹ࣮ࢱࡣࠊPJ 㛤ጞ┤ᚋ࠿ࡽ⤊஢ࡲ࡛➼᫬㛫㛫㝸࡛グ㘓ࡉࢀࡓࠊྛ᫬
Ⅼࡢ㉎㈙௳ᩘࢹ࣮ࢱ࡛࠶ࡿࠋ᫬㛫ࢆ t ሺ‫ ݐ‬ൌ 1, … , ܶሻ࡜ࡋࠊnt ࢆ t ᮇ࡟࠾ࡅࡿ㉎㈙௳ᩘ࡜ࡍࡿ
࡜ࠊࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࡢኚᩘ࡛⾲⌧ࡍࡿ Bass ࣔࢹࣝࡣ݊௧ ൌ ‫݂ݑ‬௧ ൌ ‫ ݌ݑ‬ቀ1 െே೟௨ቁ ൅ ‫ݍݑ‬

ே೟
௨

ቀ1 െ

ே೟
௨

ቁ ൌ ‫݌ݑ‬ሺ1 െ ‫ܨ‬௧ ሻ ൅ ‫ܨݍݑ‬௧ ሺ1 െ ‫ܨ‬௧ ሻ       (1)࡜࡞ࡿࠋࡇࡇ࡛ u ࡣ PJ ⤊஢᫬Ⅼࡢ₯ᅾⓗ࡞⥲㉎㈙௳ᩘࣃ࣓࣮ࣛࢱࠊ݊௧ ࡜ܰ௧ ࡣࡑࢀࡒࢀ t ᮇ࡟࠾ࡅࡿ㉎㈙௳ᩘ࡜ t ᮇࡲ࡛ࡢ⣼✚㉎㈙௳ᩘࠊp ࡜ q ࡣࡑࢀࡒࢀ࢖ࣀ࣮࣋ࢱ࣮ಀᩘ࡜࢖࣑ࢸ
࣮ࢱ࣮ಀᩘ࡛࠶ࡿࠋ݂௧ ࡜‫ܨ‬௧ ࡣࡑࢀࡒࢀ݊௧ ࡜ܰ௧ ࡟ᑐᛂࡍࡿ๭ྜࢹ࣮ࢱ࡛࠶ࡿࠋBass(1969)࡟࠶
ࡿࡼ࠺࡟ࠊ୍⯡ⓗ࡞ゎἲ࡛ࡣࠊ(1)ᘧࡢᚤศ᪉⛬ᘧࢆゎ࠸࡚ࠊ᫬㛫ࢆㄝ᫂ኚᩘ࡜ࡍࡿ㠀⥺ᙧᅇᖐ࡟ࡼࡗ࡚ࣃ࣓࣮ࣛࢱࢆ᥎ᐃࡍࡿࠋ ᮏ◊✲࡛ࡣࠊBass ࣔࢹࣝࢆᇶᮏࣔࢹࣝ࡜ࡋ࡚ࠊPJ ࡢᐇ᪋ᮇ㛫ࡀ᭷㝈࡛࠶ࡿࡇ࡜࡜ࠊࢡࣛ
࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢ㈨㔠ㄪ㐩ࣃࢱ࣮ࣥࡢ≉ᚩ࡛࠶ࡿࠊPJ ᮎᮇ࡟㉎㈙ࡀ㞟୰ࡍࡿഴྥࢆ⤌ࡳ㎸ࢇࡔࣔࢹࣝࡢᥦ᱌ࢆ⾜࠺ࠋලయⓗ࡟ࡣࠊ(1)ᘧ࡟㏻ᖖࡢ Bass ࣔࢹ࡛ࣝࡣ⾲⌧ࡋࡁࢀ࡞࠸
PJ ᮎᮇࡢ㉎㈙ࡢ㞟୰ࢆ⾲⌧ࡍࡿ㛵ᩘ݃௧ ൌ ‫ ݐݎ‬௞ ሺ‫ ݐ‬െ ‫ݏ‬ሻ, ࡓࡔࡋ ‫ ݏ‬ൌ

௞ାଵ
௞ାଶ

                       (2)ࢆ㏣ຍࡍࡿࡇ࡜࡛࠶ࡿࠋPJ ⤊஢㛫㝿ࡢ࠿ࡅࡇࡳ㉎㈙ࡀ࡝ࡇ࠿ࡽࡸࡗ࡚ࡃࡿࡢ࠿ࢆ⪃࠼ࡓ࡜
ࡁࠊPJ ࢆㄆ▱ࡋࡘࡘࡶࠊ㉎㈙ពᛮỴᐃࢆಖ␃ࡋඛ㏦ࡾࡍࡿฟ㈨⪅ࡢᏑᅾࡀ᝿ᐃࡉࢀࡿࠋ(2)ᘧࡢ݃௧ ࡣࡑࡢࡼ࠺࡞ࠊt ᮇࡢඛ㏦ࡾฟ㈨⪅ᩘ㸦㉎㈙ᩘ㸧ࠊࡘࡲࡾ t ᮇࡢඛ㏦ࡾࡋࡓ㉎㈙࡜ඛ㏦ࡾ࠿ࡽ㉎㈙࡟㌿ࡌࡓேᩘࡢྜィࢆ⾲⌧ࡍࡿࠋr ࡜ k ࡣࡑࢀࡒࢀࣃ࣓࣮ࣛࢱ࡛࠶ࡿࠋẖᮇᏑᅾࡍࡿ࡛࠶ࢁ࠺ඛ㏦ࡾ࡜ඛ㏦ࡾ࠿ࡽฟ㈨࡟㌿ࡌࡿ㉎㈙ࡣࠊ᫬Ⅼ s ࡟࠾࠸࡚ࠊඛ㏦ࡾࡍࡿฟ㉎㈙ᩘࡼࡾࡶฟ㈨࡟㌿ࡌࡿ㉎㈙ᩘࡀ㉸㐣ࡍࡿᵓᡂ࡟࡞ࡗ࡚࠸ࡿࠋࡘࡲࡾඛ㏦ࡾ㉎㈙࡟ࡘ࠸࡚ࠊ༊
㛫0 ൑ ‫ ݐ‬൏ ‫݃ࡣ࡚࠸࠾࡟ݏ‬௧ ൏ 0࡜ࡋ࡚ඛ㏦ࡾ㉸㐣ࢆ⾲⌧ࡋࠊ‫ ݏ‬൑ ‫ ݐ‬൑ ࡛ܶ݃௧ ൒ 0࡜ࡋ࡚㉎㈙㉸㐣ࢆ⾲⌧ࡍࡿࠋ(2)ᘧࡢᣲືࡣᅗ 1 ࡢࡼ࠺࡟࡞ࡿࠋ ୍᪉࡛ࠊ᫬Ⅼ s ࢆᣳࢇ࡛᭱⤊ⓗ࡟ඛ㏦ࡾ㉸㐣ࡢ㉎㈙௳ᩘ࡜㉎㈙㉸㐣ࡢ㉎㈙௳ᩘࡣ➼ࡋࡃ࡞ࡿᚲせࡀ࠶ࡾࠊ‫ ݏ‬൑ ‫ ݐ‬൑ ܶࡢ㉎㈙௳ᩘ࡜0 ൑ ‫ ݐ‬൏ ‫㉎ࡿࡅ࠾࡟ݏ‬㈙௳ᩘࡀ➼ࡋ࠸࡜࠸࠺ไ⣙ࢆ௦்௞ାଵ⨨ࡃࠋࡘࡲࡾ| ‫׬‬଴ ‫ ݐݎ‬௞ ሺ‫ ݐ‬െ ‫ݏ‬ሻ݀‫ |ݐ‬ൌ ‫׬‬௦ ‫ ݐݎ‬௞ ሺ‫ ݐ‬െ ‫ݏ‬ሻ݀‫࡚࠸ࡘ࡟ݏࢆݐ‬ゎࡁࠊ(2)ᘧ࡟࠶ࡿ‫ ݏ‬ൌࢆᚓ௞ାଶࡿࠋࡲࡓࠊ(2)ᘧ࡛⾲⌧ࡍࡿ PJ ᮎᮇࡢ㉎㈙௳ᩘࡢ㞟୰ S ࡣ
௦

்ሺୀଵሻ

ܵ ൌ ห‫׬‬଴ ݃௧ ݀‫ ݐ‬ห ൌ ‫׬‬ௌሺ௞ାଵሻೖశభ݃௧ ݀‫ ݐ‬ൌ ‫ ݎ‬ሺ௞ାଶሻೖశయ                    (3)࡜࡞ࡿࠋ༊㛫࡜ S ࡢ㛵ಀࡣᅗ 2 ࡛࠶ࡿࠋsT

ᅗ 1 ඛ㏦ࡾ㛵ᩘ݃௧ ࡢᣲື          ᅗ 2 ༊㛫࡜ S ࡢ㛵ಀBass ࣔࢹࣝ࡟(2)ᘧࢆ⤌ࡳ㎸ࡳࠊ᭷㝈ᮇ㛫 Bass ࣔࢹࣝ࡜ࡋ࡚݊௧ െ ݃௧ ൌ ݊௧ െ ‫ ݐݎ‬௞ ሺ‫ ݐ‬െ ‫ݏ‬ሻ ൌ ‫݂ݑ‬௧‫ כ‬ൌ ‫݌ݑ‬ሺ1 െ ‫ܨ‬௧‫ כ‬ሻ ൅ ‫ܨݍݑ‬௧‫ כ‬ሺ1 െ ‫ܨ‬௧‫ כ‬ሻ        (4)ࢆᥦ᱌ࡍࡿࠋࡇࡇ࡛݂௧‫ܨ࡜ כ‬௧‫݃ࠊࢀࡒࢀࡑࡣ כ‬௧ ࡟ࡼࡗ࡚ PJ ᮎᮇ‫ ݏ‬൑ ‫ ݐ‬൑ ܶ࡟࠾ࡅࡿ㉎㈙ࡢ㞟୰ࡀ
0 ൑ ‫ ݐ‬൏ ‫࡟ݏ‬᣺ࡾᡠࡉࢀࡓࠊt ᮇ࡟࠾ࡅࡿ㉎㈙௳ᩘ๭ྜ࡜ࠊࡑࡢ⣼✚๭ྜ࡛࠶ࡿࠋ
ᮏᥦ᱌ࣔࢹࣝࢆ␗࡞ࡿどⅬ࠿ࡽゎ㔘ࡍࡿ࡜ࠊBass ࣔࢹ࡛ࣝࡣྛᮇࡢ㉎㈙௳ᩘศᕸ࡟ࡘ࠸
࡚༢ᓠᛶࡢศᕸࡋ࠿⾲⌧࡛ࡁ࡞࠸ࠋࡋࡓࡀࡗ࡚ࠊPJ ࡢึᮇ࡜ᮎᮇࡢ 2 ᅇ㉎㈙ࡀ㞟୰ࡍࡿഴྥ࡟࠶ࡿࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࡢ㈨㔠ㄪ㐩ࣃࢱ࣮ࣥࢆ⾲⌧ࡍࡿࡇ࡜ࡀᅔ㞴࡛࠶ࡾࠊᥦ᱌
ࣔࢹ࡛ࣝࡣ PJ ᮎᮇࡢ㉎㈙ࢆࡼࡾ᪩࠸᫬Ⅼ㸦0 ൑ ‫ ݐ‬൏ ‫ݏ‬㸧࡟᣺ࡾᡠࡍࡇ࡜࡛ࠊBass ࣔࢹࣝࡢp ࡜ q ࡢࣃ࣓࣮ࣛࢱ࡛⾲⌧ࡋࡸࡍ࠸ᙧ࡟㈨㔠ㄪ㐩ࣃࢱ࣮ࣥࡢࢢࣛࣇࢆኚ᥮ࡋ࡚࠸ࡿࠋ ᥦ᱌ࣔࢹࣝࡣ Bass ࣔࢹࣝࡢᚤศ᪉⛬ᘧࢆ฼⏝ࡋ࡚݊௧ ൌ ‫݂ݑ‬௧‫ כ‬൅ ‫ ݐݎ‬௞ ሺ‫ ݐ‬െ ‫ݏ‬ሻ ൌ ‫ݑ‬௣‫ כ‬ሺ௣‫ כ‬ା௤ ‫ כ‬ሻమ ୣ୶୮ ሼିሺ௣‫ כ‬ା௤ ‫ כ‬ሻ௧ሽ൅ ‫ ݐݎ‬௞ ሺ‫ ݐ‬െ ‫ݏ‬ሻሾሺ௣‫ כ‬ା௤ ‫ כ‬ሻ ୣ୶୮ሼିሺ௣‫ כ‬ା௤ ‫ כ‬ሻ௧ሽሿమ          (5)࡜ࡋࠊR ࡢ optim 㛵ᩘࢆ⏝࠸ࡓ㠀⥺ᙧᅇᖐ࡟ࡼࡗ࡚᥎ᐃࡍࡿࠋࡓࡔࡋ(2)࡟ྵࡲࢀࡿ‫ ݐݎ‬௞ 㡯࡟࠾࠸࡚ r ࡜ k ࡢ㆑ูᛶࡀప࠸ࡓࡵࠊ0.75ӌ s ӌ0.975 (<T )ࡢ⠊ᅖ࡛ 0.025 㛫㝸࡛ࡢࢢࣜࢵ
ࢻࢧ࣮ࢳࢆ⾜࠺ࠋ ᐇドศᯒ࡛ࡣ᪥ᮏࡢ኱ᡭࢡࣛ࢘ࢻࣇ࢓ࣥࢹ࢕ࣥࢢࣉࣛࢵࢺࣇ࢛࣮࣒࡛࠶ࡿ Campfire ࡟ᥖ㍕ࡉࢀࡓ ALL-in ᪉ᘧ࡛ᐇ᪋ࡉࢀࡓ PJ ࡢ㈨㔠ㄪ㐩᫬⣔ิ᥎⛣ࢹ࣮ࢱࢆ౑⏝ࡍࡿࠋPJ ࡈ࡜࡟ເ㞟ᮇ㛫ࡀ␗࡞ࡾࠊm ሺ݉ ൌ 1, … , ‫ܯ‬ሻࢆྛ PJ ࡢ᪥ḟᬺୖࡢྛ᫬Ⅼ࡜ࡍࡿ࡜ࠊ᥎ᐃୖࡢၥ
㢟࠿ࡽࠊi ࢆ PJ ࡜ࡋ࡚௨ୗࡢࡼ࠺࡟ᶆ‽໬ࡋ࡚ࣔࢹࣝ᥎ᐃࡍࡿࠋ
௠

ଵ

ଶ

೔

೔

೔

ெ

  ‫ݐ‬௜ ൌ ெ೔ , ࡘࡲࡾ ‫ݐ‬௜ ൌ ெ , ெ , … , ܶ௜ ൌ ெ೔ ൌ 1                  (6)೔ࣔࢹࣝࢆ 6,901 ௳ࡢ PJ ࢹ࣮ࢱ࡟㐺⏝ࡋࡓᐇド⤖ᯝ࠿ࡽࠊBass ࣔࢹࣝࡼࡾࡶᥦ᱌ࣔࢹࣝ
ࡢ᪉ࡀ㐺ྜᗘࡢ㧗࠸⤖ᯝࢆᚓࡓࡀ୙㒔ྜ࡞⤖ᯝࡶ࠶ࡾࠊヲ⣽ࡣᙜ᪥ሗ࿌ࡍࡿࠋ

"hu. モデルによるユーザー投稿行動の分析
法政大学 長谷川翔平

はじめに
我々普段が利用するサービスには契約型と非契約型があり，契約型は顧客の契約終了によって企業側が顧客離脱を観測できるのに対し，非契約型は顧客離脱が観測できない。例えば，有料動画配信サービスは契約型に該当し，顧客が月額料金の支払いを停止すると運営企業は顧客の離脱を観測できる。一方で，1* サイトは非契約型に該当し，顧客がサービスの利用を止めても運営企業は顧客の離脱を観測できない。このような非契約型サービスの消費者行動を分析するモデルとして，"hu.（"mv hBHH uQm .B2）モデルがある。
本研究では，経営科学系研究部会連合協議会主催の令和 j 年度データ解析コンペティションで提供されたママリのデータを用いる。ママリは，コネヒト株式会社が運営する妊娠から子育てまでの悩みを解決するママ向けアプリで，ユーザーが相互に質問・回答を行う Z サービスである。ママリの Z サービスを利用するにはユーザー登録を行う必要があるが，離脱顧客の多くは退会手
続きを行わず，顧客離脱を観測できない場合が多いと考えられ，非契約型サービスの特徴を持つ。
提供データにはユーザーの質問・回答の投稿日時と投稿文章が含まれており，本研究ではこれらのデータを用いてユーザーの投稿・離脱行動と関心の関係を分析する。

モデル
ユーザーの投稿・離脱行動は，"hu. モデルの代表的なモデルである S`2iQfL". モデル
Ua+?KBiiH2BM 2i HX RN3dV によって分析する。S`2iQfL". モデルでは，購買はランダムに発生すると仮定するが，本研究のデータには R 日に複数回の投稿を行うユーザーも存在するため，モデル化する変数 ԧ は投稿回数ではなく投稿日数とする。また，消費者の異質性を考慮するため，#2
UkyyNV で提案された階層ベイズモデルを採用する。
৘৖ԅ <ԧք ]ᅶք > ৗ৖৕ᇊՎ յՎ ՝Վ ਷ᇊՎ յՎ֓Վ Ώ ԔᇊՎ ᇑՎ ՝Վ ਷ᇊՎ ᇑՎ֓Վ Ώ Ԕ

ᅽք  ԉ քᅽք ମ ԉ քԕ ᅽք  ᅷք Ԕ਷ᇋՎ ᇑՎ

ここで，Ԙ   w ԃ は消費者，ԉք は観測期間，ᅽք は生存時間である。ユーザーの関心はそのユーザーが投稿した質問または回答の文章から G. U"H2B 2i HX kyyjV によって抽出する。
ԩքֈ ୽ Ԃ ԤԛԣԘ ᅲքᅲք ୽ ӹԘԡ ᅫԦքֈ ୽ Ԃ ԤԛԣԘ ঁᅿ֕ ংՎՒᅿֆ ୽ ӹԘԡ ᅻ

ここで，ԩքֈ はユーザー Ԙ の投稿文章に含まれる単語 Ԧքֈ Ԝ   w Ԃք のトピック Ԛ   w Ԁである。投稿文章から G. によって推定されるトピック分布 ᅲք は Ԁ 個のトピックに対するユーザー Ԙ の関心と捉えることができる。本研究では，S`2iQfL". モデルのパラメータRᅱք  HQ; ᅶք HQ; ᅷք ஥ を目的変数，G. のトピック分布 ᅲք を説明変数とした階層モデルから，ユーザーの投稿・離脱行動と関心の関係を分析する。図 R は本研究の分析モデルのグラフィカルモデル
である。
ৡHQ; ᅶք ৤ ଉ ᅱ  ᅬᅲքৣৠ
քয়HQ; ᅷք ৢ

図RԔքԔք ୽ ԃ  ဋグラフィカルモデル

推定結果
質問投稿データからは「妊娠・出産」や「家族付き合い」などのトピックが抽出され，階層モデ
ルのパラメータ ᅬ からは「子育て不安・不満」に関心の高いユーザーは投稿回数が多く，離脱も遅いことが示された。また，「妊娠・出産」に関心の高いユーザーは投稿日数が多いものの，離脱が早く，出産後に離脱している可能性が示された。ユーザーの出産前後に企業側からフォローを行う
ことで生存時間を延ばすことができると考えられる。回答投稿データからも「妊娠・出産」のトピックが抽出され，質問投稿と同様にこのトピックに関心の高いユーザーは投稿日数は多いものの離脱が早いことがことが示された。回答行動からの離脱を防ぐために各ユーザーの関心に合わせた
インセンティブを導入することで，顧客の維持率を高められる可能性がある。
参考文献
RX#2- JX UkyyNVX ǳ*QmMiBM; uQm` *mbiQK2`bǴ PM2 #v PM2,  >B2``+?B+H "v2b 1ti2MbBQM iQ i?2S`2iQfL". JQ/2HX J`F2iBM; a+B2M+2- k3UjV- 89RĜ88jX
kX"H2B- .X JX- L;- X uX-  CQ`/M- JX AX UkyyjVX Gi2Mi .B`B+?H2i HHQ+iBQMX CQm`MH Q7 J+?BM2
G2`MBM; _2b2`+?- j UCMV- NNjĜRykkX
jXa+?KBiiH2BM- .X *X- JQ``BbQM- .X :X-  *QHQK#Q- _X URN3dVX *QmMiBM; uQm` *mbiQK2`b, q?Q@`2h?2v M/ q?i qBHH h?2v .Q L2ti\ JM;2K2Mi a+B2M+2- jjURV- RĜk9Xk

Product Embedding for Large-Scale Disaggregated Sales Data
Yinxing Li and Nobuhiko Terui

Marketing data are expanding in several modes nowadays, as the number of variables
explaining customer behavior has greatly increased, and automated data collection in thestore has also led to the recording of customer choice decisions from large sample sizes.
Thus, high-dimensional models have recently gained considerable importance in several
areas, including marketing. Although some models, such as Prod2Vec, involve various
marketing variables such as price and customer demographic data, the role of thevariables in forecasting is still not discussed. In light of the limitations mentioned above,
our study not only aims to propose a model with better forecasting precision but also toreveal how customer demographics affect customer behavior. we propose a Bayesian
Word2Vec based framework that incorporates marketing variables and environment byconsidering following situations in our model.
When considering the market basket, our study incorporatesWKHreceipt vector into
the model as the prior information of each purchased product in a basket, which means apreferred purchasing pattern for a certain shopping. It assumes that the customer willconsider the whole purchasing context before choosing a product. We also assume a state
space model for the receipt vector through the trips for each customer. We use theweekday, promotion information as the data for the state space model for higher
interpretability of the prior structure such as the purchasing scenarios of each customer.
Besides, we consider the purchasing probability of a certain product conditional on an
existing market basket is influenced by the following three factors - 1) The compatibility
with the marketing basket, which is represented by the inner product of productvectors, 2) customer utility for the product, which incorporate the customer
heterogeneity structure, and 3) Thinking ahead algorithm, which represents one-stepahead forecasting before purchasing the product.
Our proposed model contributes both to higher precision for forecasting by
incorporating the marketing environment and customer heterogeneity into the model, andbetter interpretability. We use receipt data from a retailer for our empirical analysis,containing the information of customer demographic, promotion and other marketing
information. We show not only the effectiveness of marketing environment for theforecasting by using the Hit Rate@K for the hold-out sample comparing to the several
benchmark models , but also the high interpretability of our proposed model in theempirical study.

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࠹నԿ
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ްིదͲ҈સ͵ϠϑϨτΡऀճ͹ࣰ‫ݳ‬͹ͪΌͶͺɼಧ൅ద͵φϧϔϩͶΓΕૺߨ෈೵ͳ͵ͮͪऄྈΝ‫ݳ‬৖Ͷ‫ͱ͢ߨٺ‬रཀྵͤΖ‫ٺە‬ϫʖχγʖϑη͗॑གྷͲ͍Ζɽ͞͹γʖϑηϪϗϩΝ޴৏ͦ͠ΖͪΌͶͺɼϤʖδʖ͖Δ͹ϪηΫϣʖགྷ੧Νण͜ͱ͖Δ෰‫׮ڈ‬྅ΉͲ͹࣎ؔΝ୻क़ͤΖ͞ͳ͗๮Ή͢͏ɽ͞͹ଶͬ࣎ؔ͹୻क़Νୣ੔ͤΖͪΌͶͺɼγʖϑη‫͵ͳ఼ڎ‬Ζవะ͹Ғ஖࠹నԿ༙͗ް͵घஊͳ͵ΕಚΖɽྪࣇ͹໲ୌͳ͢ͱɼऩགྷஏ఼ͳ࠹‫ر‬Ε͹ࢬઅؔ͹Ңಊ‫ؔ࣎཯ړ‬͹૱࿪Ήͪͺฑ‫ۋ‬Ν࠹ঘԿͤΖͪΌͶɼ෵਼͹ޫึࢬઅ͖Δ S ‫ݺ‬͹ࢬઅΝಝఈͤΖ SPHGLDQ ໲ୌʤS03ʥ༹͗ʓ͵෾໼Ͳ‫ݗ‬౾͠Ηͱ͏Ζɽͪͫ͢ɼ‫ٺە‬ϫʖχγʖϑη͹৖߻ɼऄྈ͹φϧϔϩয়‫ڱ‬Ώɼవะಝ੓ʤฯ༙रཀྵ೵ྙΏӨ‫ܙۂ‬ସʥͶΓΖड़ಊ६ඍ࣎ؔΏҢಊ࣎ؔʤྈं͹߻‫ܯ‬Νଶͬ࣎ؔͳ‫΁ݼ‬ʥ΃͹Ӫ‫ڻ‬ΝߡྂͤΖචགྷ͍͗Ζɽͨ͞Ͳɼ
ຌ‫Ͳڂݜ‬ͺɼ‫ٺە‬ϫʖχγʖϑη͹໲ୌͶಝ༙͹གྷҾΝߡྂͪ͢‫ٺە‬ϫʖχγʖϑη‫఼ڎ‬͹ࢬઅഓ஖࠹నԿ๑Ν఑ҌͤΖɽ‫ࣞה‬ճऀϔϨπηφϱ͹‫ٺە‬ϫʖχγʖϑη͹ࣰυʖνͶଲ͢ͱɼϗ΢θત‫ܙ‬յ‫ؾ‬ϠυϩͶΓΖଶͬ࣎ؔ༩଎Ϡυϩͳ S03 ϠυϩΝૌΊ߻ΚͦΖ͞ͳͲɼϤʖδʖ͹ଶͬ࣎ؔΝ୻क़ͤΖవะഓ஖͹࠹నԿΝࢾΊͪɽͨ͹݃ՎɼҢಊ‫཯ړ‬͹ΊΝߡྂͪ͢ॊཔघ๑ͳർֳ͢ͱɼ఑Ҍघ๑Ͳͺଶͬ࣎ؔ͗࠹୉ ୻क़͠ΗΖ͞ͳ֮͗೟
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