2015.6.13. The 4th International BinN research seminar “Dynamic modelingbased on bounded rationality to understand diversifying travel behavior”

Modeling shopping behavior in aneighborhood with endogenous
representation of retail attractiveness
Hiroshima University
Makoto Chikaraishi, Akimasa Fujiwara,
Fumihito Nishikawa, Hajime Seya, Junyi Zhang

Motivation (1/2)• Our ultimate goal:– Describing collective decisions through modelingsocial interactions• Some examples in our mind:– Why some communities do better collective decisions (e.g.,maintaining small market in the neighborhood), while someothers do not?
– Why some (most?) slums are in a kind of lock-in situation, whilesome others are not?

• These questions are not very new (e.g., Schelling, 1978),but we could do a better empirical analysis on this topic– Progress on modeling social interactions– Advancement of observation/estimation methods

Our focus: shopping behavior in a neighborhood

2

※ One‐day travel diary survey in Hiroshima in 2008

Motivation (2/2)
 Many newtowns were built around30-40 years ago in Japan Rapid aging population has been
observed in these areas As decreasing mobility with aging,
maintaining necessary facilities fordaily life within the neighborhood
becomes more important

59% of residents do shopping within NT

13% of residents do shopping within NT

27% of residents do shopping within NT3

Modeling social interactions

When the degreeof interactions arehigher than acertain level
under noncooperative
schemeIndividualʼschoice probability (%)
居住者全体の選択比率(%)• Social interactions in choice modeling and its
macro behavior (i.e., collective decision)
100

Stable equilibrium

80
60
40
20

Stable equilibrium

0
0

20

40

60

80

100

個人の選択比率(%)
Expected groupchoice probability (%)

Individual behavior(individual decision)

Macro behavior(Collective decision)
4Classification of social interactions
Social interactions

Market interactions

Market & non-market interactions

Differences in final consequences
are understood as differences ininitial conditions (Harris and Wilson,

Differences in final consequences
are understood as collective
decisions (e.g., Putnam, 1993; Falk and1978; Fujita et al., 2001; Guevara, 2010)

Kilpatrick, 2000)

Economical point of view

Sociological point of view5Classification of social interactions
Social interactions

Market interactions

Market & non-market interactions

Local interactions

Global interactions

Mostly cooperative scheme,
usually not causing multiple
equilibria

Mostly non-cooperative scheme,
potentially causing multiple
equilibria

We could have in-between models, but our current knowledge may be largely
restricted partly due to observation issues of social networks/interactions

Environment factors

Individual attributes,
Othersʼ behavior/attributes

Relations with others
6Classification of social interactions
Social interactions

Market interactions

Local interactions

Market & non-market interactions

Global interactions

Interactions through“average” behavior

Interactions through“aggregate” behavior

Individual decisions are affectedby the “average” behavior ofsocial group (e.g., Brock&Durlauf,
2001; Fukuda&Morichi, 2007;
Walker et al., 2011)

Individual decisions are affectedby the “aggregate” behavior ofsocial group (e.g., Ueda, 1991)

Modeling interactions through “aggregate” behavior

7

Research purpose• Developing a shopping destination choicemodel with social interactions– Modeling market/non-market interactions through“Aggregate behavior”• Similar with Brock and Durlaufʼs (2001) model– Confirming in what condition multiple equilibria
happen• Implementing empirical analysis– 10 newtowns in Hiroshima, Japan• Distinguishing endogenous effects from contextual/correlated effects, by using a modified Rustʼs (1987) Nested
Fixed Point algorithm (binary logit  a mixed binary logit)• Empirically confirm whether multiple equilibria exist or not8Model structure
Shopping destination choice model
Unknown parameters
Individual iʼschoice probabilityof destination j

exp
∑ exp

βx
Retail attractivenessat destination j

Explanatory
variables

Aggregation
Feedback
to utility
Total
shopping
demand at
destination j

RetailattractivenessTotal
shopping
trips

A fixed point problem:

exp

βx

∑ exp

βx
※ Similar with Ueda (1991)

9

Some assumptions(a) There are two alternatives→ inside and outside of the residential newtown

OutsideInside(b) Only newtown residents use shopping facilities in the newtown(assuming ③ is zero)Home③(c) Total shopping demand (number of trips) is fixed

Shop
②

①
Home

(d) The relationship between shopping demand andretail attractiveness follow a linear function010

Self-consistent equilibrium (1/2)
With the above assumptions, equilibrium properties are very similar with
Brock and Durlauf (2001), in which the basic mathematical idea is the samewith the mean field approximation of Ising model in Physics

Assuming that
represents the choice results of shopping destination where
1 when inside newtown is chosen and
1 when outside newtown is
21). Under this specification, expectation ofis:chosen (i.e.,

tanh

11

Self-consistent equilibrium (2/2)
Based on the assumptions (b)”Only newtown residents use shopping
facilities in the newtown”, and (c)” Total shopping demand is fixed”,
1⁄2

1⁄2

β x



x
2

Since ( and ), and (and2) are cannot be distinguished,′′

are assumed, and finally we obtain:
∗

β x

x

′
2

′
2

∗

12

Behavior of
equilibria

Travel cost in NT:300JPY
Individualʼschoice probability (%)
居住者全体の選択比率(%)

60
40
20
0
0

20

40

60

80

80
60
40
20
0

100

0

60
40
20
0
0

20

40

60

80

100

Individualʼschoice probability (%)
居住者全体の選択比率(%)

Individualʼschoice probability (%)
居住者全体の選択比率(%)

Pop. in NT= 9,000

80

60
40
20
0
0

20

40

60

80

100

個人の選択比率(%)
Expected groupchoice probability (%)

80

80
60
40
20
0

100

0

80
60
40
20
0
0

20

40

60

80

100

100
80
60
40
20
0
0

20

40

60

80

100

個人の選択比率(%)
Expected groupchoice probability (%)

20

40

60

80

100

個人の選択比率(%)
Expected groupchoice probability (%)

100
80
60
40
20
0
0

個人の選択比率(%)
Expected groupchoice probability (%)

Individualʼschoice probability (%)
居住者全体の選択比率(%)

居住者全体の選択比率(%)

Individualʼs choice probability (%)

Pop. in NT= 12,000

80

60

100

個人の選択比率(%)
Expected groupchoice probability (%)

100

40

100

個人の選択比率(%)
Expected groupchoice probability (%)

個人の選択比率(%)
Expected groupchoice probability (%)

100

20

Individualʼschoice probability (%)
居住者全体の選択比率(%)

80

100

20

40

60

80

100

個人の選択比率(%)
Expected groupchoice probability (%)

Individualʼschoice probability (%)
居住者全体の選択比率(%)

100

Travel cost in NT:600JPY
Individualʼschoice probability (%)
居住者全体の選択比率(%)

Travel cost in NT:100JPY
Individualʼschoice probability (%)
居住者全体の選択比率(%)

Pop. in NT= 6,000

Hypothetical settings:,: Generalized travel cost (is fixed as
1200 JPY),
0.1,
3.0,
0.9，Average number of
shopping trips: 3 (i.e., total demand in NT is:＝pop. in NT ×3)
Note that: stable equilibria,: unstable equilibrium

100
80
60
40
20
0
0

20

40

60

80

100

個人の選択比率(%)
Expected groupchoice probability (%)

13

Technical issues in model estimation• Distinguishing endogenous effects fromcontextual/correlated effects (e.g., Manski, 1993)– BLP approach (Berry et al., 1995)– Control function approach– Full maximum likelihood approach• Introducing the endogenous variable as an
exogenous variable may not be self-consistent– Nested Fixed Point (NFXP) algorithm (Rust, 1987)– A bit more efficient NFXP algorithm (Aguirregabiria
and Mira, 2002)– Bayesian estimation (Imai et al., 2009)– MPEC (Su and Judd, 2012)14

Model estimation method• NFXP(Nested Fixed Point) algorithm (Rust, 1987)
1. Given the observed choice probability
estimate a set of parameters,

2. Repeat the following steps until convergence(a) Inner fixed point algorithm:
Calculate choice probability

with parameters θ(b) Outer hill climbing algorithm:
Given, estimate parameters θWhen introducing random parameters in the 2(b) step, individual
parameters (Train, 2003) are calculated and put in the 2(a) step15

Empirical analysis• One-day travel diary survey in Hiroshima in 2008
– Sample size in the target area: 5,620 (1,453 shopping trips)• Study area
※ Because the available spatial information is limited, surrounding areas
are also included in some Newtowns.
List of newtown

Population in NT

あさひが丘
美鈴が丘
五月が丘
藤の木
向洋
井口台・井口鈴が台
山田新町・鈴が峰
矢野
高陽
高陽第一

8155
10086
6925
4948
14847
22544
11886
18617
39423
20437

16

Study area

Shopping center
Small supermarket
Focused newtowns
Newtowns

17

Basic statistics
Origin = residential area

Origin = non-residential area

Total

SampleShare of
Share of
Share of
Freq. perFreq. perFreq. persize
Shopping
Shopping
insideinsideinsideday perday perday per(persons)
newtown
newtown
trips
trips
newtown
personpersonperson
（％）
（％）
（％）

あさひが丘

312

48

0.154

39.58

36

0.115

11.11

0.269

27.38

美鈴が丘

447

56

0.125

23.21

64

0.143

4.69

0.268

13.33

五月が丘

259

29

0.112

34.48

23

0.089

13.04

0.201

25.00

藤の木

143

11

0.077

18.18

22

0.154

0.00

0.231

6.06

向洋

485

64

0.132

28.13

45

0.093

4.44

0.225

18.35

井口台・井口鈴が台

728

102

0.140

50.98

79

0.109

24.05

0.249

39.23

山田新町・鈴が峰

408

55

0.135

21.82

55

0.135

3.64

0.270

12.73

矢野

656

80

0.122

28.75

69

0.105

15.94

0.227

22.82

高陽

1394

274

0.197

71.17

123

0.088

31.71

0.285

58.94

高陽第一

788

150

0.190

52.67

68

0.086

26.47

0.277

44.50

Total

5620

869

0.155

48.68

584

0.104

17.29

0.259

36.06

18

Travel cost (accessibility) calculation
1. Estimating travel mode choice
2. Calculating logsum
 For inside of newtown, LOS variables are prepared for each 50m gridcell, and then take a population-weighted average (since we do nothave detailed information of residential location)
 For unchosen travel modesʼ LOS, we put an average value of others
who live in the same newtown
Constant (Car)Constant (Bicycle)
Constant (Walk)
Travel time (100 min)Travel cost (1000 JPY)
Age>=75 dummy (car)Initial log-likelihood
Final log-likelihood
Adjusted rho-square
Sample size

Parameter t-value
2.239
6.73
-1.204
-3.23
0.540
1.78
-3.255-2.28-2.463-1.78-0.071-0.17-1053.2-539.0
0.483
864

19

Estimation results of shopping
destination choice model
No socialinteractions
Parameter

Constant
Travel cost (logsum)
Age <=30
Age >=65
MaleHousewife
Non-worker
ln(# of shops)

t-value

4.585 8.22**‐0.019 ‐1.98*‐0.600 ‐1.78+‐0.035 ‐0.20‐0.202 ‐1.06‐0.293 ‐1.47‐0.249 ‐1.12
0.960 9.25**

With endogenous With contextual/effects
correlated effects
Parametert-value

1.068 1.03
‐0.018 ‐1.81+‐0.598 ‐1.75+
0.057 0.31
‐0.271 ‐1.39‐0.302 ‐1.50‐0.301 ‐1.34
0.356 1.96*

Parametert-value

3.901 4.10**‐0.017 ‐1.68+‐0.623 ‐1.83+
0.007 0.04
‐0.250 ‐1.28‐0.281 ‐1.39‐0.260 ‐1.14
0.824 4.69**

With all effects
Parametert-value

1.066 1.03
‐0.018 ‐1.81+‐0.598 ‐1.75+
0.057 0.31
‐0.271 ‐1.39‐0.302 ‐1.50‐0.301 ‐1.34
0.355 1.96*

Endogenous
Retail attractivenessContextual/correlated
Random effect864
Sample size
Initial log-likelihood ‐598.88
Final log-likelihood ‐546.40
1108.80
AIC※ [] indicates the result of χ2 test

1.014

864
‐598.88‐538.51
1097.03

3.93**

1.015
0.095[7.96] **864‐598.88‐542.421102.84

3.94**

3.2.E‐15 [0]864‐598.88‐538.51
1099.0320

Based on AIC comparison, the model only with endogenous effects are selectedNo multiple equilibria
Only if when

1, there is possibility to have multiple equilibria
Freq. perNT pop. day perperson

あさひが丘

8,155

0.269 0.046

美鈴が丘

10,086

0.268 0.035

五月が丘

6,925

0.201 0.026

藤の木

4,948

0.231 0.011

向洋

14,8470.225 0.049

井口台・井口鈴が台

22,5440.249 0.165

山田新町・鈴が峰

11,8860.270 0.042

矢野

18,6170.227 0.069

高陽39,4230.285 0.470

高陽第一20,4370.277 0.185

The empirical results
indicate that there are no
newtowns which
potentially have multiple
equilibria(though the significant
social interactions exist)

21

Conclusions• Model development– Modeling shopping destination choice with social
interactions• Representing retail attractiveness as endogenous Brock and Durlauf (2001)  “average” behavior of others
 This study  “aggregate” behavior of others• Model estimation– NFXP algorithm with a distinction between endogenous andcontextual/correlated effects• Empirical analysis– 10 newtowns in Hiroshima city
• Confirming the existence of endogenous effects• But, the degree of endogenous effects are not big enough tocause multiple equilibria– The situation is not like “collective decisions” through equilibrium
selection
22

Future works• Separating market interactions and non-market
interactions– Interpretation of interactions, and possible policy
discussions• Modeling residentsʼ shopping behavior fromoutside of newtown– Modeling trip chaining• Modeling frequency of shopping trips andmoney they spent– Elderly may less participate in shopping activities• Applying the model to evaluate the impacts ofimproving transportation system in newtown
23

Future tasks
LOS of PM sharing within a newtown
For each 50m grid cell
Individual
attributes, etc.

Pop data by
age group

Location of station, price, reservation
system, # of vehicles, etc.

Donation
ProfitPM sharing participation model
Sharing
participation
Non‐participants

Non‐market interactions

Participants

The current
travel cost

Reducing travel costwithin newtown

Recalculate travel cost

Trip freq.

Market interactions

Mode choice・・・

LOS for Public transport(Navitime)
LOS for road transport(road network data)

Shopping
destination

Service level of shops

Individual
attributes, etc.

Variety, open/close time,
price, etc.

Profit

The proposed model
Shopping
demandNon‐market
interactions

Market interactions

24

Initial trial

25References
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