On-Demand Transit User Preference Analysis using Hybrid Choice Models
OOn-Demand Transit User Preference Analysis using Hybrid Choice Models
Nael Alsaleh
Laboratory of Innovations in Transportation (LiTrans) Department of Civil Engineering, Ryerson University, Toronto, ON Canada, M5B 2K3 Email: [email protected]
Bilal Farooq*
Laboratory of Innovations in Transportation (LiTrans) Department of Civil Engineering, Ryerson University, Toronto, ON Canada, M5B 2K3 Email: [email protected]
Yixue Zhang
Department of Geography & Planning, University of Toronto, Toronto, ON Canada, M5S 1A1 Email: [email protected]
Steven Farber
Department of Geography & Planning, University of Toronto, Toronto, ON Canada, M5S 1A1 Email: [email protected]
Abstract
In light of the increasing interest to transform the fixed-route public transit (FRT) services into on-demand transit (ODT) services, there exists a strong need for a comprehensive evaluation of the effects of this shift on the users. Such an analysis can help the municipalities and service providers to design and operate more convenient, attractive, and sustainable transit solutions. To understand the user preferences, we developed three hybrid choice models: integrated choice and latent variable (ICLV), latent class (LC), and latent class integrated choice and latent variable (LC-ICLV) models. We used these models to analyze the public transit user’s preferences in Belleville, Ontario, Canada. Hybrid choice models were estimated using a rich dataset that combined the actual level of service attributes obtained from Belleville's ODT service and self-reported usage behaviour obtained from a revealed preference survey of the ODT users. The latent class models divided the users into two groups with different travel behaviour and preferences. The results showed that the captive user’s preference for ODT service was significantly affected by the number of unassigned trips, in-vehicle time, and main travel mode before the ODT service started. On the other hand, the non-captive user’s service preference was significantly affected by the Time Sensitivity and the Online Service Satisfaction latent variables, as well as the performance of the ODT service and trip purpose. This study attaches importance to improving the reliability and performance of the ODT service and outlines directions for reducing operational costs by updating the required fleet size and assigning more vehicles for work-related trips.
Keywords:
On-demand transit (ODT); On-demand mobility; Behavioural modelling; Latent class model (LCM); Integrated choice and latent variable (ICLV); Hybrid choice models. * Corresponding author lsaleh, Farooq, Zhang, and Farber
1. Introduction
In low demand areas, on-demand public transit (ODT) service is emerging as an attractive solution that can address key issues associated with the existing fixed-route public transit (FRT) service. In such settings, as a compromise between the occupancy of the vehicle and their operational cost, FRT is often operated with very low frequency, limited operating hours, and inadequate spatial coverage (Papanikolaou et al., 2017; Sanaullah et al., 2021). These circumstances can make FRT inconvenient and unattractive for residents, especially for non-captive users, who have alternative travel options available to satisfy their travel needs. Alternatively, the main philosophy behind an ODT service is to minimize the operational cost of the service by dynamically adjusting to the user schedules instead of reducing the service frequency. The ODT proponents argue that it may provide higher service quality and lower operational cost than FRT in low-demand and low-density areas (Papanikolaou et al., 2017). Early adoptions in North America include Chatham-Kent, Sault Sainte Marie, and Belleville in Ontario, St. Albert, Calgary, Cochrane, and Okotoks in Alberta, as well as Regina and Saskatoon in Saskatchewan (Klumpenhouwer, 2020). Unlike ride-hailing, in the ODT service the fare is predominantly fixed, fleet-size remains stable, vehicles are mainly owned by an organization (e.g. municipality), and drivers receive a fixed salary. In September 2018, one of the first ODT projects started in Belleville, Ontario, Canada, where the city collaborated with a private sector partner to convert its late-night FRT service operated on route 11 (RT-11) into an ODT service. The resulting service altered its operating routes according to the real-time spatio-temporal demand the system received. The service was no longer limited to the original RT-11 stops. Instead, it covered the entire city based on the pickup and dropoff requests. Users booked their trips online using the service app, website, or by calling the phone number. The Belleville ODT service runs for 5 hours during the weekends and 3 hours during the weekdays, from 7:00 PM to 12:00 AM and from 9:00 PM to 12:00 AM, respectively (Alsaleh and Farooq, 2020; Sanaullah et al., 2021). Certain key features of the ODT service, for instance, route flexibility and larger service areas, may render the service inconvenient for some users. Waiting time of the user (the difference between the actual pickup time and the requested pickup time) and in-vehicle time might be different each time an ODT trip request is placed, even if the requests are made at the same time of the day or day of the week, from the same origin to the same destination. Unlike the FRT, which runs along a predefined fixed route with a predefined schedule, an ODT user's waiting and in-vehicle times would depend on the number of detours the bus makes. Moreover, the performance of an ODT service is affected by the number of requests the system receives, especially when the supply side (maximum number of available vehicles) is limited. Therefore, users might experience long waiting and in-vehicle times when the ODT service encounters unusually high demand, for instance, during public holidays, special events, and on frigid winter days. This pattern was confirmed by the study conducted by Sanaullah et al. (2021), which showed that both the number of ODT trips and service performance were unstable during the first three months of operation, starting October 2018. The average waiting time in November and December 2018 was 7 minutes (30%) longer than the average waiting time before and after, due to the holiday season related increase in the number of requested trips. The preference of ODT as a sustainable mode choice for users may vary based on their experience and attitudes towards the service. Thus, for the sustainable adoption of the ODT service, this study investigates the following key questions: • Do the attitudes and perceptions towards the ODT service affect user’s preference between the FRT and ODT services? • Is there a difference in the service preference between the ODT captive and non-captive users? • What can transit operators do to attract more users and influence the non-captive users to become regular ODT service users? lsaleh, Farooq, Zhang, and Farber
2. Background
This section reviews previous studies that modelled and analyzed user preference for flexible transit services. We also present recent advancements in the use of discrete choice modelling to address travel behaviour issues. It is important to note that currently, there is a lack of literature that directly models the behaviour of the ODT users in general and their service preferences in particular. This lack is due to the limited number of ongoing ODT projects in the market and availability of revealed as well as stated preference data on the topic. 2.1. Discrete Choice Modelling Traditional random utility maximization (RUM) based discrete choice models have been used extensively in modelling the individual travel behaviour (Ben-Akiva and Lerman, 1985; Pryanishnikov and Zigova, 2003). These models are generally based only on the observable variables and do not consider the impact of decision-makers’ attitudes, perceptions, and lifestyles on their decision-making behaviour (Ababio-Donkor et al., 2020). Furthermore, the parameter estimates of these models might be ambiguous as a consequence of assuming that the entire population has the same preference structure and choice behaviours, given that the transportation market has different segments (Hurtubia et al., 2014; Alizadeh et al., 2019; Zhou et al., 2020). Therefore, several RUM based hybrid choice models have been developed to overcome these limitations, for instance, integrated choice and latent variable (ICLV) model, latent class (LC) model, and the latent class integrated choice and latent variable (LC-ICLV) model. The ICLV model, which was proposed by McFadden (1986), is a modified version of RUM based logit model. It incorporates the individual’s attitudes, perceptions, norms, or lifestyles into the systematic component of the utility function as latent variables (Alizadeh et al., 2019; Ababio-Donkor et al., 2020). Cantillo et al. (2015) used ICLV model to capture the impact of the attractiveness and the safety/security latent variables in addition to other directly measured variables on the pedestrian crossing behaviour in urban roads. The study reported that both latent variables had a significant impact on pedestrians crossing behaviour. To explain the car purchase decision among the Indonesian students, Belgiawan et al. (2016) estimated an ICLV model with symbolic/affective, arrogance prestige, independence, comfort, and lsaleh, Farooq, Zhang, and Farber lsaleh, Farooq, Zhang, and Farber lsaleh, Farooq, Zhang, and Farber
3. Data Description
Figure 1 shows the steps taken to prepare the dataset for the modelling exercise. Two data sources were used to develop the fused data for this study: (a) a web-based revealed preference survey that was distributed to Belleville’s ODT users through email in November 2019, and (b) operational data collected from Belleville’s ODT pilot project from October till December 2018. It is worth mentioning that both datasets have been independently analyzed in previous studies. The revealed preference data were employed to describe the user profiles and explore the relationship between satisfaction with the ODT service and activity participation (Zhang et al., 2020a and Zhang et al., 2020b). The operational data were used to perform spatiotemporal analysis of supply, level of service, and origin-destination patterns, as well as to develop trip production and distribution models (Sanaullah et al., 2021 and Alsaleh and Farooq, 2020). However, to better understand the ODT user preference between the FRT and ODT services, both datasets were merged and analyzed collectively in this study. In the revealed preference survey, the following information were collected for each participant: • Sociodemographic and socioeconomic characteristics, for instance age, gender, marital status, education level, income, household size, and car ownership. lsaleh, Farooq, Zhang, and Farber • Experience with the ODT service, such as trip purpose, in-vehicle time with the ODT service compared to the FRT service, and preferred mode at night between the FRT and ODT services. • Travel history in the past few months, including the main travel mode before the ODT service was launched, and the main travel mode when the FRT was running at night. • Attitudinal and perceptional questions about the ODT features. Participants were asked about their attitudes towards 7 statements, that were based on psychometric indicators, to capture their attitudes and perceptions towards the flexibility and quality of the ODT service, as shown in Table 1. More specifically, participants were asked to rate the importance of the waiting time, in-vehicle time, reliability, and the flexibility of ODT service on their decision to use the ODT service using a five-point Likert scale ranging from not at all important to extremely important. Besides, participants were asked to provide their satisfaction with the ODT mobile app interface, website interface, and their available services using a five-point Likert scale ranging from very unsatisfied to very satisfied.
Table 1.
Attitudinal and perceptional questions
No. Question How important is the waiting time in influencing your choice of using ODT at night? How important is the time on the ODT bus in influencing your choice of using ODT at night? How important is the reliability (bus shows up when it is supposed to) in influencing your choice of using ODT at night? How important are the convenience and the flexibility in influencing your choice of using ODT at night? How satisfied are you with the user interface of the ODT app? How satisfied are you with the user interface of the ODT website? How satisfied are you with the availability of schedule/maps/fares?
The survey was sent via email to 1,342 users and 263 responses were received. For more details about the revealed preference survey used in this study, interested readers are referred to Zhang et al. (2020b). On the other hand, the ODT service's operational data were collected from October to December 2018. These data contained detailed information about the trip’s history for 430 users, including their IDs (email addresses), trip request creation date and time, trip request time, trip status (assigned or not assigned), actual pickup time, number of riders, pickup stop, and dropoff stop. For further details on the operational data analysis of Belleville's ODT service, we refer the readers to Sanaullah et al. (2021). In this study, the revealed preference survey was used to obtain the socioeconomic and sociodemographic characteristics, psychometric indicators, self-reported attributes of the ODT service, and alternative travel modes of participants. Participant’s choice preference between the ODT and the FRT services was based on their answers to the following statement: “I would prefer to have fixed route busses at night”.
We considered those with “Strongly Agree” or “Agree” answers to prefer the FRT alternative, and those with “Strongly Disagree” or “Disagree” answers to prefer the ODT alternative. However, respondents who answered “Neither agree nor disagree” were considered to be indifferent between the FRT and ODT services. On the other hand, the operational data were used to obtain the number of assigned trips, the number of unassigned trips, and the average waiting time for the users. Then, the information obtained from both the revealed preference survey and the operational data of the ODT service were merged based on the common “email address” information, forming a fused dataset of 72 observations. It is worth noting that the differences between the fused dataset and both the operational and the revealed preference data were statistically verified. The results showed that there are no significant differences between the three samples (see Appendix B for details). lsaleh, Farooq, Zhang, and Farber Figure 1.
Data collection steps
Table 2.
Description of the observed variables
Variable N % Variable N %
Socioeconomic and Sociodemographic
Less than FRT
19 26.4 Age Equal to FRT 25 34.7 Young (18 – 24) 29 40.3 More than FRT 28 38.9 Adults (25 – 44) 33 45.8 Trip Purposes Middle-age (45 – 64) 10 13.9 Work-based 29 40.3 Old (more than 64) 0 0 Nonwork-based 11 15.3 Gender Mixed purposes 32 44.4 Male 34 47.2 Travel mode when FRT was running at night Female 36 0.5 Active Mode (walking or cycling) 25 34.7 Other 2 2.8 Car as a driver or passenger 25 34.7 lsaleh, Farooq, Zhang, and Farber Marital Status FRT service 14 19.5 Single 45 62.5 Mobility Bus Service 3 4.2 Married 9 12.5 Not applicable 5 6.9 Widowed 2 2.8
Actual Attributes
Divorced 5 6.9 Assigned trips levels Other 11 15.3 Low (less than 3)
46 63.9 Education Level Medium (3 – 7) 16 22.2 Secondary School 30 41.7 High (more than 7) 10 13.9 Diploma 24 33.3 Unassigned trips levels Undergraduate 9 12.5 Low (less than 5) 46 63.9 Graduate 9 12.5 Medium (5 – 11) 16 22.2 Annual Income Level (Thousand CAD) High (12 – 23) 8 11.1 Low (less than 20) 39 54.1 Very High (more than 23) 2 2.8 Medium (20 – 50) 22 30.6 Average waiting time levels (minutes) High (more than 50) 11 15.3 Low (less than 10) 19 26.4 Household Size Level Medium (10 – 20) 28 38.9 Low (1 – 3) 44 61.1 High (21 - 33) 20 27.8 High (+4) 28 38.9 Very High (more than 33) 5 6.9 Car ownership
Choice Alternatives
0 68 94.4 FRT 40 55.6 +1 4 5.6 ODT 23 31.9
Self-reported Attributes
Indifferent 9 12.5
4. Methodology and Model Specifications
To investigate the user preference, three hybrid choice models were developed, namely Latent Class (LC), Integrated Choice and Latent Variable (ICLV), and Latent Class Integrated Choice and Latent Variable (LC-ICLV) model. Moreover, a Multinomial Logit (MNL) model was used for comparison purposes. The variables used to formulate our models are described in Table 3. This section presents the framework as well as the four model specifications. However, readers can refer to (Alizadeh et al., 2019; Hurtubia et al., 2014) for the detailed econometric formulation of the LC, ICLV, and LC-ICLV models.
Table 3.
Description of the transformed observed variables used in modelling
Variable Definition Variable Definition
Choice =1 if the preference is FRT 2 for ODT 3 for indifferent !" =1 if user’s gender is male %&'(&)*+),- =1 if user used the ODT service for non-work purposes .&/'0 =1 if user is young !,1$2+),- =1 if user used the ODT service for work and non-work purposes !,22 =1 if user is middle-aged =1 if user used FRT mode when it was running at night =1 if user’s income level is low =1 if user used walking or cycling modes when the FRT service was running at night <,0ℎ9'7&:$ =1 if user’s income level is high =1 if user reported that the in-vehicle time of the ODT trips is less compared to the FRT trips lsaleh, Farooq, Zhang, and Farber <ℎ =1 if user is living in a household size of 3 or fewer people. =1 if user reported that the in-vehicle time of the ODT trips is higher compared to the FRT trips <ℎ =1 if user is living in a household size of 4 or more people. =1 if user’s assigned trips level is low =1 if user’s marital status is single =1 if user’s assigned trips level is high =1 if user’s highest education level is a secondary school A",;,'0_8 =1 if user experienced a low waiting time level <,0ℎ$)B2/ =1 if user has an undergraduate or graduate degree
A",;,'0_< =1 if user experienced a high waiting time level
C") =1 if user has a car
D'"@@,0'$2_8 =1 if user’s unassigned trips level is low
A&)*+),- =1 if user used the ODT service for work purposes
D'"@@,0'$2_< =1 if user’s unassigned trips level is high
Table 4.
Multinomial logit (MNL) model specification
Parameter Variables ODT FRT Indiff.
EFG !" - - 1
EFG %
1 - - H '() - - <,0ℎ$)B2/ H *'+(', - - !" H --.( <ℎ - - H /*' !,22 - - H /001*+'(_3,140 - H %&'(&)*+),- A&)*+),- - H - H - H A",;,'0_8
A",;,'0_< - lsaleh, Farooq, Zhang, and Farber
11 other travel modes (Krizekand El-Geneidy, 2007). The clustering analysis based on previous trip history and income revealed the existence of these two classes in our case study. Accordingly, the class membership functions were defined with a binary logit model structure based on the definition of public transit captive user (Table 5). For both latent classes, ODT captive and non-captive users, specific utility functions were developed using socioeconomic and demographic characteristics as well as ODT service self-reported and actual attributes (Table 6).
Figure 2.
Latent Class modelling framework
Table 5.
Class membership function specification
Parameter Class 1 (Captive Users) Class 2 (Non-Captive Users) I :;<
1 - I !":%=> - I =% - Table 6.
Latent class (LC) model specification
Parameter Class 1 (Captive Users) Class 2 (Non-Captive Users) ODT FRT Indiff. ODT FRT Indiff.
EFG %
1 - - - - -
EFG !" - - 1 - - - H !,1$2+),- %&'(&)*+),- - - - - H - - - - H A",;,'0_8
A",;,'0_< - - - - H )+/001*+'(_3,140:? D'"@@,0'$2_8
D'"@@,0'$2_< - - - - H - - - - H '():? - - <,0ℎ$)B2/ - - - lsaleh, Farooq, Zhang, and Farber H *'+(',:? - - !" - - - EFG % - - - 1 - -
EFG !" - - - - - 1 H - - - %&'(&)*+),- A&)*+),- - H - - - - H - - - A",;,'0_8
A",;,'0_< - H /001*+'(_3,140:@ - - - - H '():@ - - - - - <,0ℎ$)B2/ H *'+(',:@ - - - - - !" Time Sensitivity latent variable and the second component as the
Online Service Satisfaction latent variable. The measurement equations of the indicators are presented in Appendix D. lsaleh, Farooq, Zhang, and Farber Figure 3.
ICLV modelling framework
Table 7.
Indicators description and factor loading values
ID Indicator Indicator Type Description Factor Loading
Time Sensitivity (TS) Online Services’ Satisfaction (OSS) WAIT_IMPO
Attitude
The importance of the waiting time in influencing the user’s choice of using ODT. 0.877463 RELIA_IMPO
The importance of the reliability in influencing the user’s choice of using ODT. 0.740253 TIME_BUS
The importance of the in-vehicle time in influencing the user’s choice of using ODT. 0.793222 FLEXIBILITY
The importance of the convenience and the flexibility in influencing the user’s choice of using ODT. 0.568935 APP_INTER
Perception
User’s satisfaction with the ODT app interface. WEB_INTER
User’s satisfaction with the ODT website interface. lsaleh, Farooq, Zhang, and Farber AVAIL_SERV
User’s satisfaction with the availability of schedules/maps/fares.
Moreover, the structural equations of the Time Sensitivity and Online Service Satisfaction latent variables were defined using socioeconomic and demographic characteristics, as described in Table 8. Table 9 shows the systematic utility functions for the three alternatives. It is worth mentioning that both latent variables were added to the systematic utility function of the ODT alternative to find out how the users’ attitudes and perceptions towards the ODT features can affect their preference towards the ODT alternative.
Table 8.
Structural equation specifications
Parameters Latent Variables Time sensitivity ( !" ) Online services’ satisfaction ( ('_&$)*_&+! ) J :%"A&A
1 - J /*'&A .&/'0 - J <,0ℎ9'7&:$ - J B/,&A
C") - J --.(&A <ℎ - J *'+(',&A !" - J - K &A
1 - J :%"A%AA - 1 J /*'%AA - !,22 J - J '()%AA - K %AA - 1 Table 9.
Integrated Choice and Latent Variable (ICLV) model specification
Parameter Variables ODT FRT Indiff.
EFG !" - - 1
EFG %
1 - - H '() - - <,0ℎ$)B2/ H *'+(', - - !" H --.( <ℎ - - H /*' !,22 - - H /001*+'(_3,140 - H %&'(&)*+),- A&)*+),- - H - H - H A",;,'0_8
A",;,'0_< - H &A +9!B_5B% - - H %AA L%_5BM>_53+ - - lsaleh, Farooq, Zhang, and Farber
15 in Section 4.3 into the LC model defined in Section 4.2. The class membership functions are presented in Table 10 and the class-specific utility functions for alternatives are outlined in Table 11.
Figure 4.
LC-ICLV modelling framework
Table 10.
Class membership function specifications for the IC-ICLV model
Parameter Class 1 (Captive Users) Class 2 (Non-Captive Users) I :;<
1 - I !":%=> - I =% - Table 11.
Latent Class Integrated Choice and Latent Variable (LC-ICLV) model specification
Parameter Class 1 (Captive Users) Class 2 (Non-Captive Users) ODT FRT Indiff. ODT FRT Indiff.
EFG %
1 - - - - -
EFG !" - - 1 - - - H !,1$2+),- %&'(&)*+),- - - - - H - - - - H A",;,'0_8
A",;,'0_< - - - - H )+/001*+'(_3,140:? D'"@@,0'$2_8 - - - - - H - - - - H '():? - - <,0ℎ$)B2/ - - - H *'+(',:? - - !" - - - H &A:? +9!B_5B% - - - - - H %AA:? L%_5BM>_53+ - - - - -
EFG % - - - 1 - -
EFG !" - - - - - 1 lsaleh, Farooq, Zhang, and Farber H - - - %&'(&)*+),- A&)*+),- - H - - - - H - - - A",;,'0_8
A",;,'0_< - H /001*+'(_3,140:@ - - - - H '():@ - - - - - <,0ℎ$)B2/ H *'+(',:@ - - - - - !" H &A:@ - - - +9!B_5B% - - H %AA:@ - - - L%_5BM>_53+ - -
5. Results
All models were estimated using PandasBiogeme software package in Python (Bierlaire & Fetiarison, 2009; Bierlaire, 2003), which is based on the maximum likelihood estimation technique. During the estimation process, we considered starting with simpler models and specifications to get good starting values and minimize the estimation cost of more complex models (Alizadeh et al., 2019; Hurtubia et al., 2014). The ICLV and the LC-ICLV models were estimated using the full information estimation method, described by Bierlaire (2018), to jointly estimate the parameters of the choice model, latent variable model, and the class membership functions (Alizadeh et al., 2019; Bierlaire, 2018). Detailed estimation results of the four models are presented in Appendix E. In this section, we discuss the impacts of the observed as well as latent variables on the service preference. 5.1. Impact of Observed Variables on User Service Preference Here we discuss the impact of user’s characteristics and attributes of alternatives on the service preference decision. As all the models are giving us consistent parameter values, we are able to generalize various trends. 5.1.1. General User Preferences
Figure 5 summarizes the impact of observed variables on service preference. All else equal, the FRT alternative is generally the preferred alternative of ODT users, followed by the indifferent alternative. It is worth mentioning that the performance of Belleville’s ODT service was unstable during the first three months of its operation, from October till December 2018. As a result, waiting time was higher compared with the first three months of 2019 (Sanaullah et al., 2021). Our results suggest that the performance of the service in this period had a significant influence on preferences. Users have a higher tendency to prefer the ODT alternative, if they took fewer trips and experienced shorter waiting time. However, users are more likely to prefer the FRT alternative if they took more trips and experienced higher waiting times. Hence, operators delivering new ODT projects should give more attention to the early-stage performance of the service to make it more convenient and attractive. In addition, the trip purpose, main mode before the ODT service started, and in-vehicle travel time using the ODT service had significant impact on user preference. Users are more likely to prefer the ODT alternative if they use the ODT service mainly for non-work purpose, used non-motorized travel modes before the ODT service started, and their in-vehicle travel time with the ODT service is less when compared to the FRT service. Whereas users who used the ODT service mainly for commuting to and from work, used the FRT service before the ODT service started, and whose in-vehicle travel time after converting the service became longer, they had a higher tendency to prefer the FRT alternative. It is noted that being a middle-aged user and living in a large household increase the preference for ODT alternative. Moreover, males and highly educated users, who had an undergraduate or graduate degree, are most likely to be indifferent between ODT and FRT services. This could be either due to the availability of alternative travel modes for this category or their limited overnight trips that, in return, influenced their preferences. lsaleh, Farooq, Zhang, and Farber Figure 5.
Impact of observed variables on service preference 5.1.2. Captive and Non-captive User Preferences Figure 6 describes the impact of observed variables on the preferences of captive and non-captive users. It is observed that the probability of a user belonging to Class 1 increases with having low-income and with FRT service being the main travel mode before the ODT service started. As pointed out earlier, the clustering analysis based on previous trip history and income revealed the existence of these two classes in our data. Hence, users belonging to Class 1 are entitled as “Captive Users”, since their characteristics are consistent with the definition of public transit captive users described in Krizek and El-Geneidy (2007). Accordingly, individuals in Class 2 are considered as “Non-captive Users”. Captive user’s service preferences are most affected by the number of their unassigned trips during the early stages of the service. Users are more likely to prefer the ODT alternative if they encountered a low level of unassigned trips. Additionally, in-vehicle travel time had the second-highest impact on captive user’s service preference. Captive users had a higher tendency to prefer the ODT alternative if the service had reduced their in-vehicle times in comparison to FRT. However, they are more likely to prefer the FRT alternative if the new service increased their in-vehicle times. In accordance with these results, captive users generally prefer the FRT service more than the ODT alternative, most likely due to their negative experience with the ODT service, especially during the early stages of the service. It is also seen that user’s primary mode before the ODT started had a significant impact on the preference. Users who used non-motorized travel modes were more likely to prefer the ODT alternative, while those who used the FRT service had a higher tendency to prefer the FRT service. This indicates that ODT trips are likely to substitute for non-motorized trips the captive users make. Furthermore, highly educated captive users are indifferent between ODT and the FRT services, possibly due to their limited over-night trips (average trips for the category was 1.3, compared to 2.79 for the sample) that, in return, influenced their preference. lsaleh, Farooq, Zhang, and Farber Figure 6.
Impacts of observed variables on the preferences of captive and non-captive ODT users On the other hand, there is a significant difference in the service preference between captive and non-captive users. The service preferences of non-captive users are most affected by the trip purpose. Non-captive users are more likely to prefer the ODT alternative if they use the service to perform non-work trips. This indicates that the ODT service has the potential to satisfy non-captive user’s needs to engage in various activities across the city, due to its flexibility and the large coverage area. However, non-captive users have a higher tendency to prefer the FRT alternative if their use is limited to work—probably because their travel time increased using the ODT service. Moreover, non-captive users who took a high number of trips in the first three months of the operation and experienced a high waiting time are more likely to prefer the FRT alternative. In contrast, non-captive users have a higher tendency to prefer the ODT alternative if they took fewer trips and experienced a low waiting time. These findings further stress the influence of the early-stage performance of the ODT service on convenience and attractiveness. It can also be noted that the in-vehicle time has a significant impact on non-captive user’s service preferences. Non-captive users are more likely to prefer the ODT alternative if their in-vehicle time is less compared with the FRT service. Furthermore, male and highly educated users are indifferent between ODT and the FRT services. This may be because of the availability of alternative travel modes. 5.2. Impact of Latent Variables on User Service Preference The Time Sensitivity latent variable is positively correlated with the importance of the waiting time, in-vehicle time, and the reliability of the service (see Appendix E). The Online Service Satisfaction latent variable is positively correlated to the user’s satisfaction with the ODT mobile app interface, website interface, and the available features. lsaleh, Farooq, Zhang, and Farber
19 Figure 7 outlines the estimation results for the structural equations of the latent variables and shows their impacts on ODT user’s service preferences. It is seen that the Time Sensitivity attitude is associated with being a male, young user, having a high income, and living in a household size of 3 or less. This is a logical finding, as it represents the category of people who usually participate in different recreational activities at night and can use alternative travel modes. Hence, their decision to use the ODT service is subjected to waiting time, in-vehicle time, and the reliability of the service. In contrast, single users are less likely to have the Time Sensitivity attitude, possibly because they have fewer responsibilities and more free time than other users. It is also observed that the Online Service Satisfaction latent variable corresponds to middle-aged users who have low income and a secondary school degree level education. We believe that this category may represent users who have not used any app-based ride-hailing services before, given that they generally tend to be unsatisfied with the online services provided to them. These findings suggest that the online services of the current ODT system need further improvements. 5.2.1. General User Preferences
As Figure 7 illustrates, time-sensitive users are more likely to prefer the ODT alternative. Similarly, users who are satisfied with the online service provided by the ODT mobile app and website have a higher tendency to prefer the ODT alternative. However, the parameter estimates of both latent variables, are insignificant at 95% confidence level (t = 1.29 and 1.12, respectively). The insignificance of these parameters is most probably due to the smaller sample size, which is a limitation of this study. Nevertheless, the inclusion of the latent variables in the MNL model improved its model fit (Rho-square-bar = 0.299 for ICLV model compared to 0.26 for the MNL model).
Figure 7.
Impact of Latent variables on the ODT user’s service preferences 5.2.2. Captive and Non-captive User Preferences The Time Sensitivity and Online Service Satisfaction latent variables have insignificant impacts on the service preferences of ODT captive users. In contrast, both latent variables have a significant positive impact on non-captive user’s preference for the ODT alternative. Thus, non-captive users who have the Time Sensitivity attitude are more likely to prefer the ODT alternative, indicating that their experience lsaleh, Farooq, Zhang, and Farber
20 with the ODT service was positive. Similarly, non-captive users have a higher tendency to prefer the ODT alternative if they are satisfied with the online services provided by the ODT mobile app and website. This suggests that improving the functionality of the service app and website might make ODT service more attractive.
6. Discussion and Recommendations
This study modelled the impact of observed as well as latent variables on the preference between ODT and FRT services. In this section, we compare our findings with the existing studies and outline the main recommendations that can be derived from our results. 6.1. Discussion One of the main factors that has been used to investigate the user’s preference for flexible transit is the performance of service. The study conducted by Khattak and Yim (2004) found that traveller's willingness to use a hypothetical ODT service is most affected by the reliability of the service. A recent study in Ontario, Canada, found that ODT user’s willingness to engage in activities is most affected by their satisfaction with the reliability and the performance of the service (Zhang et al., 2020a). In line with these studies, we found that the Time Sensitivity latent variable, which represents user’s attitude towards the reliability, in-vehicle time, and waiting time of the ODT service, has a significantly positive impact on non-captive user’s preference for the ODT alternative. We also found that the service preference of captive users is most affected by the performance of ODT service, especially during the early stages in particular. User’s socioeconomic and demographic characteristics are also found to be important factors in explaining their preferences. A recent study in Michigan, USA, showed that males and highly educated travellers are more likely to prefer MOD transit service (Yan et al., 2019b). Another recent study in Sydney, Australia, found that individuals with work-based trips have a higher uptake rate for MOD transit service than those with non-work trips (Saxena et al., 2020). On the contrary, we found that males and highly educated users are indifferent between ODT and FRT services. Furthermore, the users taking work-based trips had a higher tendency to prefer FRT service, while for non-work trips they were more likely to choose ODT service. We believe that this is probably due to the differences in the operational characteristics between the two services, as discussed in Section 2.1. Moreover, Jittrapirom et al. (2019) found that unfamiliarity with the microtransit service app is one of the main barriers for the elderly to use the service. Leistner and Steiner (2017) also reported that unfamiliarity with smartphones and apps is the main barrier for the elderly to use app-based transportation services. However, we found that the Online Service Satisfaction latent variable, which measures user’s satisfaction with the ODT mobile app interface, website interface, and available features, has a significantly positive impact on non-captive user’s preference. Thus, user’s satisfaction with online services is another important factor that should be considered when studying their preferences for any app-based mobility service. Also, it is important to note that the impact of Time Sensitivity and Online Service Satisfaction latent variables, as well as the early-stage performance of the ODT service (including assigned trips, unassigned trips, and waiting time), have not been investigated in the literature before. Furthermore, we found several advantages to using hybrid choice models to explain user’s service preferences between the ODT and FRT services. Using the ICLV model, we investigated the impact of the Time Sensitivity and the Online Service Satisfaction on the ODT user’s service preferences. The inclusion of these latent variables in the MNL model has improved its predictive power (see Table 12), which is in line with the previous studies (Ababio-Donkor et al., 2020; Kamargianni et al., 2015). In addition to explaining the service preference heterogeneity among ODT captive and non-captive users, the LC model has provided higher goodness of fit, when compared with the MNL model. This finding is consistent with the previous literature (Greene and Hensher, 2013; Hess et al., 2009; Shen, 2009; lsaleh, Farooq, Zhang, and Farber
21 Massiani et al., 2007). Moreover, the use of the LC-ICLV model has enabled us to apprehend the impact of the Time Sensitivity and Online Service Satisfaction on captive and non-captive users of the ODT service. It is noticed that the LC-ICLV model has the highest explanatory power and model fit among the hybrid choice models. On the other hand, developing hybrid choice models encounters some challenges. During the estimation process of the LC models, several trials had to be performed to find the final structure for the class membership function. In addition, both the ICLV and the LC-ICLV models need to be estimated using the full information estimation method, described by Bierlaire (2018), to jointly estimate the parameters of the choice model, latent variable model, and the class membership functions. In this approach, it is recommended to start with simpler models and specifications in order to get good starting values and minimize the estimation cost of the complex models. However, it is computationally expensive and difficult to obtain, especially when two or more latent variables are used (Bierlaire, 2018). Furthermore, multiple trials were performed in order to find the final form of the structural equations for the latent variable model component of the ICLV and LC-ICLV models.
Table 12.
Performance comparison between MNL, LC, ICLV, and LC-ICLV models
Performance Measures MNL LC ICLV LC-ICLV
Rho-square-bar 0.26 0.286 0.299 0.351 Initial log-likelihood -79.1 -79.1 -882.69 -951.43 Final log-likelihood -47.49 -36.47 -577.93 -567.44 No. of parameters 11 20 41 50 Features - Compare the service preferences of ODT captive and non-captive users Investigate the impact of the Time Sensitivity and the Online Services’ Satisfaction on ODT users’ service preferences Investigate the impact of the Time Sensitivity and the Online Services’ Satisfaction on ODT captive and non-captive users’ service preferences lsaleh, Farooq, Zhang, and Farber
22 On the other hand, we found that the service preferences of non-captive users are mainly affected by their satisfaction with the online services, the performance of the ODT service, and their trip purposes. Non-captive users who were satisfied with the online services had a positive experience with the ODT service in terms of in-vehicle and waiting times, and use the service for non-work trips, had a higher tendency to prefer the ODT service. In contrast, those who were unsatisfied with the online services had a negative experience with the ODT service or used the service for work-related trips, were more likely to prefer the FRT service. In light of these findings, we provide the following suggestions to transit operators to further enhance the attractiveness of ODT services: • Transit operators should consider improving the user-interface and the functionality of the service app and website. • Agencies wanting to deliver new ODT projects should give more attention to early-stage performance, as it has a significant impact on non-captive user’s service preferences. • Transit operators should consider medium occupancy vehicles instead of using the 40-ft buses in order to minimize the in-vehicle and the waiting times of ODT users. However, in cases where small municipalities already have a fleet of high-capacity buses and they cannot afford to invest in smaller vehicles, the ride-matching algorithm should give priority to minimization of wait times and detours, rather than maximization of capacity utilization. • To make ODT services more efficient and convenient for work trips, we suggest serving such trips independently from non-work trips. In other words, transit operators should ask users to provide their trip purpose, while requesting their trips and dedicate a predefined number of vehicles for work trips. However, a simulation-based study is needed to verify the feasibility and the validity of this suggestion, as well as to determine the required vehicle type, fleet size, service area, and cost to operate such a service.
7. Conclusions
This study investigated the impact of sociodemographic, performance, and latent variables on the preference between the ODT and FRT service of captive and non-captive users. The service preference heterogeneity is untangled to help transit operators design, plan, and operate more convenient and attractive ODT service. Previous studies revealed that the hybrid choice modelling techniques can improve the explanatory power and the predictive accuracy of the traditional discrete choice models by incorporating the individual’s behavioural variables and/or accounting for the behavioural heterogeneity across the population's latent classes in the modelling process (Alizadeh et al., 2019; Hurtubia et al., 2014). Therefore, the study modelled the ODT user preferences using three hybrid choice models, namely ICLV, LC, and LC-ICLV models. The data used in the modelling process was generated by fusing the actual level of service attributes obtained from Belleville's ODT service and individual level self-reported data obtained from a revealed preference survey of the ODT users. The study showed that the preference for ODT service of captive users was significantly affected by the number of unassigned trips, in-vehicle time, and primary travel mode before the ODT started. However, the number of unassigned trips had the highest impact on their preferences. The results also indicated that the ODT service is likely to replace non-motorized modes. On the other hand, the preference of non-captive users was significantly affected by the ODT service performance and trip purpose. In terms of latent variables, the Time Sensitivity and Online Service Satisfaction variables had a significant positive impact on non-captive user’s preference for the ODT service. By considering these variables during the planning, designing, and operations of new as well as ongoing ODT projects, one can expect a significant positive effect on the users and their choice-making process, resulting in the increased ridership of the service. An important finding that has emerged from this study is that non-captive user’s preference for the ODT services is most affected by their trip purpose. lsaleh, Farooq, Zhang, and Farber
23 We provide important recommendations to the agencies wanting to deliver new ODT projects as well as to enhance the performance of the ongoing projects. The results suggest that the attractiveness of ODT service can be further enhanced by (a) improving the user-interface and the functionality of the service app and website, (b) giving more attention to the early-stage performance, (c) continuously updating the required fleet size based on the real-time spatio-temporal demand the system receives, (d) using medium sized vehicles rather than the current 40-ft buses, and (e) serving work-related trips independently from non-work-related trips. The main limitations of our work include: (a) the small size of the sample used in this study, and (b) the fact that the actual level of service attributes do not cover the performance of the ODT service in the later stages, which can be of use to compare the impact of the ODT performance in different stages on the user’s service preferences. In the future, we intend to improve the findings of this study by incorporating more behavioural variables, exploring different market segments, and increasing the number of observations. We also intend to develop count models for predicting the number of trips users are expected to take using the ODT service.
ACKNOWLEDGEMENTS
We greatly appreciate the Canadian Urban Transit Research & Innovation Consortium (CUTRIC), Ryerson University, and the Social Sciences and Humanities Research Council (SSHRC), for providing funding for this study. We are also thankful to Pantonium and the City of Belleville for providing us access to the data used in this study. lsaleh, Farooq, Zhang, and Farber Appendix A. Summary of Previous Literature
Table A13 summarizes the previous research conducted on user preference for flexible transit services. Figure A8 provides a summary of the existing discrete choice literature.
Table A13.
Summary of the previous research conducted on user preferences for flexible transit services
Flexible Transit Services Study Details Objectives Location Data Source Analysis Tools Main Findings
Demand Responsive Transit (DRT) System Microtransit Service Anspacher et al. (2004) Examining user preference for a proposed microtransit service. San Francisco Bay Area, California. Stated preference survey Ordered logit model • Users who were more willing to use the proposed service are: -
Park and ride users. -
Users who carpooled or used public transit to get to and from the rail station. • User’s willingness to use the proposed service increased as their distances to the nearest station increased. Tarigan et al. (2010) Investigating the impact of negative experiences on the user’s willingness to use microtransit service. Bandung, Indonesia. Revealed preference survey Ordered probit model Microtransit attributes that had the highest impact on the user’s willingness to use the service: -
For men: the cost, practicality, and the accessibility. -
For women: safety. Miah et al. (2020) Identifying the main barriers for impaired passengers to adopt microtransit. Arlington, Texas. Interview-based survey Survey analysis The main barriers for impaired passengers to use microtransit were: -
Lack of spatial coverage. -
Lack of walking access. -
Difficulty to use. Jittrapirom et al. (2019) Investigating the perspectives of elderly people on the Breng flex service.
Netherlands
Revealed preference survey Survey analysis Main reasons for the elderly not using the microtransit service were: -
Having more comfortable travel options. -
Inconvenience of the microtransit service. -
Unfamiliarity with the service app. lsaleh, Farooq, Zhang, and Farber On-demand Transit (ODT) Khattak and Yim (2004) Examining travellers’ willingness to use a hypothetical personalized DRT (ODT service). San Francisco Bay Area, California. Stated preference survey Survey analysis The reliability, cost, pickup and dropoff locations were the most important attributes of the proposed ODT service for most of the respondents. Yu et al. (2017) Investigating user’s willingness to use a hypothetical ODT service. Jinan Qilu Software Park, China. Stated preference survey Survey analysis Females, enterprise employees, participants with a college degree or higher, and participants with higher incomes were more willing to use the proposed service. Zhang et al. (2020) Investigating the relationship between ODT user’s satisfaction and their activity participation. Belleville, Ontario. Revealed preference survey Structural equation models • Participants were most satisfied with drivers’ qualifications and attitudes. • Participants were least satisfied with the waiting time and reliability of the service. • The activity participation of participants was most affected by their satisfaction with the reliability and the performance of the service. Mobility On-Demand (MOD) Transit Service FRT and Ride-hailing Yan et al. (2019a) Examining user’s response to a proposed MOD transit service. University of Michigan Ann Arbor campus. Stated preference survey Mixed logit model Replacing the FRT service in the low demand areas with ride-hailing services could slightly increase the ridership of the public transit system while minimizing the operational cost of the service. FRT and Microtransit Yan et al. (2019b) Investigating disadvantaged user preference for a proposed MOD transit service. Detroit and Ypsilanti, Michigan. Stated preference survey Ordered logit model Males, highly educated travellers, travellers who have not heard or used the ride-hailing services before, and travellers who had a negative experience with the FRT service, were more likely to prefer the MOD transit service. Saxena et al. (2020) Examining user preferences for a proposed MOD transit service. Northern Beaches area of Sydney, Australia. Stated preference survey Latent class (LC) model Individuals with work-based trips had a higher uptake for the MOD transit service than those with non-work trips. lsaleh, Farooq, Zhang, and Farber Figure A8.
Summary of the recent research conducted on the hybrid choice modelling lsaleh, Farooq, Zhang, and Farber Appendix B. Comparison between Fused and Individual Samples
The differences between the fused dataset (reduced sample) and both the operational data and the revealed preference data were verified statistically using t-test and chi-square test, respectively, and the results are presented in Tables B14 and B15. It should be noted that there are no significant differences between the reduced sample and the full samples. Thus, the fused sample used in the modelling process is a representative sample for Belleville’s ODT users.
Table B14.
Statistical difference between the fused data (reduced sample) and the operational data (full sample)
ID Actual Level of Service Attribute Sample Type Average Standard Deviation Sample Size t-test !(|$| ≥ $ !" ) Significance
1 Waiting Time (min) Full Sample 21.69 19.16 430 1.87 0.065 Not significant Reduced Sample 18.40 12.7 72 2 Assigned Trips (trips) Full Sample 2.62 5.46 430 0.358 0.721 Not Significant Reduced Sample 2.79 3.37 72 3 Unassigned Trips (trips) Full Sample 6.17 12.97 430 1.73 0.088 Not Significant Reduced Sample 8.39 9.54 72
Table B15.
Statistical difference between the fused data (reduced sample) and the revealed preference data (full sample)
ID Self-reported Attributes Categories Observed Distribution (Reduced Sample) Expected Distribution (Full Sample) Chi-Square Calculated p-value Significancy
1 Income (Thousand CAD) Under 10 18 19.7 8.64 0.19 Not Significant 10 to 19.999 21 24.4 20 to 29.999 12 9.4 30 to 39.999 10 11.8 40 to 49.999 5 3.9 50 to 59.999 3 0.8 60 and over 3 2 2 Gender Male 34 35.2 4.18 0.12 Not Significant Female 36 36.3 Other 2 0.5 3 Marital Status Single 45 50.5 8.63 0.07 Not Significant Married 9 11.6 Widowed 2 1.7 Divorced 5 3.15 Other 11 5.3 4 Age Young 29 31.5 1.15 0.76 Not Significant Adults 33 33.1 Middle-aged 10 7.4 Old 0 0 lsaleh, Farooq, Zhang, and Farber
5 Travel Mode Active Mode 25 29.9 1.44 0.86 Not Significant Car as a driver or passenger 25 22 FRT 14 12.6 Mobility Bus Service 3 2.3 Not Applicable 5 4.2 6 Trip Purpose Work-Based 29 23.6 3.93 0.14 Not Significant Nonwork-Based 11 17.9 Mixed Purposes 32 30.5 7 Education level No Formal Education 0 0.5 10.78 0.06 Not Significant Primary School 0 1.6 Secondary School 30 23.1 Diploma 24 17.6 Undergraduate 9 15.5 Graduate 9 13.7 8 Household Size 1 person 13 12.9 6.88 0.14 Not Significant 2 persons 17 11.3 3 persons 14 11.3 4 persons 16 16.3 5 or more persons 12 20.2
Appendix C. K-Means Clustering and Elbow Method Results
Figure C9 depicts that users’ assigned trips can be best represented by 3 clusters: low assigned trips level (less than 3 trips), medium assigned trips level (3 to 7 trips), and high assigned trips level (more than 7 trips). The optimum number of clusters for users’ unassigned trips is 4, which are: low unassigned trips level (less than 5 trips), medium unassigned trips level (5 to 11 trips), high unassigned trips level (12 to 23 trips), and very high unassigned trips level (more than 23 trips) as shown in Figure C10. Similarly, Figure C11 shows that users’ waiting time can be best represented by 4 clusters: low waiting time levels (less than 10 minutes), medium waiting time levels (10 to 20 minutes), high waiting time level (21 to 33 minutes), and very high waiting time level (more than 33 minutes). a) elbow method results b) optimum clusters representation Figure C9.
Users’ assigned trips a) elbow method results b) optimum clusters representation lsaleh, Farooq, Zhang, and Farber a) elbow method results b) optimum clusters representation Figure C10. U sers’ unassigned trips a) elbow method results b) optimum clusters representation a) elbow method results b) optimum clusters representation Figure C11.
Matched users’ average waiting time a) elbow method results b) optimum clusters representation
Appendix D. Measurement Equations for Latent Variables
Equations (D1) through (D7) represent the measurement equations for the indicators presented in Table 7, where the responses given to these indicators were used to identify the Time Sensitivity and the Online Services’ Satisfaction latent variables. !" !" + - !" . /012_324 + 5 !" ; + !" = 0, - !" = 1, 5 !" = 1 (D1) :;< )*+ + - )*+ . /012_324 + 5 )*+ (D2) $ $ + - $ . /012_324 + 5 $ (D3) @<;A /+*0 + - /+*0 . /012_324 + 5 /+*0 (D4) "''_ "''_ + - "''_ . D4_32EF_3G/ + 5 "''_ ; + "''_ = 0, - "''_ = 1, 5 "''_ = 1 (D5) !;=_ !*,_ + - !*,_ . D4_32EF_3G/ + 5 !*,_ (D6) lsaleh, Farooq, Zhang, and Farber "H" "3" + - "3" . D4_32EF_3G/ + 5 "3" (D7) where, !" and )'_&$*+_&,! are the Time Sensitivity and the Online Services’ Satisfaction latent variables, respectively. - !" , - )*+ , - $ , - /+*0 , - "''_ , - !*,_ , and - "3" are scale parameters to be estimated. It is worth mentioning that the first measurement equation of the Time Sensitivity and the
Online Services’ Satisfaction latent variables (WAIT_IMPO and APP_INTER equations, respectively) were normalized by setting their constants to 0 and their coefficients and scale parameters to 1 for identification purposes (Ababio-Donkor et al., 2020; Alizadeh et al., 2019; Bierlaire, 2018).
Appendix E. Model Estimates
Tables E16 and E17 provide the estimation results of the MNL and ICLV models. Tables E8 and E19 present the estimation results of the LC and LC-ICLV models.
Table E16.
Estimation results of the measurement equations of the ICLV model
Indicator Parameter Estimate
Rob. t-test
WAIT_IMPO + - RELIA_IMPO + ;<=65_689: * - ;<=65_689: * ;<=65_689: TIME_BUS + -0.140 -0.41 ** - FLEXIBILITY + A=
APP_INTER + - WEB_INTER + ** - AVAIL_SERV + - * Not statistically significant at 95% confidence level ** Not statistically significant at 90% confidence level
Table E17.
Estimation results of the choice and latent variable models
Parameter MNL ICLV Estimate Rob. t-test Estimate Rob. t-test
Choice Model
G3I -1.89 -2.60 -1.89 -2.64
G3I (F$ -2.61 -2.71 -3.66 -2.68 lsaleh, Farooq, Zhang, and Farber - GHHIJKLM_NOIPH ** ** - PQOPRHL - SRML - IKTULV - WGINIKJ - VVXM - GJL * * - LMQ - JLKMLO - $. - - 0.668 1.29 ** - (.. - - 0.385 1.12 ** Latent Variable Model + Y(2.$. - - 0.334 0.92 ** + GJL$. - - 1.080 2.29 + IKZRSL$. - - 0.687 2.14 + ZGO$. - - -0.620 -1.21 ** + VVXM$. - - 0.724 2.14 + JLKMLO$. - - 1.110 2.77 + SGOINGX$. - - -1.040 -2.31 $. - - -0.113 -0.48 ** + Y(2.(.. - - -0.858 -3.85 + GJL(.. - - 1.290 3.34 + IKZRSL(.. - - 1.360 4.94 + LMQ(.. - - 0.640 3.62 (.. - - 1.300 7.69 Performance Indicators
Number of parameters 11 41 Initial log-likelihood -79.10 -882.69 Final log-likelihood -47.49 -577.93 Rho-square-bar 0.26 0.299 * Not statistically significant at 95% confidence level ** Not statistically significant at 90% confidence level
Table E18.
Estimation results of the measurement equations of the LC-ICLV model
Indicator Parameter Estimate
Rob. t-test
WAIT_IMPO + - RELIA_IMPO + ;<=65_689: - ;<=65_689: * ;<=65_689: TIME_BUS + -0.058 -0.20 ** - lsaleh, Farooq, Zhang, and Farber FLEXIBILITY + A=
APP_INTER + - WEB_INTER + ** - AVAIL_SERV α β σ * Not statistically significant at 95% confidence level ** Not statistically significant at 90% confidence level
Table E19.
Estimation results of the choice model, latent variable model, and class membership functions
Parameters LC LC-ICLV Estimate Rob. t-test Estimate
Rob. t-test
Choice Model
G3I (F$Y[ -11.600 -11.30 -11.600 -5.30
G3I -2.430 -2.01 -2.540 -2.18 - PQOPRHLY[ ** ** - IKTULVY[ - WGINIKJY[ ** ** - QKGHHIJKLM_NOIPHY[ - SRMLY[ - LMQY[ * * - JLKMLOY[ ** ** - $.Y[ - - -0.138 -0.17 ** - (..Y[ - - 0.053 0.10 ** G3I (F$Y\ * - - G3I -9.100 -14.50 - - - PQOPRHLY\ - IKTULVY\ - WGINIKJY\ ** - GHHIJKLM_NOIPHY\ - LMQY\ - JLKMLOY\ - $.Y\ - - 9.440 2.27 - (..Y\ - - 5.630 2.17 Latent Variable Model + Y(2.$. - - 0.266 0.69 ** + GJL$. - - 1.150 2.40 + IKZRSL$. - - 0.617 1.80 * lsaleh, Farooq, Zhang, and Farber + ZGO$. - - -0.485 -0.93 ** + VVXM$. - - 0.684 1.90 * + JLKMLO$. - - 1.130 2.85 + SGOINGX$. - - -0.979 -2.01 $. - - -0.224 -0.91 ** + Y(2.(.. - - -0.470 -1.58 ** + GJL(.. - - 0.991 2.31 + IKZRSL(.. - - 0.600 2.12 + LMQ(.. - - 0.605 1.69 * (.. - - 1.14 5.20 Class Membership Functions M Y"' -10.600 -21.30 -10.700 -40.00 M M &(F* Performance Indicators
Number of parameters 20 50 Initial log-likelihood -79.10 -951.43 Final log-likelihood -36.47 -567.44 Rho-square-bar 0.286 0.351 * Not statistically significant at 95% confidence level ** Not statistically significant at 90% confidence level
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