Asian Transport Studies, Volume 1, Issue 1 (2010), 77-89© 2010 ATS All rights reserved

An Evaluation Method of Transportation Policies by the Quality ofMobility Index based on Capability approach
Youhei EITOKU a, Shoshi MIZOKAMI baKumamoto Office, Fukuyama Consultants Co., LTD., 1-21 Minami-Sendanbata, Kumamoto
City, 860-0842 Japan; E-mail: eitoku@fukuyamaconsul.co.jpbGraduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami,
Kumamoto City, 860-8555 Japan; E-mail: smizo@gpo.kumamoto-u.ac.jp

Abstract: This study aims to develop a model for the evaluation of Quality of Mobility(QOM) based on the Capability approach pioneered by Amartya Sen. It seeks to illustrate how
to use such model in the evaluation QOM among regions by applying this to the condition in
Yamaga City, Japan. Evaluation results indicate that the transportation service level in this city
will decrease and the inequality will expand in the future. Therefore, some policies wereprepared and evaluated. Using the model, it was concluded that the policy that will encourage
people to live in the city center and improve road will enhance QOM.
Keywords: Capability approach, Structural equation modeling, Vector Product1. INTRODUCTION
The depopulation trend due to the ageing population is expected to become more serious inlocal cities of Japan in the coming years. Thus, it is more important than ever to integrate
villages and cluster them together to maintain the social base efficiency and share social
welfare facilities. How to maintain transportation service levels is very important to evaluate
these factors. QOL (Quality Of Life) must be evaluated by concerning the maintenance ofInfrastructure. In this paper, the Quality of Mobility (QOM) is defined as an integrated index
which evaluates the transportation service level. This paper proposes a method for evaluating
service levels and the equity in the entire region using Capability approach. It then outlines themodel to calculate QOM. The model is then applied to evaluate the transportation policy to be
adopted for a local City in Japan.

2. EVALUATION TECHNIQUE BY CAPABILITY APPROACH
2.1 A Framework of Capability Approach
Capability approach has been put forward by Sen (1985). A person’s capability to achieve
functioning that he or she has reason to value provides a general approach to the evaluation ofsocial arrangements, and this yields a particular way of the assessment of equality andinequality.(Sen, 1992) The core concepts of Capability approach are functionings andcapabilies. Functionings are the “beings and doings” of a person, whereas a person’ capability
is “the various combinations of functionings that a person can achieve. Capability is thus a setof vectors functionings, reflecting the person’s freedom to lead one type of life or another.
(Sen, 1992)
In Capability approach, there is no established measurement scale for functionings, and77

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there is not a method for aggregating functioning. There is rich literature on how to model
Capability approach. Non-statistical methods include the Human Development Index (HDI)
adopted by the United Nations Development Programme (UNDP), Fuzzy-sets-theory(Oizilbash, 2002), and Analytic-Hierarchy-Process (Inoi, 2005). The common feature of thesemethodologies is that the value of functioning can be easily interpreted with subjective
evaluations. On the other hand, the common weakness is the high dependence of the results ofthe evaluation on the competence of the evaluator. Statistical analysis methods include Factor
Analysis (Lelli, 2001), Principal Components Analysis (Klasen, 2000), and Structural
Equation Modeling (Kuklys, 2004). The common feature of these methods is that informationfrom the data itself is used to determine the weights.
The construction of the index for composing QOM, its functioning’s expression,functioning’s measurement, functioning’s ranking and functioning aggregation is difficult. The
authors proposed a methodology which can approximate the four functions using statisticalanalysis to keep the objectivity of the solutions.
2.2 Functioning’s Expression
In his book “Commodities and capabilities”, Sen (1985) formalized the following relationshipbetween commodities and capabilities as follow:
The achieved function of person i is:bi = f i (c( xi ))(1)

where xi :the vector of commodities possessed by person ic(⋅) :the function (not necessary linear) converting a commodity vector into a vector ofcharacteristics of those commodities
f i (⋅) :a personal ‘utilization function’ of i reflecting one pattern of use of commodities
that i can actually makeThe vector bi reflects the beings and doing a person can achieve, because “Well-being
then, can plausibly be seen as an evaluation of this bi , indicating the kind of being he or she isachieving.” (Sen, 1985, p.12.) As the list of functioning decides capability’s value, the list anddescription method of functioning become problems.
2.3 Functioning’s Measurement
The commodity and happiness of a being can be observed directly, but the functioning cannot
be observed. In this section, the measurement method for the functioning is explained.
By Capability approach, the happiness that an individual will enjoy is given by u i :u i = hi (bi ) = hi ( f i (c( xi )))(2)

where hi (⋅) :the happiness function of person i related to the functionings achieved by i

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The functioning vector bi can be expressed by using the model following equations (1) and(2). As can be seen, the functioning is described by the latent variable which exists in the
middle of the commodities and the happiness by using Structural Equation Model. When thehappiness is an endogenous variable and commodities are exogenous variables, thefunctioning is conceptualized as a latent variable which can only be measured with error ofdata.
2.4 Method of Measuring Value of Functioning Vector
In the Capability approach, the value of a single functioning vector bi is given by the real-valued functioning vectors vi (⋅) , which is person i ’s valuation function.
vi = vi (bi )(3)There are two problems for measuring value of functioning vector.
The first problem is the difficulty of comparing functionings because the directions of thevector are too different to measure the value. For example, it is difficult to judge which ismore important, the mobility of shopping or the mobility of going to the hospital. According
to Sen, evaluating a functioning vector can take the form of giving a scalar value to thisvector. Because it is difficult to rank all functioning vectors, Sen has proposed a range of
methods including “Dominance ranking” for extending incomplete orderings.
The second problem is that posed by the possibility of high multi-collinearity because thefunctioning vectors are mutually related. Actually, since each mobility purpose is consecutive
in one day or one month, mobility purposes correlate mutually. For this, functioning vectors
should be independent of each other.
In the light of these challenges, the authors propose a method for converting two or morefunctioning vectors bi into principal integrated vectors bi' by using Principal Component
Analysis. As a result of Principal Component Analysis, multi-collinearity is eliminated.
Moreover, because the sums of squared loadings obtained by Principal Component Analysis
shows the volume of information of converted functioning vector, the size of functioning
vector bi' can be assumed to be proportional to sums of squared loadings.
2.5 Method of Aggregating Value of Functioning Vector
In Capability approach, the capability set of a person is given by the set Qi ( xi ) of all thefunctioning vectors that are feasible for person i :Qi ( xi ) = [bi bi = f i (c( xi )), for some f (⋅)i ∈ Fi and for some xi ∈ X i ](4)where Fi is the set of ‘utilization function’ f i (⋅) , any one of which person i can in factchoose.
The capability set Qi ( xi ) represents the freedom of choice of a person, who can decide
between several combinations of functionings what are the most valuable for him. Among all
feasible vectors of functionings, one will be chosen and will be the achieved vector of79

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functionings. The values of all functioning vectors present in a capability set are given by Vi .

Vi ( xi ) = [vi vi = vi (bi ), for some bi in Qi ](5)

Sen (1992) insists that the equality should be sought in the space of capability. Capability
is a set of such functioning n-tuples, which means that capability is defined in the space offunctionings (Sen, 1993). Because functioning vectors bi' intersect squarely, the value of set offunctioning vectors is shown by the size of the space, which is composed of functioning
vectors bi' , as shown in Fig.1. In a word, the value is calculated by the Product of the size ofthe converted functioning vectors bi' .

図３－６ functioningベクトルの空間の大きさ

Figure 1. Size of the Functioning Vector Space

3. MODELING OF QOM
3.1 Outline of Modeling of QOM
Figure 2 shows the structure of the models used to calculate QOM. The right part of Figure 2
shows a model of transportation possibility, which is modeled according to equations (1) and(2). The left part shows a model of selected transportation possibility, constructed on the basisof using equations (3) and (5). The model is analyzed by using data obtained through aquestionnaire survey in Yamaga City, Japan.
3.2 Factor of Transportation Possibility
Among all feasible vectors of functionings, one will be chosen. Thus, it is necessary to
enumerate the selected functioning for the mobility. In this paper, these are identified as:
selection of transportation, selection of the migration pathway, selection for mobility purpose
and selection of the target facilities. In this study, selection for mobility purpose and selection80

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of the target facilities are described in the functioning. There are nine transportation purposes
defined.
■Model of selected the transportation
possibilities
Total satisfaction
ratingSatisfaction
rating■ Model of the transportation
possibilities

Frequency

Daily
mobility
in dailyMobility fordaily shopping

QOM

Non-daily
mobility

Mobility by travel
time

Travel time

Mobility bytransportation
selection

Car license

Comfortin transportation
facilities

Drivability※an example for daily shopping

Mobility tolarge–scalecommercial

Figure 2. Outline of two models
3.3 A Model of Transportation Possibilities
In this study, transportation possibilities constitute three concerns, “mobility by travel time”,“mobility by transportation selection” and “comfort in transportation facilities”. The model of“mobility by transportation selection” uses the effect value of the modal choice model. The
relation between transportation frequencies and permissible times in a year is analyzed, andthen the model of “mobility by travel time” is built. The model of “comfort in transportation
facilities” is used to evaluate the comfort between the origin and the destination with a set ofdrivability data provided in the “Road drivability Map”.
These three factors are integrated according to Structural Equation Model. Latent variablesof Structural Equation Model are defined as transportation possibility functionings (see Figure3). Table 1 shows the result by Structural Equation Model, because CFI value is a rough value,
about 0.9 or more, so the accuracy is guaranteed.
3.4 A Model of Selected Transportation Possibilities
The model of selected transportation possibilities is composed of two models. The first one is
the model of “ease of selecting plural destinations”. This model is a gravity model in which
the attractiveness of the destination is given through a certain weight.
The second one is the model of “ease of selecting transportation purposes”. Capability is
described by a set of the vectors of functioning (the transportation possibility). The magnitudeof Capability is same as the magnitude of Vector Product of these functioning’s vectors, which
is defined as QOM. Through Principal Component Analysis on the values calculated by the81

EITOKU, Y. and MIZOKAMI, S. / Asian Transport Studies, Volume 1, Issue 1 (2010), 77-89“ease of selecting plural destinations” model, the values for various transportation purposes
are synthesized to two principal ingredients. With these two principal perpendicularingredients x1i , x 2 i , QOM can be expressed by the Cobb-Douglas Production Function inequation (6). Here, the ratio of squared loadings is assumed to be the share parameter in the
Cobb-Douglas Production Function. For the adult male in Table 2, the first principal
component can be interpreted as non-daily mobility.
QOM i＝ax1αi x 12−i α(6)Frequency

Mobility by travel time
(TCM)

Mobility

Mobility by transportation
selection (MCM)

Satisfaction rating( SAT)

Comfort in transportation
facility (FCM)

Figure 3. A model of transportation possibility
Table 1. Variables and CFI for adult males
CommutingBusiness
Daily shopping
Large-scalecommercial facility
Community facilities
Hospital in a region
Emergency hospital
Sight seeing←Mobility
SAT
FRQ**0.71 *-0.17**0.490.07**1.12 **0.45**1.21**0.99**0.48**1.04**1.05

Mobility←
TCM MCM FCM**-0.57 *-0.15 0.74－**-0.61 **-0.72 1.33－**-0.28-0.07 0.52－

0.12 **-0.10**0.41
0.04
*0.16
0.15

*-0.08*-0.280.02*-0.08

CFI
0.97
1.00
0.81

-0.01 0.69－

0.73

0.0
*-0.29
-0.01
0.01

1.00
0.82
0.94
1.00

0.86－
1.40－
0.92－
0.82－

※１）**t>1.96，*1.00<ｔ<1.96

Table 2. Principal component score
Emergency hospital
Hospital in a region
Sight seeing
Caltural facilities
Community facilities in a region
Emergency hospital
Daily shopping
Business
CommutingAccumulated proportion

Adult male
Adult female Senior citizens
first second First second First second
0.87 -0.03
0.85-0.02 0.71
0.36
0.69
0.47
0.78
0.13 0.82
0.13
0.85
0.20
0.70
0.17 0.13
0.88
0.78
0.26
0.82
0.08 0.27
0.87
0.74
0.27
0.20
0.14 0.84
0.35
0.71
0.45
0.61
0.19 0.72
0.22
0.67
0.31
0.12
0.80 0.81
0.04
0.05
0.91
0.28
0.48
0.33
0.58 -0.03
0.81
67%
55%
71%

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3.5 Setting of Evaluation Index
By using feasible maximum and smallest QOM values, QOMR is expressed as a percentage
of QOM value. The entire region is evaluated by three indices. The first index is the meanvalue ( QOMR ) of QOMR .It is used to evaluate the service level in the whole region. The
second index is an Atkinson index ( AI ), which evaluates the inequality in equation (7). The
third index ( QOMA ) is an index with an Atkinson type function for evaluating the service
level and inequality of the region in equation (8). The Atkinson index ( AI ) is evaluated by
specifying the parameter ε, which shows the evasion level of inequality.
1 / (1−ε ) n  QOMR 1−ε i / n 
AI = 1 − ∑  i  QOMR (7)
1 / (1−ε ) n  QOMR 1−ε i / n
QOMA = QOMR ∑ 

QOMR
i
 


_________(8)

where, n is population.

4. EVALUATION OF TRANSPORTATION POLICY IN LOCAL CITIES
4.1 Outline of Target Area
Yamaga City is a local city that was formed through the merging of four towns in 2003 andhas a population of 50,000 (see Figure 4). It takes about one hour to travel from this city toprefecture capital, Kumamoto City. This city is an independent region with simple
transportation purposes such as work and school commuting.
4.2 Setting of Transportation Condition
The transportation policy is evaluated on the assumption of the following conditions.
1) The rank of the country and prefecture road is set by the data of “Road drivability Map”.
2) Input data that concerns the information on the car license and the car ownership, etc. is
obtained by the questionnaire survey.
3) The evaluation is carried out for both the year 2000 and 2030. The estimated population
issued by National Institute of Population and Social Security Research is used.
4) The position of target facilities according to transportation purposes will not change in the
future. Table 3 shows the target facilities and the public attractiveness according totransportation purposes.
4.3 Analysis of the Current State and the Trend in the Future
As an example of the analysis result, Figure 5 shows the distribution of QOMR at the current
population of senior citizens. In urban area, QOMR is higher than the mean value 82%. But it
is very low in other regions. Figure 6 shows the population composition rate according to the83

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rank of QOMR . Persons in areas with a QOMR of around 20% are in a service level lower
than the mean value ( QOMR ). Table.4 shows QOMR , Atkinson index ( AI ), and QOMA
value of 2000 and 2030. QOMR decreases, AI increases. The result shows that thetransportation service level will decrease and the inequality will expand. The important reason
is that the public attractiveness of each facility decreases in proportion due to the population
decrease in the future.
Table 3. Target facilities and public attractivenessPurposeCommuting, Business

Daily Shopping.
Community facilities in aregionLarge-scale commercial
facility, Large-scale
hospitals, Large-scalecommunity facilities
Hospitals in a region
Sightseeing

Target facilities and Public attractivenessDistricts in which number of employees is concentrated
The public attractiveness is proportional to the number of employees.
The proportion will decrease as the population decreases in the
future.
Shops in this city and Community facilities in a region
The public attractiveness of each facility is assumed to be constant.
The proportion will decrease as the population decreases in the
future.
Downtown of the prefecture capital
The public attractiveness is constant.

Hospitals in this city
The public attractiveness is constant.
Kikuchi (sightseeing location) The public attractiveness is constant.

Figure 4. Distribution of population of Yamaga City
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Figure 5 Distribution of QOM value at current state (The senior citizens)
100
90rate of accumulationaccording to rank
the Q o M R mea n 82.89

share of population

80
70
60
50
40
30
20
10
0
0

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
QoM R (％ )Figure 6 Population composition by the rank

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Table 4. QOMR value
2000
2030
59491
45927
15635
17778
82.89
80.55

Population
Elderly Population
QOMR (%)
QOMA

81.12
0.0214

Atkinson index

2030/2000
0.77
1.14
0.97

78.50
0.02550.97
1.19(AI value is calculated as ε=0.8.)
4.4 Scenarios Used for Evaluation
Two scenarios are evaluated to solve the problems presented in Subsection 4.3. The firstscenario is to improve the road, and the second scenario is to distribute the population
properly to each district. Three cases were evaluated for the first scenario. The first case is thatnew roads do not need improvement. The second case is to improve sections ranked “D” to“C” in the “Road drivability Map”, which is called “road in region”. The third case is toupgrade Ueki Bypass (10 km) to the main road between Yamaga City and Kumamoto City,
which is called “main road”.
Table 5. Criteria for ranking of road
Rank
A
B
C
D

Criteria
2 or more lanes, gentle curves/slopes.
2 or more lanes, fully gentle curves/slopes.
One lane road with sharp curves.
2 or more lanes, many sharp curves and steep slopes.
One lane road with continuous sharp curves.
Road shoulders are always narrow.

The second scenario is to distribute the population properly to each district. Similarly,
three cases were evaluated in this scenario, as shown in Table 6.
Table 6. Cases Evaluated in Scenario 2: Population Distribution
Case
Maintain the current condition

Maintain the population ofmountainous districts
Concentrate the population
around the city center

MethodThe rate of change of the population according to the group’s
age for the four towns is multiplied by the current populationaccording to the age's group of each zone.
The rate of change of the population according to the group’s
age for this city is multiplied by the current populationaccording to the group’s age for each zone.
Population in the zone with QOMR less than 60% is transferredto the zone with QOMR more than 75%.

4.5 Evaluation of Cases for Scenario 1
The results of the evaluation of QOM in three cases to improve the road are shown in Figure 7
and Table 7. By improving main roads between cities, a large effect of improving of QOMR
is achieved, but the effect of improving the inequality ( AI ) is small. On the other hand,
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improving roads around this region has a large effect on improving the inequality ( AI ), but asmall effect on improving QOMR . However, the ratio of the low service population ( QOMR
is 60% or less) is the same in both cases. In 2030, compared with 2000, the transportation
service level ( QOMR ) will decrease and the inequality ( AI ) will expand. So the service levelat the current state could not be maintained only by this road improvement method.
0.026

Atkinson index

current
st at e(2030)

Mainroad(2030)

0.024

0.022
Road inregion(2030)

2000

0.02
79

80

81
mean of QOMR

82

83

Figure 7. QOM of cases to improve the road
4.6 Evaluation of the Different Cases to Distribute the Population
Figure 8 shows the evaluation results of QOM in the future in three cases to distribute thepopulation. In the case of concentrating the population around the city center, both QOMR
and the inequality ( AI ) are improved compared with the current state. However, in the case ofmaintaining the population in mountainous districts, QOMR decreases and the inequality( AI ) increase, much worse than the current state.
4.7 Direction of Transportation Policy of Yamaga City
In the future, the population will decrease due to the increasing number of senior citizens. To alarge extent, the population will concentrate in the city center and the public attractiveness ofvarious facilities will decrease. As a result, the transportation service level will decrease andthe inequality will expand in the future.
In the condition that the investment is limited, it is suggested that the administration
improve QOM, and keep equality in the entire region. This will ensure that investment will
not be wasted. This analysis shows that concentrating the population around the city centerand improving the main road from Yamaga City to Kumamoto City is a good measure thatshould be considered in the policy.

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T o maint ain of
mount ainous dist rict s(2030)

0.03

Atkinson index

current
st at e(2030)

2000

0.02

0.01
T o concent rat e aroundt he cit y cent er(2030)

0
79

80

81
82
83
mean of QOMR

84

85

Figure 8. QOM of cases to distribute population
Table 7. QOM of cases to improve the road
Traffic condition
QOMA
Total
QOMR
Adult
male
(%)
Adult female
Senior citizens
Atkinson index( AI )The ratio of the low～60%
service (QOMR)～80%
population

2000
Current state
81.1
78.5
82.9
80.6
85.5
83.2
82.2
79.9
80.9
79.3
0.02140.0255
6.3
7.2
23.9

27.5

2030
Main road Road in region
79.4
79.1
81.5
80.9
83.9
83.6
80.7
80.3
80.4
79.6
0.02530.0223
6.7
6.7
25.8

25.8

(AI value is calculated as ε=0.8.)

5. CONCLUSION
In this paper, the technique for evaluating transportation service levels by using models whichbased on Capability approach, such as model of the transportation possibilities and the modelof selected the transportation possibility was proposed. As a result, the transportation service
level can be evaluated by using the QOM value according to region attributes. Some policies
are evaluated in Yamaga City, and it was proposed that the policy of persuading individuals to
the center part be pursued
In the current transportation plan technique of person trip and other similar trip attributes,
the transportation demand is assumed to be the index for the evaluation. In the proposed
method, the transportation service level among regions is defined to be an index for theevaluation. Therefore, by this method, it becomes possible to evaluate a public transportation
planning such as bus. Moreover, it becomes possible to evaluate the overall urban planning
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because more attention is given to the place of residence and target facilities.

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