Journal of the Eastern Asia Society for Transportation Studies, Vol.12, 2017

Can Public Transportation Service Provide Maximum Satisfaction?

Min Seok KIM a, Jin Hyuk CHUNG b

a,b Dept. of Urban Planning and Engineering, Yonsei University 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea a E-mail: [email protected] b E-mail: [email protected]

Abstract: Many countries have conducted various kinds of user satisfaction surveys for public transportation services. It is necessary to develop a methodology to understand how Likert scores represent a user’s satisfaction. Satisfaction is a subjective indicator that depends on individual interpretation. For this study, we developed two such methodologies: “maximum satisfaction” and “ratio of satisfaction (ROS).” To evaluate maximum satisfaction, we developed bivariate ordered probit (BOP) models for user satisfaction with headway and access time using survey data from Korea. The ratio of maximum satisfaction to observed user satisfaction (i.e., ROS) provides valuable insight. Based on the ROS, caution should be exercised when interpreting the observed satisfaction level because the maximum satisfaction is not a perfect score of seven. Better understanding of users’ attitudes and satisfaction will be essential to attracting more people to public transportation.

Keywords: Maximum satisfaction, Public transportation, Bivariate ordered probit, Headway, Access time, Ratio of satisfaction

1. INTRODUCTION

Along with the rapid economic growth of Korea in the 1990s, the number of registered vehicles has steadily increased, with a high annual growth rate of 8.8%, from 3.39 million in 1990 to 20.1 million in 2014 (KOSIS, 2015). This growth has resulted in various transportation related problems, such as congestion, accidents, and environmental pollution that degrade urban and social life, especially in mega cities such as Seoul and its surrounding areas. Public transportation offers the promise of sustainable urban transportation systems as well as a way to resolve the problems mentioned above. Since the 2000s, intensive investment in public transit has been carried out to cope with climate change and mitigate greenhouse gases, with a high priority given to big cities (MLIT, 2011). Public transportation in Korea accounted for 45.2% of trips, and in Seoul the share was an even higher 65.6% in 2012. Although those numbers do not look bad, no significant increase in public transportation use has been experienced since then. To encourage people to use public transportation, federal and local governments have been looking to improve services. Naturally, those governments want to measure the efficacy of their new services from the users’ points of view. What are proper indicators to measure the level of public transportation services? The “Transit Capacity and Quality of Service Manual” proposes two kinds of measurement: level of service (LOS) and user satisfaction (NRC, 2013). Obviously, better services can attract more passengers and make more passengers happier, so better LOS should correlate with higher levels of satisfaction. For instance, better LOS, such as shorter travel times made possible by

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bus-exclusive lanes and improved user satisfaction with bus information systems can make bus transit more attractive. Because LOS is a purely quantitative and objective indicator, it is relatively simple and easy to measure and interpret. On the other hand, user satisfaction is qualitative and subjective; nonetheless, it is frequently adopted as an informative indicator. Contrary to expectation, better LOS does not always guarantee increased user satisfaction. Although a 5 min headway transit service can provide an excellent LOS and result in high satisfaction levels during non-peak hours and in non-urbanized areas, such service does not guarantee the same satisfaction level during peak hours in urbanized areas. Therefore, correlating LOS with satisfaction is an interesting subject, and understanding it can be helpful in the policy-making process. Many countries, including Korea, have conducted various kinds of user satisfaction surveys for public transportation service. Since 2006, the Korea Transportation Safety Authority has conducted an annual nationwide user satisfaction survey for public transportation service. The survey uses a 7-point Likert scale to investigate the linguistic degree of satisfaction for overall service and diverse service elements. Survey results are usually summarized using average values or the mode of the Likert scores to express user satisfaction. Our research questions here are “What is the true meaning of a Likert score representing a user’s satisfaction?” and “Does an average 4.5 Likert score indicate a 64% level of satisfaction if a perfect satisfaction level assumes a 7 Likert score?” If that interpretation is correct, governments and public transportation agencies should make extra efforts to reach 7 points. Is reaching a 7 Likert score realistically possible? If not, what is the highest Likert score (e.g., maximum satisfaction) that can realistically be achieved? To answer those questions, we must clearly define user satisfaction. According to the Cambridge dictionary, satisfaction is "A pleasant feeling that you get when you receive something you wanted, or when you have done something you wanted to do." That definition implies that “the pleasant feeling” can differ among individuals who receive the same service. From that perspective, user satisfaction with public transportation service can be defined as “overall level of attainment of a customer's expectations, measured as the percentage of the customer expectations actually fulfilled” (Tyrinopoulos and Antoniou, 2008). Satisfaction is thus a subjective indicator that depends on individual feelings, so users’ satisfaction levels, especially those collected from surveys, should be interpreted carefully. For this study, we were motivated to develop a new way of interpreting satisfaction measures. We therefore developed two metrics, “maximum satisfaction” and “ratio of satisfaction (ROS).” The former is a quantitative value representing the highest satisfaction level reachable in reality, and the latter is the ratio of the maximum satisfaction to current satisfaction. In other words, maximum satisfaction can be reached only if the highest quality of public transit service is provided under prevailing constraints. Hence, maximum satisfaction is not always a perfect Likert score of 7 because of physical and operational constraints. To determine the maximum satisfaction, we developed bivariate ordered probit (BOP) models for user satisfaction with headway and access time using survey data from Korea. This paper is organized as follows. Section 2 reviews previous studies on public transit satisfaction and the bivariate ordered probit models adopted in this study. Section 3 briefly describes the theoretical background of the methodology. Data in use and descriptive statistics are expressed in section 4. Section 5 re-interprets user satisfaction using the maximum satisfaction concept. Finally, we make conclusions and recommendations in section 6.

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2. PREVIOUS STUDIES

Many structural equation modeling (SEM) studies have been carried out to identify the factors that affect users’ levels of satisfaction. Shaaban and Khalil (2013) analyzed three classes of variables on the level of user satisfaction with stations, buses, and driver behavior using SEM. Their results showed that congestion and noise levels have a large influence on user satisfaction at bus stations. At the same time, punctuality and travel time have crucial effects on user satisfaction with bus service. For satisfaction with driver behavior, respecting traffic laws and driver appearance were the significant factors. Choocharuku and Sriroongvikrai (2013) analyzed user satisfaction with ’s Mass system by considering 31 service quality attributes. According to their findings, the most important factor for overall satisfaction was travel convenience, represented by 6 variables. They also distinguished four user groups by their characteristics with different variables affecting the satisfaction of each group. For example, regular users considered transit fare an important factor, whereas choice riders regarded convenience and information as fundamental aspects. Silva and Bazrafshan (2013) constructed a SEM to assess the relationship between various service elements and user characteristics. Eboli and Mazzulla (2007) analyzed the overall satisfaction of bus users using three latent variables: network configuration, service and reliability, and comfort. Among those variables, service and reliability was users’ main concern. Tyrinopoulos and Antoniou (2008) found that different factors affected satisfaction by mode. Vehicle cleanliness, staff attitudes, fare collection system for , service frequency, and network coverage area for buses and trolley buses were important factors, respectively. In summary, factors affecting user satisfaction vary by region, mode, and user characteristics. Perceptions of transportation service also influence user satisfaction under the same quality of service. However, few studies have attempted to match quality of service and user satisfaction. Various empirical models have been applied to investigate factors that affect user satisfaction. Among them, the BOP model has been frequently adopted in the transportation field because it can consider correlations between unobserved endogenous factors. Such correlations can provide additional information to interpret empirical relationships. Yamamoto and Shankar (2004) analyzed the correlation of driver injury severity (IS) and the most severely injured passenger IS using BOP. Error terms of BOP are highly and positively correlated in urban and rural areas. Log-likelihood values also improved when considering the correlation. They positively demonstrated the efficacy of the BOP model in the analysis of endogenous variables. Panagiotis et al. (2012) applied a random coefficients model of BOP to household automobile and motorcycle ownership in 2012. They found that ownership of automobiles and motorcycles had a statistically significant negative correlation between error terms. In terms of goodness of fit, the log-likelihood value was significantly improved compared with a univariate ordered model. Last but not least, Chang and Hong (2013) adopted a BOP model for route choice behaviors between main freeways and alternative routes under three different traffic conditions in Taiwan, which also showed the efficacy of BOP. However, very few studies have used the BOP model in the field of satisfaction analysis for public transportation services.

3. METHODOLOGY

We applied a BOP model to reinterpret user satisfaction with the concept of maximum satisfaction. BOP has the advantage of considering two closely related dependent variables by means of the correlation between their error terms. That correlation can provide extra

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information to interpret the system of equations, which makes BOP an attractive model for analyzing traffic accident studies, agriculture and industrial research, and so forth (Russo et al., 2014; Chun and Mun, 2013; Kwon et al., 2010). In our BOP model, we consider satisfaction with headway and access time as two endogenous variables. Satisfaction is measured by survey using a 7 point Likert scale, which can be identified with a total of 49 cases, as shown in Figure 1.

Figure 1. A probability distribution applied using a bivariate ordered probit model

The correlation of two variables, dependent variables (yi *) describing public transit user (푖)’s satisfaction with headway and access time and explanatory variable (X) affecting headway, can be represented as follows (Greene and Hensher, 2009).

∗ ′ ∗ 푦푖,1 = 휷1휲푖,1 + 휀푖,1, 푦푖,1 = 푗 푖푓 휇푗−1 < 푦푖,1 < 휇푗, 푗 = 0, … , 퐽1, (1) ∗ ′ ∗ 푦푖,2 = 휷2휲푖,2 + 휀푖,2, 푦푖,2 = 푗 푖푓 훿푗−1 < 푦푖,1 < 훿푗, 푗 = 0, … , 퐽2, (2) To consider the mutual effects of two variables, the correlation of the error terms can be represented by the following.

휀푖,1 0 1 휌 (3) ( ) ~푁 [( ) , ( ) ] 휀푖,2 0 휌 1 Where 훸 = vector of explanatory variables that determine headway and access time, 훽 = vector of estimable parameters, 휇 and 훿 = estimable parameters (thresholds) that define y and are estimated jointly with model parameters 훽, 푦 = integer ordering, 푗 = integer ordered choice (for headway and access-time, these are zero to six) 휀 = disturbance terms [assumed to be normally distributed (푁) with zero mean and variance of one], 휌 = cross-equation correlation coefficient of error terms.

The BOP model with joint probability (푝) for 푦푖,1 = 푗, 푦푖,2 = 푘 is then defined as 푃푟표푏(푦푖,1 = 푗, 푦푖,2 = 푘 | 휲푖,1, 휲푖,2) =

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′ ′ ′ ′ 훷2[(휇푗 − 휷1휲푖,1), (훿푘 − 휷2휲푖,2), 휌] 훷2[(휇푗 − 휷1휲푖,1), (훿푘−1 − 휷2휲푖,2), 휌] [ ′ ′ ] − [ ′ ′ ](4) −훷2[(휇푗−1 − 휷1휲푖,1), (훿푘 − 휷2휲푖,2), 휌] −훷2[(휇푗−1 − 휷1휲푖,1), (훿푘−1 − 휷2휲푖,2), 휌]

Where 훷2(∙) denotes the cumulative density function for the bivariate standard normal distribution with correlation 휌. Finally, we use the joint probability from the BOP to calculate the maximum satisfaction for a given headway and access time, as shown in Eq. (5).

7 푆̂푚푎푥 = ∑ 푃푟 (푆 = 푖) × 푖 (5) 푖=1 where 푖, 푆 = satisfaction (between 1 and 7)

푆̂푚푎푥 = maximum satisfaction.

4. DATA IN USE

A satisfaction survey targeting nationwide public transportation users has been conducted annually in Korea since 2006. The sample size of the survey is more than 65,000, and data are collected by on- and off-line methods. The data have been used for various purposes, such as evaluating the satisfaction level in local administrative areas, developing new public transit policies, and measuring the efficacy of transportation-related policies from the viewpoint of user satisfaction. In this study, we used data from the 2014 survey acquired from the Traffic Safety Authority. The 2014 survey included several additional questions to identify the relationship between satisfaction and experienced quantitative values (e.g., headway, access time, information, and so forth). Questionnaires including the extra questions were distributed to 1,543 people (bus: 1,076 persons, subway: 467 persons) by stratified random sampling method, taking into account gender/age and population of the administrative region. Satisfaction with public transportation service was measured by a 7-point Likert scale (very dissatisfied= 1, dissatisfied = 2, a little dissatisfied = 3, neutral = 4, a little satisfied = 5, satisfied = 6, very satisfied = 7). In this survey, we asked the major travel pattern of the administrative unit but the analysis variable was determined as city/transportation (bus, subway) due to lack of samples on total administrative district. The five service items (headway, fee, access time, operating accuracy, safe driving) were surveyed in order to quantify the satisfaction. The analysis was performed on headway and access time with the highest correlation among these items. For the purpose of this study, we proposed a methodology for quantitatively analyzing satisfaction by considering the correlation between two variables. It is also necessary to take into account the remaining variables in the future. According to the descriptive statistics, 61.7% of subway users have an automobile available for commuting, which is 13.4% higher than among bus users. Subway users are more satisfied with the headway than bus users, 4.43 and 3.94, respectively. Those numbers are reasonable because the bus headway, 14.68 minutes, is much longer than the subway headway of 8.67 minutes. The average access times for bus and subway are 9.50 min. and 8.99 min., respectively. The average satisfaction score for bus is higher than for subway (4.73 for bus and 4.46 for subway). The data used in this study are summarized in Table 1.

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Table 1. Descriptive statistics Bus (N=1,076) Subway (N=467) Attribute Number of Number of Ratio (%) Ratio (%) Respondents Respondents Male 407 37.8 236 50.5 Gender Female 669 62.2 231 49.5 Younger than 20 131 12.2 16 3.4 20–29 342 31.8 142 30.4 30–39 319 29.6 161 34.5 Age 40–49 202 18.8 102 21.8 50–59 69 6.4 39 8.4 60 and above 13 1.2 7 1.5 Seoul 150 13.9 150 32.1 City Metropolitan 583 54.2 317 67.9 Other 343 31.9 - - Commuting 581 54.0 309 66.2 School 227 21.1 60 12.8 Purpose Work 73 6.8 33 7.1 Leisure 106 9.9 37 7.9 Other 89 8.3 28 6.0 Car With car 520 48.3 288 61.7 ownership Without car 556 51.7 179 38.3 Bus (N=1,076) Subway (N=467) Mean SD Mean SD Time (min) 14.68 9.802 8.67 6.599 Headway Satisfaction 3.94 1.345 4.43 1.269 Time (min) 8.99 8.245 9.50 6.226 Access time Satisfaction 4.73 1.241 4.46 1.208 Note 1) SD =standard deviation.

5. EMPERICAL MODELS AND FINDINGS

Calculating maximum satisfaction requires a determination of ideal service conditions for headway and access time. The ideal service indicates the best service considering the prevailing operational and infrastructural constraints. For headway, we applied the concepts of minimum headway proposed by Vuchic (2005): Way headway and Station headway. Way headway indicates the time determined by the physical characteristics (e.g., technology, method of driving and control, degree of safety required) of a transit system between stations. Station headway indicates factors (e.g., rate of boarding/alighting, departure control, etc.) that influence station operations. In this study, we use the shortest headway between the two as the ideal minimum headway: 3 min for bus and 2 min. for subway, the shortest headways observed in the Seoul metropolitan area. The ideal access time would be zero. We investigated the factors that affect user satisfaction in two models. Model 1 includes service and regional variables to determine how regional characteristics affect the level of user satisfaction. Model 2 has additional personal characteristics, such as gender, age, driving purpose, and car ownership.

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Using LIMDEP Econometrics software, we estimated our BOP models as shown in Tables 2 and 3. Parameters estimated for satisfaction with headway and access time are mostly statistically significant, with (-) indicating negative effects and (+) indicating positive effects on satisfaction. We interpret the results of Model 1 as follows: Users in Seoul are more satisfied with the bus than users living in regional metropolitan areas and other cities when the same headway and access services are provided. The correlation parameters (휌) of the bus and subway are 0.382 and 0.587, respectively, which demonstrates the efficacy of the BOP models. In other words, the model reveals the correlation between unobserved variables related to satisfaction with access time and headway. Evidence of correlation can be found in the log-likelihood values as well. The log-likelihood for the bus improves from -3,397.96 to -3,325.80 and that for the subway improves from - 1,464.79 to -1,382.19. Log-likelihood values higher than those in the univariate model verify the need to consider the correlation of endogenous variables.

Table 2. Bivariate ordered probit model of satisfaction with headway and access time (Model 1) Bus (N=1,076) Subway (N=467) Variable Coefficient SE t-value p-value Coefficient SE t-value p-value Constant 2.295*** 0.093 24.640 0.000 2.442*** 0.177 13.76 0.000 Headway -0.045*** 0.002 -23.520 0.000 -0.035*** 0.006 -6.30 0.000 Headway Seoul city 0.364*** 0.099 3.670 0.000 -0.164* 0.107 -1.54 0.124 Local city 0.274*** 0.072 3.800 0.000 - - - - Constant 2.650*** 0.125 21.220 0.000 2.809*** 0.189 14.85 0.000 Access Access time -0.036*** 0.003 -11.330 0.000 -0.047*** 0.008 -6.22 0.000 time Seoul city 0.253*** 0.103 2.450 0.014 -0.198** 0.106 -1.87 0.062 Local city -0.008 0.071 -0.110 0.915 - - - - Threshold parameters probability model for headway and access time μ1 0.604*** 0.059 10.280 0.000 0.629*** 0.141 4.48 0.000 μ2 1.315*** 0.070 18.710 0.000 1.231*** 0.147 8.35 0.000 Headway μ3 2.219*** 0.080 27.760 0.000 2.065*** 0.156 13.26 0.000 μ4 3.086*** 0.090 34.440 0.000 3.005*** 0.164 18.33 0.000 μ5 4.149*** 0.131 31.760 0.000 3.832*** 0.188 20.39 0.000 δ1 0.561*** 0.100 5.620 0.000 0.662*** 0.136 4.87 0.000 δ2 1.156*** 0.115 10.100 0.000 1.318*** 0.143 9.20 0.000 Access δ3 2.176*** 0.120 18.070 0.000 2.304*** 0.152 15.20 0.000 time δ4 3.059*** 0.123 24.880 0.000 3.331*** 0.163 20.41 0.000 δ5 3.794*** 0.129 29.470 0.000 4.093*** 0.190 21.51 0.000 LL(β1) a -3,397.96 -1,464.79 LL(β) -3,325.80 -1,382.19 Disturbance correlation = ρ(X1, X2) ρ(X1, X2) 0.382 0.026 14.630 0.000 0.587*** 0.026 22.370 0.000 Note 1) a: The log-likelihood at convergence obtained by setting ρ=0. 2) ***, **, * : Significance at 5%, 10%, 20% level.

Model 2 provided the following information: Users younger than 30 years old have lower satisfaction with headway and access time on the bus, whereas they have higher satisfaction with access time on the subway compared with other age groups. Users who have their own cars, choice riders, are more satisfied than users without cars, captive riders, with both the bus

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and subway (except for access time on the bus). Users making commuting trips have lower satisfaction for the same bus access time than riders for other trip purposes. Commuters are more sensitive to access time because time on commuting trips is much more valuable than on trips for other purposes. Correlation parameters (휌) for the bus and subway are 0.367 and 0.582, respectively, which demonstrates the efficacy of the BOP model, as with model 1. The log-likelihood for the bus improves from -3,370.49 to -3,303.89, and that for the subway improves from -1,450.37 to -1,370.24, with implications similar to those given for model 1.

Table 3. Bivariate ordered probit model for satisfaction with headway and access time (Model 2) Bus (N=1,076) Subway (N=467) Variable Coefficient SE t-value p-value Coefficient SE t-value p-value Constant 2.337*** 0.120 19.500 0.000 2.233*** 0.188 11.880 0.000 Headway -0.046*** 0.002 -23.880 0.000 -0.036*** 0.006 -6.390 0.000 Seoul city 0.343*** 0.101 3.400 0.001 -0.154* 0.108 -1.420 0.155 Local city 0.298*** 0.073 4.060 0.000 - - - - Headway Male 0.165*** 0.065 2.530 0.011 0.097 0.090 1.080 0.280 Younger than 30 -0.134** 0.073 -1.820 0.069 - - - - Older than 50 - - - - 0.235* 0.159 1.480 0.139 Commuter -0.206*** 0.071 -2.890 0.004 - - - - Car ownership 0.235*** 0.076 3.110 0.002 0.284*** 0.110 2.590 0.010 Constant 2.707*** 0.131 20.710 0.000 2.492*** 0.209 11.900 0.000 Access time -0.036*** 0.003 -11.190 0.000 -0.046*** 0.008 -5.790 0.000 Seoul city 0.294*** 0.105 2.790 0.005 -0.185** 0.108 -1.710 0.087 Local city -0.014 0.072 -0.190 0.849 - - - - Access Male ------time Younger than 30 - - - - 0.245*** 0.102 2.400 0.017 Older than 50 - - - - 0.317* 0.202 1.570 0.117 Commuter -0.250*** 0.068 -3.670 0.000 - - - - Car ownership 0.199*** 0.070 2.860 0.004 0.369*** 0.110 3.370 0.001 Threshold parameters probability model for headway and access time μ1 0.620*** 0.060 10.280 0.000 0.635*** 0.142 4.470 0.000 μ2 1.346*** 0.072 18.680 0.000 1.248*** 0.150 8.330 0.000 Headway μ3 2.267*** 0.082 27.650 0.000 2.098*** 0.159 13.210 0.000 μ4 3.151*** 0.092 34.250 0.000 3.057*** 0.168 18.220 0.000 μ5 4.226*** 0.133 31.690 0.000 3.893*** 0.192 20.330 0.000 δ1 0.566*** 0.101 5.590 0.000 0.678*** 0.143 4.740 0.000 δ2 1.165*** 0.116 10.060 0.000 1.338*** 0.149 9.010 0.000 Access δ3 2.192*** 0.122 17.920 0.000 2.335*** 0.157 14.890 0.000 time δ4 3.084*** 0.125 24.610 0.000 3.382*** 0.170 19.940 0.000 δ5 3.826*** 0.131 29.120 0.000 4.156*** 0.198 20.990 0.000 LL(β1) a -3,370.49 -1,450.37 LL(β) -3,303.89 -1,370.24 Disturbance correlation = ρ(X1, X2) ρ(X1, X2) 0.367*** 0.026 13.960 0.000 0.582*** 0.027 21.640 0.000 Note 1) a: The log-likelihood at convergence obtained by setting ρ=0. 2) ***, **, * : Significance at 5%, 10%, 20% level.

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Table 4 represents the choice probabilities for satisfaction when providing ideal LOS for headway and access time to subway users in the city of Seoul using Model 1. The choice probabilities for pairs of satisfaction with headway and access time vary when considering correlations (휌 ≠0) or not (휌 =0). The choice probability shows that as headway gets longer, the choice probability of lower satisfaction with headway tends to increase. On the other hand, if headway gets shorter, the choice probability of higher satisfaction with headway tends to increase. The maximum satisfaction with headway and access time can be calculated using marginal probability. For instance, the maximum satisfaction score with 2 min. of headway (i.e., the shortest headway that can be provided in reality) is 4.59 points when considering correlations (휌 ≠0). We then calculate the maximum satisfaction score as follows. The first and second numbers in parenthesis represent the probability of choosing the Likert scores under the given conditions and Likert scores, respectively. In other words, maximum satisfaction is the weighted average of the Likert scores by choice probability under ideal conditions.

푆̂max (ℎ푒푎푑푤푎푦_푆푢푏푤푎푦_푆푒표푢푙) = [(0.0137 × 1) + (0.0437 × 2) + (0.1072 × 3) + (0.2791 × 4) + (0.3439 × 5) + (0.1605 × 6) + (0.0520 × 7)] = 4.59

Table 4. Choice probability for satisfaction with subway headway and access time in Seoul Univariate model Access time satisfaction (훒 = ퟎ) 1 2 3 4 5 6 7 Total 1 0.0000 0.0000 0.0001 0.0032 0.0086 0.0021 0.0001 0.0141 2 0.0000 0.0000 0.0003 0.0093 0.0252 0.0063 0.0002 0.0414 3 0.0000 0.0000 0.0013 0.0349 0.0943 0.0236 0.0008 0.1548 Headway 4 0.0000 0.0000 0.0020 0.0547 0.1477 0.0370 0.0012 0.2426 satisfaction 5 0.0000 0.0001 0.0027 0.0761 0.2056 0.0515 0.0016 0.3376 6 0.0000 0.0000 0.0013 0.0359 0.0969 0.0243 0.0008 0.1592 7 0.0000 0.0000 0.0004 0.0113 0.0306 0.0077 0.0002 0.0503 Total 0.0000 0.0002 0.0081 0.2255 0.6089 0.1526 0.0048 1.0000 ↓ Bivariate model Access time satisfaction (훒 ≠ ퟎ) 1 2 3 4 5 6 7 Total 1 0.0012 0.0028 0.0042 0.0045 0.0010 0.0000 0.0000 0.0137 2 0.0013 0.0049 0.0110 0.0189 0.0070 0.0006 0.0000 0.0437 3 0.0011 0.0061 0.0190 0.0485 0.0284 0.0037 0.0004 0.1072 Headway 4 0.0007 0.0057 0.0258 0.1075 0.1100 0.0253 0.0041 0.2791 satisfaction 5 0.0001 0.0016 0.0111 0.0827 0.1604 0.0685 0.0196 0.3439 6 0.0000 0.0001 0.0012 0.0173 0.0653 0.0506 0.0260 0.1605 7 0.0000 0.0000 0.0001 0.0018 0.0129 0.0182 0.0191 0.0520 Total 0.0045 0.0211 0.0723 0.2811 0.3849 0.1668 0.0692 1.0000 Note: The shaded areas indicate an increased probability of selection area.

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The maximum satisfactions with headway and access time by region can be evaluated using model 1, as shown in Table 5. The “user satisfaction” column represents the observed average satisfaction scores for a certain user group under prevailing conditions, and the “maximum satisfaction” column indicates the estimated maximum satisfaction for a certain user group under the assumed ideal conditions shown in the “best condition” column. The ratio of maximum satisfaction to observed user satisfaction (ROS) provides valuable insights. For instance, the average value of observed satisfaction in the metropolitan cities is 3.81, which seems to require immediate improvement at first glance. However, the estimated maximum satisfaction score of 4.40 indicates that the current score has already reached 86.6% of maximum satisfaction (i.e., ROS is 86.6%). In Seoul, ROS for headway on the subway is 94.8%. Thus, ROS indicates that caution should be exercised when interpreting observed satisfaction levels because the maximum satisfaction is not a perfect score of 7.

Table 5. Level of satisfaction with headway and access time by region Best Ratio of User Maximum Attribute condition satisfaction satisfaction satisfaction (min) [ROS] Seoul city 4.47 4.86 92.0% Bus Metropolitan city 3.81 3.00 4.40 86.6% Headway Local city 3.93 4.71 83.4% Seoul city 4.35 4.59 94.8% Subway 2.00 Metropolitan city 4.47 4.78 93.5% Seoul city 5.03 5.34 94.2% Bus 0.00 Access Metropolitan city 4.67 5.06 92.3% time Seoul city 4.32 4.80 90.0% Subway 0.00 Metropolitan city 4.52 5.01 90.2%

Model 2 provides more fruitful interpretations. Because the models include several dummy variables, the maximum satisfaction of various user groups can be evaluated, as shown in Table 6. The individual/regional characteristics with statistical significance were subdivided into nine groups. It is possible to improve the understanding of the characteristics of the users by purpose and region. We can compare ROS according to regional/individual characteristics on headway and access time by analyzing the characteristics of each group. For example, Group 1, 2 and 3 users commonly are more than 30 years old, and own an automobile but take buses for commuting trips. They have different regional characteristics. The result indicates that ROS of head is highest in metropolitan city, followed by Seoul and local city. Group 4 and 5 includes users who are more than 50 years old, own a car, and use the subway. It is showed that Seoul city is more satisfied than the metropolitan city. Satisfaction on access time could be also compared to bus and subway users as in the previous methods. According to Table 7, group 6 has the highest satisfaction score, but group 4 has the highest ROS. Hence, user satisfaction and ROS are different measurements that can give analysts and policy makers different information.

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Table 6. User groups for analysis Headway Access time

Attribute Bus Subway Bus Subway Group Group Group Group Group Group Group Group Group 1 2 3 4 5 6 7 8 9 Seoul city ○ - - ○ - ○ - ○ - Metropolitan - ○ - - ○ - ○ - ○ city Local city - - ○ ------Male ○ ○ ○ ------Younger than 30 x x x ------Older than 50 - - - ○ ○ - - ○ ○ Commuter ○ ○ ○ - - ○ ○ - - Car ownership ○ ○ ○ ○ ○ ○ ○ ○ ○

Table 7. ROS for headway and access time by user group Best Ratio of User Maximum Attribute condition satisfaction satisfaction satisfaction (min) [ROS] Group 1 4.38 4.99 87.8% Bus Group 2 4.11 3 4.61 89.2% Headway Group 3 4.27 4.97 85.9% Group 4 4.87 4.91 99.2% Subway 2 Group 5 4.86 5.08 95.7% Group 6 5.18 5.37 96.5% Bus 0 Access Group 7 4.54 5.04 90.1% time Group 8 4.60 5.15 89.3% Subway 0 Group 9 5.00 5.34 93.6%

6. CONCLUSIONS AND RECOMMENDATIONS

Satisfaction is the overall level at which expectations are met, measured as the percentage actually fulfilled. Because it is subjective, satisfaction is difficult to measure in reality. Nevertheless, various satisfaction surveys have been conducted in transportation, and the results are frequently used to understand user satisfaction and make policies to provide better services. The maximum satisfaction calculation we developed in this study can allow analysts and policy- makers to reinterpret the results of satisfaction surveys and derive additional information from them. Maximum satisfaction is the highest satisfaction score achievable in reality. To evaluate it, we constructed two BOP models with consideration of correlations between unobserved factors for satisfaction with headway and access time. Whereas Model 1 used only service and

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regional variables to determine how regional characteristics affect user satisfaction, Model 2 included additional personal characteristics. The models showed that choice riders have higher satisfaction with bus and subway service than captive riders. Commuters have lower satisfaction with access time and headway because time spent commuting is more valuable than that spent on trips made for other purposes. Moreover, correlations between unobserved terms of endogenous variables were statistically significant, which shows the efficacy of our BOP models. The increment of log-likelihood values provides more evidence for the appropriateness of the BOP models. Another role of the models is to evaluate the maximum satisfaction for various user groups under ideal service conditions. In the models, we applied achievable service conditions for headway and access time. The resulting ratio of maximum satisfaction to current satisfaction [ROS] provides valuable information to policy makers and offers another way to interpret the satisfaction scores collected from surveys. According to the raw survey results, the average value of observed satisfaction in the metropolitan cities is 3.81 from a perfect score of 7. However, when considering the ROS, the current score has already reached 86.6% of an achievable maximum satisfaction score of 4.40. Likewise, the ROS for subway headway in Seoul of 94.8% suggests that caution is required in interpreting the observed satisfaction score of 4.35. Our newly developed maximum satisfaction and ROS calculations can be used to evaluate current public transportation services and determine which service elements need to be improved. At the same time, the new measures can provide useful insights to policy makers. This study is a small stride toward understanding user satisfaction from a different point of view and needs to be expanded to consider other factors that significantly affect user satisfaction. Better understanding of users’ attitudes and satisfaction will be an essential platform for attracting more people to public transportation.

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