- Email: [email protected]
Modeling the impact of pre-trip information on commuter departure time and route choice
Transportation Research Part B 35 (2001) 887±902
www.elsevier.com/locate/trb
Modeling the impact of pre-trip information on commuter departure time and route choice Rong-Chang Jou * Department of Trac and Transportation Engineering and Management, Feng Chia University, Taichung, Taiwan, Republic of China Received 20 January 1999; received in revised form 2 February 2000; accepted 18 February 2000
Abstract The objective of this paper is to investigate the impact of pre-trip information on auto commutersÕ choice behavior. The analysis is based on an extensive home-interview survey of commuters in the Taichung metropolitan area in Taiwan. A joint model for route and departure time decisions with and without pretrip information is formulated. The model speci®cations are developed for both the systematic and random components. In particular, econometric issues associated with specifying the random error structure are addressed for parameter estimation purposes. Insights into the eects of attributes are obtained through the analysis of the model's performance and estimated parameter values. A probit model form is used for the joint model, allowing the introduction of state dependence and correlation in the model speci®cation. The results underscore the important relationship between the dierent characteristics and the propensity of commuter choice behavior under two scenarios, with and without pre-trip information. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Pre-trip information; Departure time; Route; Probit model
1. Introduction Methods to reduce congestion by either increasing capacity (supply-side measures) or reducing demand (demand-side measures) have gained much attention recently. It is also well accepted that emerging ITS technologies oer promising system eciency through the exploitation of local imbalances between supply and demand, using information as the primary mechanism to in¯uence user decisions (Mahmassani, 1997). Among possible alternatives of ITS, Advanced Traveler
*
Tel.: +011-886-4-451-6122; fax: +011-886-4-451-6122. E-mail address: [email protected] (R.-C. Jou).
0191-2615/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 1 - 2 6 1 5 ( 0 0 ) 0 0 0 2 8 - X
888
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
Information Systems (ATIS) improves highway productivity by oering trac information to travelers and provides a unique opportunity to enhance our transportation system. The ultimate goal for designers of ATIS is to provide travelers with the best information possible to make trip planning ecient and eective. The decisions in¯uenced by the ATIS-supplied information take place at two principal instances: at the trip origin or en-route. The ®rst are referred to as ``pre-trip'' decisions and may be the results of both long-term factors and real-time elements. The pre-trip information is provided to travelers at origins (home or workplace) prior to their trips through television, radio, telephone inquiry, and computer on-line services. Pre-trip information can help reduce the degree of uncertainty when commuters encounter travel time variation on their routes. With the information provided, the users of systems could make trips more eciently by changing most attributes of the journey, including departure time, route, mode, destination, or even whether to make the trip at all. Therefore, pre-trip information indeed plays a vital role in travelersÕ trip planning. The success of systems greatly depends on the ability of the system to provide travelers with useful information. In addition, the system needs to make information available and have it accessible to all users. The Intermodal Surface Transportation Eciency Act (ISTEA) bill passed by Congress in 1990 further emphasized the fact that eective dissemination of information regarding transportation services is essential in promoting a balanced use of dierent transportation modes, which would, in turn, alleviate trac congestion (Kikuchi et al., 1994). Since many of these ATIS technologies are aimed at relieving congestion during congested commuting periods of the day, the behavior of commuters must be treated as a central element in the formulation and implementation of these congestion relief measures. On the other hand, pretrip trac information systems are important because they potentially provide commuters with the greatest ¯exibility. Therefore, a better understanding of how a pre-trip information will in¯uence commutersÕ choice behavior is required. Based on the pre-trip information, commuters can change either departure time or route choice in response to congestion and various strategies in the short term. The objective of this paper is to investigate the impact of pre-trip information on urban auto commutersÕ choice behavior. It is based on a large-scale survey conducted in the Taichung metropolitan area of Taiwan in 1996. Probit models are developed to capture the principal attributes of the dierent characteristics that in¯uence urban commutersÕ choice behavior, including departure time and route, with and without the information provided. The results underscore the important relationship between the dierent characteristics and the propensity of commuter choice behavior under two scenarios, with and without pre-trip information. The results obtained from this study provide a basis for the subsequent development of information system architecture in Taiwan. This paper is divided into four sections. Section 2 of this paper provides a review of relevant literature and discussion of background material that is important to the study of urban commutersÕ behavior with and without pre-trip information. Section 3 discusses the development for modeling the decisions of route and departure time, taken jointly, and incorporating pre-trip information. The eect of pre-trip information on commutersÕ choice behavior is presented ®rst, followed by model framework, and model speci®cation. The estimation results of the probit models and concluding comments are presented in Sections 4 and 5.
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
889
2. Background This section provides a review and discussion of background material pertaining to two subjects that are important to this study. Section 2.1 is to investigate current literature on the subject of commuter behavior when in¯uenced by pre-trip information, followed by dynamic models and related econometric issues that are essential to the methodological development of route and departure time decisions incorporating pre-trip information. 2.1. Commuter behavior when in¯uenced by pre-trip information Over the past decade, there has been an extensive investigation of departure time and route choices in interactive laboratory-like experiments (Mahmassani, 1997). Mahmassani and Liu (1997) focused on the day-to-day dynamics of commutersÕ departure time and route decision process in response to the supplied information. The results showed that younger commuters tend to switch their departure time decisions, while male commuters tend to switch their route decisions. Vaughn et al. (1993) developed an interactive experiment to investigate drivers' learning and pre-trip route choice behavior under ATIS. The results indicated that drivers can rapidly identify the accuracy level of provided information and adjust their behavior accordingly. Although these works provide valuable insights into complex human decision behavior, they are primarily based on theoretical concepts or simulated experiments, and the transferability of these insights to commuter behavior in real trac networks has not been adequately established. Polak and Jones (1992) developed a stated preference (SP) approach to investigate the eects of pre-trip information on travel behavior. Initial results from the study indicated that the approach worked well and is able to provide useful quantitative data on the key parameters of the information acquisition process. Stephanedes and Zografos (1994) developed empirical models that can provide a better understanding of the relationship between pre-trip departure time and route choice decisions, and the duration of the announced delay. In a survey of Seattle commuters, pretrip trac information in¯uenced route choice for only 11% of the respondents and departure time for 13% (Beaton and Sadana, 1994). Survey conducted in the New York metropolitan area indicated that if people are able to obtain more timely and reliable trac information, they are more likely to use it (Harris and Konheim, 1995). Abdel-Aty et al. (1994) found that commuters might value and use pre-trip information more than en-route, because it gives them the situation on their routes in advance, which enables them to change route and/or departure time. Abdel-Aty et al. (1997) further investigated the factors that in¯uence route choice with particular emphasis on the eect of trac information and travel time variability on route choice, and found that receiving pre-trip trac information was a signi®cant factor in the model. Khattak et al. (1995) proposed a combined revealed and SP model to explore how driversÕ pre-trip decisions are aected by ATIS in the context of unexpected congestion. Jha et al. (1998) developed a Bayesian updating model to capture the mechanism by which travelers update their travel time perceptions from one day to next in light of information provided by ATIS and their previous experience. In Taiwan, most of the pre-trip information is provided to commuters through radio service (Jou et al., 1997). Studies showed that commuters are willing to change their departure time,
890
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
route, and transportation mode under a well-developed route guidance system. Although a very signi®cant amount of eort has been invested in US, Europe, and Japan to promote an ATIS industry, in Taiwan only recently have researchers started to address some of the issues associated with analyzing and modeling commutersÕ reactions to ATIS (Jou et al., 1997). 2.2. Dynamic modeling and related econometric issues Heckman (1981) presented a general dynamic model for the analysis of discrete panel data that can be used to analyze the structure of discrete choices made over time. Dynamic models are typically estimated with repeated observations for each respondent. Under these conditions, the estimation gives rise to an obvious correlation of disturbances, or heterogeneity, which refer to variations in unobserved contributing factors across behavioral units. If unobserved factors are correlated with the measured explanatory variables, then estimated coecients will be biased if the heterogeneity is not properly taken into account. Abdel-Aty et al. (1997) had a more extensive and thorough review of discrete choice models with repeated measurement data and the correction procedures. For example, Abdel-Aty et al. (1997) assumed a parametric functional form for the pattern of the heterogeneity to account for unobserved heterogeneity. This approach is introduced hereinafter for the illustration purpose. Let the probabilities that the event occurs and does not occur, respectively, as: 0 Xit b a ; P occurs P dit 1=a; b; Xit P Hit P 0=a; b; Xit U ru 1 Xit0 b a ; P not occur P dit 0=a; b; Xit P Hit < 0=a; b; Xit U ru where Hit Vit uit Xit0 b a uit ; a is a constant, b is a vector of parameters, and Xit is a vector of exogenous variables. The distribution of the dit is generated by the distributions of uit and Vit . This model is similar to the multivariate probit model if the uit is assumed to be jointly normally distributed with mean zero and variance r2u . The in¯uence of the unobserved variables in Eq. (1) is captured by the constant term a. The probability of observing di di1 ; di2 ; di3 ; di4 ; . . . ; diTi given Ti in this speci®cation is: dit Ti 0 Y Xit b a Xit0 b U U P di =a; b; Ti ; Xit ru ru t1
a
1
dit
:
2
To investigate the heterogeneity, Eq. (1) is rewritten as Eq. (3) by assuming the probabilities are conditional on both Xit and an individual speci®c error term, ti , which represents all the other in¯uences. 0 Xit b a ti P occurs P dit 1=a; b; Xit ; ti P Hit P 0=a; b; Xit ; ti U ; ru 3 Xit0 b a ti : P not occur P dit 0=a; b; Xit ; ti P Hit P 0=a; b; Xit ; ti U ru
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
891
The ti : i 1; . . . ; I are assumed to be identically distributed with density function f ti independent of the Xi , so that Eq. (2) becomes dit 1 dit Z 1Y Ti 0 Xit b a Xit0 b a P di =a; b; Ti ; Xit ; f ti U U f ti d ti : 4 ru ru 1 t1 Eq. (4) is a marginal likelihood function. The unknown variables, ti , are integrated out. The distribution of ti is called a mixing continuous distribution. The log-likelihood function is dit 1 dit Z 1Y Ti 0 I X Xit b a Xit0 b a L ln U U f ti d ti : 5 ru ru 1 t1 i1 The parametric form of ti can be assumed to be normally distributed with mean zero and variance r2t . The maximum likelihood estimates can then be obtained by general MLE packages such as the one provided with GAUSS statistical software (Aptech Systems, 1992). Alternative structural framework gives rise to a variety of interesting and important models useful in the analysis of discrete panel data. Mahmassani and Chang (1987) initially developed a boundedly rational model formulation of departure time and route switching in day-to-day commute. Jou and Mahmassani (1998) extended the previous work by combining early and late side indierence bands of tolerable schedule delay (de®ned as the dierence between the preferred arrival time and the actual arrival time for a given commute). The boundedly rational mechanism governing day-to-day departure time and route switching decisions postulates that commuter does not switch his/her next dayÕs departure time and/or route so long as the corresponding schedule delay on current day remains within the commuterÕs indierence bands for departure time and route choices. Based on the literature review, the following comments can be made: 1. To test for the heterogeneity presented in the model, the procedures proposed by Abdel-Aty et al. (1997) are applied in this paper. A parametric functional form for the pattern of the heterogeneity is assumed to account for unobserved heterogeneity. 2. A joint model, conceptually similar to the one proposed by Jou and Mahmassani (1998), for route and departure time decisions with and without pre-trip information is applied in this paper. 3. Several assumptions in conjunction with the model speci®cations made in Section 3.3 are based on the empirical evidence highlighted in Section 2.1. 3. Model development This section discusses the development for modeling the decisions of route and departure time, taken jointly, and incorporating pre-trip information. The eect of pre-trip information on commutersÕ choice behavior is presented ®rst, followed by model framework, and model speci®cation. 3.1. Role of pre-trip information The role that pre-trip information plays in the process of commuterÕs decision making is shown in Fig. 1. Fig. 1 shows that whether a commuter receives pre-trip information depends on his/her
892
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
Fig. 1. The eect of pre-trip information on commutersÕ choice behavior.
socioeconomic characteristics, working place characteristics, and experienced trac system characteristics. These three characteristics and whether receiving pre-trip information together form a fundamental mechanism of commuterÕs decision making, that is, whether accept or switch his/her departure time and route. Sid in Fig. 1 is an indicator variable of departure time (d) switch
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
893
for commuter i, Sid 1, if commuter i switches his/her departure time; Sid 0, otherwise. Sir is an indicator variable of route (r) switch for commuter i. Sir is de®ned similarly as Sid . As such, commuter i has four possible combinations, i.e., (1,1), (1,0), (0,1), (0,0). For example, (1,1) represents that commuter i changes his/her departure time and route, and (0,0) represents commuter i does not change his/her departure time and route. 3.2. Model framework In this study, latent variable, internal to each individual, is part of the mechanism underlying the switching, and therefore can neither be observed nor measured directly. Commuters switch departure times and routes as long as the corresponding latent variable is greater than a certain threshold (set to zero in this study). Given actual observations of commutersÕ decisions to switch or not to switch their departure times and routes in response to exogenous information and experienced trac conditions, the functional structure can be derived. Observations can be either cross section data or times series data depending on limitations of time and ®nancial consideration. In this study, cross section data is applied ®rst. Further studies can conduct diary survey to capture the dynamics of the commuterÕs decision process. The objective of this study is to investigate the eects of pre-trip information on commuterÕs decision including departure time and route. Two scenarios, with and without pre-trip information, are analysed. Instead of performing estimations for these two scenarios (models) separately and then comparing the dierence and similarity between these two models, a joint latent variable incorporating with and without pre-trip information is introduced and derived for simplifying the estimation procedures. Because of the assumption of normal distributed error term in the latent variable, probit framework is applied in this study. The probit model is well known for the allowance of more ¯exible model speci®cation through parameters in the variance±covariance matrix. Two scenarios, with and without pre-trip information, are introduced to theoretically model the choice of commuterÕs departure time and route in this section. A joint model incorporating these two scenarios is further derived to facilitate the estimation procedures. The various terms incorporated in the following expressions are de®ned in Table 1. Table 2 lists the parameters and de®nitions of variance±covariance matrix in latent variables. Table 1 De®nitions of latent variable elements Element
De®nition
I N f() h() Xi Zid Zir hid and hir eid sir wi
With pre-trip information Without pre-trip information Systematic component of departure time Systematic component of route Socioeconomic characteristics for commuter i Attribute vectors of departure time for commuter i Attribute vectors of route for commuter i Parameters to be estimated Error term of departure time for commuter i Error term of route for commuter i A binary indicator variable; 1, if with pre-trip information; 0, otherwise
894
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
Table 2 Parameters and de®nitions of variance±covariance matrix in latent variables Parameter
De®nitions
r21 r22 r23 r24
Variance of departure time latent variable with pre-trip information Variance of route latent variable with pre-trip information Variance of departure time latent variable without pre-trip information Variance of route latent variable without pre-trip information Covariance of departure time and route latent variables with pre-trip information Covariance of departure time and route latent variables without pre-trip information
c1 c2
1. Separate models: (scenarios one and two). As described before, the latent variables of departure time and route for commuter i with and without pre-trip information can be expressed as Eq. (6). These latent variables consist of systematic and random components. YidT f T Xi ; Zid ; hid eTid ;
YirT hT Xi ; Zir ; hir sTir ;
6
where T: if T I, scenario one (with pre-trip information); if T N , scenario two (without pretrip information); f T and hT are the systematic components of departure time and route, Xi the socioeconomic vector for commuter i, Zid and Zir the alternative-speci®c vector for commuter i, hid and hir the parameters to be estimated, eTid and sTir are the random terms. The random terms eIid and sIir , are also assumed to be multivariate normal with zero means and general covariance matrices and can be expressed as 2 r1 c 1 I R : 7 c1 r22 c1 is the covariance of departure time and route with pre-trip information. It assumes a contemporaneous correlation between departure time and route choices for a certain commuter, re¯ecting dependence on the same set of experienced trac conditions. r21 and r22 are the variance of departure time and route latent variables, respectively, with pre-trip information. Similarly, general covariance matrix RN can then be expressed as follows: 2 r3 c2 N R : 8 c2 r24 c2 is the covariance between departure time and route choices without pre-trip information. r23 and r24 are the variance of departure time and route latent variables, respectively, without pre-trip information. 2. Joint model (with and without pre-trip information). The latent variables of departure time and route for a commuter w/o pre-trip information can be further developed from Eq. (6) and expressed as Eq. (9). Yid wi YidI 1
Yir wi YirI 1
wi YidN ;
wi YirN :
9
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
895
For illustration purpose, Yid in Eq. (9) can be derived as Eq. (10). Yid wi f I Xi ; Zid ; hid eIid 1 wi f I Xi ; Zid ; hid 1
wi f N Xi ; Zid ; hid eNid
wi f N Xi ; Zid ; hid wi eIid 1
10
wi eNid ;
wi is an indicator variable, equals to 1 when commuter i receives pre-trip information, with wi 0, otherwise. Let eid wi eIid 1
wi eNid ;
f Xi ; Zid ; hid wi f I Xi ; Zid ; hid 1
wi f N Xi ; Zid ; hid ;
11
then Eq. (10) can be rewritten as follows: Yid f Xi ; Zid ; hid eid : Similarly Yir h Xi ; Zir ; hir sir :
12
R (joint) can then be derived as Eq. (13). 2 rD cDR ; R cDR r2R
13
where r2D wi r21 1
wi r23 ;
r2R wi r22 1
wi r24 ;
cDR wi c1 1
wi c2 :
Since the probability distribution of Sid can be assumed to be related to probability density of Yid by Pr Sid 1 Pr Yid > 0 and the probability distribution of Sir can be assumed to be related to probability density of Yir by Pr Sir 1 Pr Yir > 0, the sample strata for the choice of commuter i Sid ; Sir can then be de®ned as follows: (1) S1 : Sid 1 and Sir 1; (2) S2 : Sid 1 and Sir 0; (3) S3 : Sid 0 and Sir 1; (4) S4 : Sid 0 and Sir 0. The likelihood for the entire sample can be derived as Eq. (14) (Maddala, 1983). " Z #" Z # Y 1 Z 1 Y 1 Z h : W e; s de ds W e; s de ds L f :
S1
"
YZ S3
h :
f : 1
Z
S2
1 h :
#" W e; s de ds
f :
YZ S4
1
f : 1
Z
h : 1
#
14
W e; s de ds ;
where W is the standard bivariate normal density function, and can be expressed as Eq. (15) (Daganzo, 1979): xR 1 xT 1 W 2pjRj exp ; 15 2 where R is de®ned as Eq. (13), and x eid ; sir .
896
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
To test for the heterogeneity presented in the model, the procedures proposed by Abdel-Aty et al. (1997) (as described in Section 2.2) are applied in this paper. The likelihood function is then rewritten as Eq. (16). #" Z # Z 1 "Y Z 1 Z 1 Y 1 Z h : W e; s de ds W e; s de ds L 1
"
f :
S1
YZ S3
f :
Z
1
h :
1 h :
f :
S2
#" Z Y W e; s de ds S4
f : 1
Z
1
h : 1
#
16
W e; s de ds f ti d ti :
The parametric form of ti is assumed to be normally distributed with mean zero and variance r2t . 3.3. Model speci®cation The latent variable is assumed to include the following components: (1) initial component, (2) commuter characteristics component, (3) dynamic component, and (4) myopic component. The myopic component captures the short-term dynamic eect while the long-term dynamic eect is captured by the dynamic component. In addition, as noted previously, the latent variable speci®cations must re¯ect dierent behaviors for a commuter with pre-trip information vs. without pre-trip information. This is achieved through the indicator variable wi 1 for commuter i receives pre-trip information, and wi 0 otherwise. The detailed departure time model speci®cation can then be expressed as: f Xi ; Zid ; hid wi f I Xi ; Zid ; hid 1
wi f N Xi ; Zid ; hid
wi a0 a1 AGEi a2 GENDERi a3 NFAILid a4 SDi 1
17
wi a5 a6 AGEi a7 GENDERi a8 NFAILid a9 SDi :
The route model speci®cation can be expressed as: h Xi ; Zir ; hir wi hI Xi ; Zir ; hir 1 wi hN Xi ; Zir ; hir wi b0 b1 AGEi b2 GENDERi b3 NFAILir b4 SDi 1
18
wi b5 b6 AGEi b7 GENDERi b8 NFAILir b9 SDi :
The de®nitions of the variables included in Eqs. (17) and (18) are given in Table 3. Several assumptions are made in conjunction with the above model speci®cations. First, an initial component exists for both departure time and route, this initial band is asymmetric for a commuter with pre-trip information vs. without pre-trip information. Second, a commuterÕs age may aect departure time and route switching decisions, with older commuters less likely to switch than younger ones. Third, a commuterÕs gender may in¯uence departure time and route switching decisions, with female commuters generally less likely to switch than males. Fourth, the latent variables may increase in response to more switches over a period of time, re¯ecting the relaxation of aspiration levels due to the uncertainty of experienced trac conditions. Fifth, a variable ``SD'' is de®ned as the dierence of actual arrival time and work starting time in absolute value. This variable re¯ects inherent preferences and risk attitudes of each commuter, as well as the characteristics of the working place. The latent variables may increase with a greater SD value.
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
897
Table 3 De®nitions of latent variable elements Element
De®nition
AGEi
Age of commuter i; 1 if age < 18; 2 if age 2 18; 30; 3 if age 2 31; 40; 4 if age 2 41; 60; 5 if age > 61 Gender of commuter i; 1, if male; 0, otherwise Number of unacceptable arrivals (number of departure time changes) for commuter i in the most recent week Number of unacceptable arrivals (number of route changes) for commuter i in the most recent week Average absolute schedule delay of commuter i in the most recent week; abs(actual arrival time±work start time)
GENDERi NFAILid NFAILir SDi
4. Model estimation 4.1. Data Three hundred households in the Taichung metropolitan area in Taiwan were randomly selected and interviewed in April of 1996. All commuters in the household were requested to complete separate questionnaires. A total of 296 households accepted the survey and 925 questionnaires were completed. The total valid sample size of auto commuters was 671. This survey comprised two main parts: personal characteristics and commuting behavior characteristics. The survey was designed to collect the necessary SP data because the focus of this paper is to investigate the attributes that in¯uence urban commutersÕ choice behavior with and without pre-trip information. This type of information can only be obtained through hypothetical questioning using the SP approach. A detailed description of the survey can be found in JouÕs work (1997). To learn how commuters adjust their decisions in response to supplied information, there is a need to identify the factors that lead commuters to alter their choice behavior with and without the pre-trip information. Building a model that predicts commutersÕ choice behavior will aid in evaluating the development of pre-trip information and assessing its impact. The model described here was developed to relate commuter behavior to personal and travel behavior characteristics. In this section, only departure time and route decisions of commuters are investigated. It is also important to note that the dependent variable in the switching models is not an actual decision to switch for a particular commuter but a response to the survey of whether the commuter switches departure time or route. A commuter is considered as departure time or route switching whenever he/she switches departure time or route 3 out of 5 weekdays per week. This current commuter is considered as a departure time switch from the previous day whenever the absolute value of the dierence between two departure times is greater than or equal to 10 min, and is considered as a route switch whenever the chosen route is dierent from the previous day. Thus, these models describe the factors behind the tendency or likelihood to make a switch rather than an actual switch. A commuter is de®ned as receiving pre-trip information if he/she normally listens to trac reports before leaving their homes.
898
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
4.2. Estimation results Two separate models for departure time and route were speci®ed in Eqs. (17) and (18). Each model consists of two scenarios, with and without pre-trip information. The full model with a more general variance±covariance matrix that includes correlation, as speci®ed in Eq. (13), is estimated. Likelihood ratio tests are then performed to examine the equality of parameters between two scenarios, with and without pre-trip information, both for departure time and route. A ®nal model speci®cation is obtained following this procedure. By maximizing the likelihood function, parameters h; r, and c can be estimated. The statistical signi®cance of the coecient c will indicate the presence of correlation between departure time and route choice. The heterogeneity is also investigated by the signi®cance of rt . The estimation results are presented in Table 4. The log-likelihood value at convergence (obtained from the maximization of the joint maximum likelihood function in Eq. (16)) for the joint model system is )535.82. The log-likelihood when all the parameters are zero is )930.21. A loglikelihood ratio test clearly rejects the null hypothesis that all variable parameters and error correlations are zero. An informal goodness-of-®t index q2 , which is most useful in comparing two speci®cations developed on the exact same data, is used to examine the performance of the joint model system. This value is on the high side at 0.42 indicating a good explanatory power of the model. In addition, the signi®cance of rt con®rms the existence of unobserved heterogeneity and the need to capture it in the estimation process. The results of likelihood ratio test for pre-trip information eects on departure time and route, separately and jointly, are summarized in Table 5. The results of ®rst two rows in Table 5 indicate that one can reject the null hypotheses that the coecients of attributes (with pre-trip information) are respectively equal to the corresponding coecients (without pre-trip information) for both departure time and route. The results of last two rows also indicate that one can reject the null hypotheses that the coecients of attributes (departure time) are respectively equal to the corresponding coecients (route) for both scenarios (w/o pre-trip information). The results indicate that the coecients associated with pre-trip information dier signi®cantly from those associated with the no pre-trip information scenario, implying that pre-trip information has a dierent in¯uence on both departure time and route latent variables. On the other hand, the coecients associated with departure time also signi®cantly dier from the one associated with route in both scenarios, implying the dierent switching behavior between departure time and route decisions for a given scenario. The behavioral interpretation and discussion are based on the results in Table 4, as Eqs. (17) and (18) are considered as the ®nal models. The results in Table 4 reveal that the initial latent variable with pre-trip information is larger than that without pre-trip information. This is shown by the respective values of a0 and a5 for departure time, and b0 and b5 for route. The socio-economic variable coecients, a1 ; a2 ; a6 , and a7 for departure time and b1 ; b2 ; b6 , and b7 for route, have the correct signs. The results suggest that younger commuters tend to switch than older ones for both departure time and route switching decisions. Male commuters are more likely to switch than females for both departure time and route switching decisions. These results indicate that male and younger commuters are more risk prone as found in a previous work (Abdel-Aty et al., 1997). The dynamic component parameters are a3 and a8 for departure time switching decisions and b3 and b8 for route. These parameters capture the dynamic eect of commutersÕ learning through
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
899
Table 4 Estimation results for the joint model Component
Attributes/parameter
Estimates
t
DT initial (I) DT initial (N) DT Socio-economic 1 (I) DT Socio-economic 1 (N) DT Socio-economic 2 (I) DT Socio-economic 2 (N) DT Dynamic (I) DT Dynamic (N) DT Myopic (I) DT Myopic (N) R initial (I) R initial (N) R Socio-economic 1 (I) R Socio-economic 1 (N) R Socio-economic 2 (I) R Socio-economic 2 (N) R Dynamic (I) R Dynamic (N) R Myopic (I) R Myopic (N) DT standard deviation (I) DT standard deviation (N) R standard deviation (I) R standard deviation (N) Covariance for the con-temporaneous correlation of R and DT (I) Covariance for the con-temporaneous correlation of R and DT (N)
a0 I a5 N AGEi I=a1 AGEi N =a6 GENDERi I=a2 GENDERi N=a7 NFAILi I=a3 NFAILi N =a8 SDi I=a4 SDi N =a9 b0 I b5 N AGEi I=b1 AGEi N =b6 GENDERi I=b2 GENDERi N=b7 NFAILi I=b3 NFAILi N =b8 SDi I=b4 SDi N =b9 r1 r3 r2 r4 c1
)3.91 )4.49 )1.30 )2.50 1.75 1.28 )1.52 )2.75 1.45 0.81 )11.31 )13.50 )5.78 )6.95 1.15 0.75 )3.78 )4.05 0.89 0.30 15.12 12.32 14.98 10.56 5.99
)10.21 )5.36 )2.05 )6.36 6.02 3.92 )2.69 )4.63 8.06 6.45 )3.54 )3.62 )5.78 )4.90 3.03 2.19 )3.64 )5.12 3.08 9.30 4.60 5.97 2.98 3.45 5.21
c2
5.10
3.45
Standard deviation of t Log-likelihood at convergence Log-likelihood at zero Likelihood ratio index
rt
2.48 )535.82 )930.21 0.42
5.92
Table 5 Log-likelihood ratio test for pre-trip information eects on departure time and route (separately and jointly) Restricted on
L U
L R
Test statistics
Signi®cant
DT w/o pre-trip information R w/o pre-trip information DT and R w pre-trip information DT and R o pre-trip information
)535.82
)554.12 )555.32 )551.79 )560.12
36.60 39.00 31.94 48.60
Yes Yes Yes Yes
previous experience. The results indicate that commuters tend to engage in less departure time or route switching after experiencing conditions that require them to switch in the most recent week. Jou and Mahmassani (1998) observed a similar ®nding in a ®eld survey where pre-trip information is not available. The parameters for the myopic component are a4 and a9 for departure
900
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
time and b4 and b9 for route. The results imply that if commutersÕ actual arrival time is substantial early or late with respect to their working start time, they will be more likely to switch departure time and route decisions. The presence of both correlation and state dependence is one of the concerns in the model speci®cation. The latter, to a large extent, is captured by speci®cation of the modelÕs systematic components, such as the dynamic and myopic components. Correlation is re¯ected in the covariance matrix of the random terms, As expected, the r's and c's in Table 4 are signi®cant at a reasonable level, which con®rms the need to incorporate the respective correlation term for departure time and route. The covariance terms are smaller than the main variance terms. As expected, all the correlation terms exhibit positive signs indicating positive correlation between the unobserved disturbances. Comparing the results for scenario one with those for scenario two, the coecients of socioeconomic variables for scenario one are greater than those for scenario two for both departure time and route switching, re¯ecting the dierence in in¯uence of commuter characteristics (AGE and GENDER) on the two scenario latent variables. This is also true for the dynamic and myopic components, implying that the number of unacceptable arrivals (NFAIL) and absolute schedule delay (SD) have dierent eect on latent variables of scenarios one and two for both departure time and route switching. The parameters of scenario one are greater than those of scenario two which suggests that commuters are indeed more likely to switch with pre-trip information than without pre-trip information. Comparing the results for route with those for departure time, the estimated values for the departure time latent variable are usually greater than those for route switching, with respect to the same attributes, both for scenarios one and two. These results are consistent with earlier ®ndings (Jou and Mahmassani, 1998) con®rming a commuter is very likely to switch departure time whenever s/he switches route. 5. Concluding comments This paper establishes the model framework to investigate the eects of pre-trip information on commuterÕs decision including departure time and route. Two scenarios, with and without pre-trip information, are analysed. Instead of performing estimations for these two scenarios (models) separately and then comparing the dierence and similarity between these two models, a joint latent variable incorporating with and without pre-trip information is introduced and derived for simplifying the estimation procedures. Because of the assumption of normal distributed error term in the latent variable, probit framework is applied to take advantage of the allowance of more ¯exible model speci®cation through parameters in the variance±covariance matrix. In addition, this paper also addresses unobserved heterogeneity with individual-speci®c random error components in binary probit models with a normal mixing distribution. The results of log-likelihood ratio test clearly rejects the null hypothesis that all variable parameters and error correlations are zero. The high value of q2 indicates a good explanatory power of the model. In addition, the signi®cance of rm con®rms the existence of unobserved heterogeneity. The results of likelihood ratio test indicate that the coecients associated with pre-trip information do signi®cantly dier from the one associated without pre-trip information, implying that pre-trip information has a dierent in¯uence on both departure time and route latent vari-
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
901
ables. On the other hand, the coecients associated with departure time also signi®cantly dier from the one associated with route in both scenarios, implying that there exists dierent switching behavior between departure time and route for a given scenario. The behavioral interpretation and discussion of ®nal models reveal that the initial latent variable with pre-trip information is larger than that without pre-trip information. The socio-economic variable coecients have the correct signs. The results suggest that younger commuters tend to switch than older ones for both departure time and route switching decisions. Male commuters are more likely to switch than females for both departure time and route switching decisions. The dynamic component parameters capture the dynamic eect of commutersÕ learning through previous experience. The results indicate that commuters tend to engage in less departure time or route switching after experiencing conditions that require them to switch in the most recent week. The estimated parameters for the myopic component imply that if commutersÕ actual arrival time is substantial early or late with respect to their working start time, they will be more likely to switch departure time and route decisions. The estimates of the variance and covariance terms are all signi®cant at a reasonable level, which con®rms the need to incorporate the respective correlation term for departure time and route. The parameters of scenario one are greater than those of scenario two suggesting that commuters with pre-trip information are more likely to switch than those without pre-trip information. The estimated values for the departure time are usually greater than those for route, with respect to the same attributes, both for scenarios one and two, con®rming that a commuter is very likely to switch departure time whenever s/he switches route. Although this study has generated valuable insights into the eect of pre-trip information on commuter choice behavior, possible further research directions suggested by the ®ndings of this study are discussed hereafter. 1. Only whether receiving pre-trip information (yes or no) was investigated in this study. Future study could extend the developed model to examine the impacts of amount and accuracy of trac information on commuter behavior. As such, the results will be more useful to oer insights into the eects of information strategies on the system's performance. 2. The data obtained from home interview was cross-sectional in this study. A detailed diary survey could provide suciently rich and ¯exible database for analyzing the impacts of trac information on day-to-day dynamics of commuter decisions of departure time and route. 3. Dierent survey strategies and alternative model-®tting techniques could lead more naturally to the work in the remainder of the paper, e.g. contrasting those where before/after chosen routes need to be explicitly observed against those using latent variables. 4. The signi®cance of the standard deviation of the error components shows clearly the need for some formal statistical correction to account for heterogeneity. The non-parametric approach can be used in the future to compare with the results presented in this paper. Acknowledgements This paper is based on research at FCU which was funded by the National Science Council of Taiwan. The cooperation of the participants and the numerous research assistants conducting the survey and coding data is particularly appreciated. The quality of this paper was enhanced by three anonymous referees' comments and suggestions.
902
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
References Abdel-Aty, M.A., Vaughn, K.M., Kitamura, R., Jovanis, P.P., Mannering, F., 1994. Models of commuters information use and route choice: Initial results based on a southern california commuter route choice survey. Transportation Research Record 1453, 46±55. Abdel-Aty, M.A., Kitamura, R., Jovanis, P.P., 1997. Using stated preference data for studying the eect of advanced trac information on drivers' route choice. Transportation Research C 5 (1), 39±50. Aptech Systems Inc., 1992. Gauss Version 3.0 User's, Manual, Kent, Washington. Beaton, W.P., Sadana, A., 1994. The demand for and the change in commuting behavior attributed to the use of a corridor speci®c ATIS pre-trip incident alert system. In: Proceedings of the IVHS America 1994 Annual Meeting. Atlanta, GA, pp. 814±822. Daganzo, C.F., 1970. Multinomial Probit: The Theory and its Application to Demand Forecasting. Academic Press, New York. Harris, P., Konheim, C.S., 1995. Public interest in, and willingness to pay for enhanced traveler information as provided by IVHS in the New York metropolitan area. In: Proceedings of the ITS America 1995 Annual Meeting. Washington, DC, pp. 247±252. Heckman, J.J., 1981. Statistical models for discrete panel data. In: Manskiv, C.F., McFadden, D. (Eds.), Structural Analysis of Discrete Data with Econometric Applications. pp. 114±175 (Chapter 3). Jha, M., Madanat, S., Srinivas, P., 1998. Perception updating and day-To-day travel choice dynamics in trac networks with information provision. Transportation Research C 6, 189±212. Jou, R.C., Mahmassani, H.S., 1998. Day-to-day dynamics of urban commuter departure time and route switching decisions: joint model estimation. In: de Dios Ortuzar, J., Hensher, D., Jara-Diaz, S. (Eds.), Travel Behaviour Research: Updating the State of Play. pp. 365±384 (Chapter 20). Jou, R.C., Hu, T.Y., Lin, C.W., 1997. Empirical results from Taiwan and their implications for advanced travelers' pretrip information systems. Transportation Research Record 1607, 126±133. Khattak, A., Polydoropoulou, A., Ben-Akiva, M., 1995. Commuter normal and shift decisions in unexpected congestion: pretrip response to ATIS. Presented at the 74th Annual Meeting of Transportation Research Board, Washington, DC. Kikuchi, S., Aneja, S., Chakroborty, P.A., Hofmann, J., Machida, M., Perincherry, V., 1994. Advanced traveler aid systems for public transportation ± the intelligent transit mobility system (ITMS). Final report prepared for Federal Transit Administration, US DOT. Maddala, G.S., 1983. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press, Cambridge, MA. Mahmassani, H.S., 1997. Dynamics of commuter behaviour: Recent research and continuing challenges. In: Stopher, P., Martin Lee-Gosselin, (Eds.), Understanding Travel Behaviour in an Era of Change. Pergamon Press, Oxford, pp. 279±313. Mahmassani, H.S., Chang, G.L., 1987. On boundedly-rational user equilibrium in transportation systems. Transportation Science 21 (2), 89±99. Mahmassani, H.S., Liu, Y.S., 1997. Models of user pre-trip and en-route switching decisions in response to real-time information. In: Proceedings of the Eighth IFAC Symposium on Transportation Systems'97. Chania, Greece. Polak, J.W., Jones, P.M., 1992. The acquisition of pre-trip information: a stated preference approach. Presented at the 71st Annual Meeting of the Transportation Research Board, Washington, DC. Stephanedes, Y.J., Zografos, K.G., 1994. Modeling the impact of pre-trip freeway delay advisories on commuter departure time and route choices. Presented at the 73rd Annual Meeting of the Transportation Research Board, Washington, DC. Vaughn, K.M., Abdel-Aty, M.A., Kitamura, R., Jovanis, P.P., Yang, H., Kroll, Neal E.A., Post, R.B., Oppy, B., 1993. Experimental analysis and modeling of sequential route choice under ATIS in a simplistic trac network. Presented at the 72nd Annual Meeting of the Transportation Research Board, Washington, DC.
www.elsevier.com/locate/trb
Modeling the impact of pre-trip information on commuter departure time and route choice Rong-Chang Jou * Department of Trac and Transportation Engineering and Management, Feng Chia University, Taichung, Taiwan, Republic of China Received 20 January 1999; received in revised form 2 February 2000; accepted 18 February 2000
Abstract The objective of this paper is to investigate the impact of pre-trip information on auto commutersÕ choice behavior. The analysis is based on an extensive home-interview survey of commuters in the Taichung metropolitan area in Taiwan. A joint model for route and departure time decisions with and without pretrip information is formulated. The model speci®cations are developed for both the systematic and random components. In particular, econometric issues associated with specifying the random error structure are addressed for parameter estimation purposes. Insights into the eects of attributes are obtained through the analysis of the model's performance and estimated parameter values. A probit model form is used for the joint model, allowing the introduction of state dependence and correlation in the model speci®cation. The results underscore the important relationship between the dierent characteristics and the propensity of commuter choice behavior under two scenarios, with and without pre-trip information. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Pre-trip information; Departure time; Route; Probit model
1. Introduction Methods to reduce congestion by either increasing capacity (supply-side measures) or reducing demand (demand-side measures) have gained much attention recently. It is also well accepted that emerging ITS technologies oer promising system eciency through the exploitation of local imbalances between supply and demand, using information as the primary mechanism to in¯uence user decisions (Mahmassani, 1997). Among possible alternatives of ITS, Advanced Traveler
*
Tel.: +011-886-4-451-6122; fax: +011-886-4-451-6122. E-mail address: [email protected] (R.-C. Jou).
0191-2615/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 1 - 2 6 1 5 ( 0 0 ) 0 0 0 2 8 - X
888
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
Information Systems (ATIS) improves highway productivity by oering trac information to travelers and provides a unique opportunity to enhance our transportation system. The ultimate goal for designers of ATIS is to provide travelers with the best information possible to make trip planning ecient and eective. The decisions in¯uenced by the ATIS-supplied information take place at two principal instances: at the trip origin or en-route. The ®rst are referred to as ``pre-trip'' decisions and may be the results of both long-term factors and real-time elements. The pre-trip information is provided to travelers at origins (home or workplace) prior to their trips through television, radio, telephone inquiry, and computer on-line services. Pre-trip information can help reduce the degree of uncertainty when commuters encounter travel time variation on their routes. With the information provided, the users of systems could make trips more eciently by changing most attributes of the journey, including departure time, route, mode, destination, or even whether to make the trip at all. Therefore, pre-trip information indeed plays a vital role in travelersÕ trip planning. The success of systems greatly depends on the ability of the system to provide travelers with useful information. In addition, the system needs to make information available and have it accessible to all users. The Intermodal Surface Transportation Eciency Act (ISTEA) bill passed by Congress in 1990 further emphasized the fact that eective dissemination of information regarding transportation services is essential in promoting a balanced use of dierent transportation modes, which would, in turn, alleviate trac congestion (Kikuchi et al., 1994). Since many of these ATIS technologies are aimed at relieving congestion during congested commuting periods of the day, the behavior of commuters must be treated as a central element in the formulation and implementation of these congestion relief measures. On the other hand, pretrip trac information systems are important because they potentially provide commuters with the greatest ¯exibility. Therefore, a better understanding of how a pre-trip information will in¯uence commutersÕ choice behavior is required. Based on the pre-trip information, commuters can change either departure time or route choice in response to congestion and various strategies in the short term. The objective of this paper is to investigate the impact of pre-trip information on urban auto commutersÕ choice behavior. It is based on a large-scale survey conducted in the Taichung metropolitan area of Taiwan in 1996. Probit models are developed to capture the principal attributes of the dierent characteristics that in¯uence urban commutersÕ choice behavior, including departure time and route, with and without the information provided. The results underscore the important relationship between the dierent characteristics and the propensity of commuter choice behavior under two scenarios, with and without pre-trip information. The results obtained from this study provide a basis for the subsequent development of information system architecture in Taiwan. This paper is divided into four sections. Section 2 of this paper provides a review of relevant literature and discussion of background material that is important to the study of urban commutersÕ behavior with and without pre-trip information. Section 3 discusses the development for modeling the decisions of route and departure time, taken jointly, and incorporating pre-trip information. The eect of pre-trip information on commutersÕ choice behavior is presented ®rst, followed by model framework, and model speci®cation. The estimation results of the probit models and concluding comments are presented in Sections 4 and 5.
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
889
2. Background This section provides a review and discussion of background material pertaining to two subjects that are important to this study. Section 2.1 is to investigate current literature on the subject of commuter behavior when in¯uenced by pre-trip information, followed by dynamic models and related econometric issues that are essential to the methodological development of route and departure time decisions incorporating pre-trip information. 2.1. Commuter behavior when in¯uenced by pre-trip information Over the past decade, there has been an extensive investigation of departure time and route choices in interactive laboratory-like experiments (Mahmassani, 1997). Mahmassani and Liu (1997) focused on the day-to-day dynamics of commutersÕ departure time and route decision process in response to the supplied information. The results showed that younger commuters tend to switch their departure time decisions, while male commuters tend to switch their route decisions. Vaughn et al. (1993) developed an interactive experiment to investigate drivers' learning and pre-trip route choice behavior under ATIS. The results indicated that drivers can rapidly identify the accuracy level of provided information and adjust their behavior accordingly. Although these works provide valuable insights into complex human decision behavior, they are primarily based on theoretical concepts or simulated experiments, and the transferability of these insights to commuter behavior in real trac networks has not been adequately established. Polak and Jones (1992) developed a stated preference (SP) approach to investigate the eects of pre-trip information on travel behavior. Initial results from the study indicated that the approach worked well and is able to provide useful quantitative data on the key parameters of the information acquisition process. Stephanedes and Zografos (1994) developed empirical models that can provide a better understanding of the relationship between pre-trip departure time and route choice decisions, and the duration of the announced delay. In a survey of Seattle commuters, pretrip trac information in¯uenced route choice for only 11% of the respondents and departure time for 13% (Beaton and Sadana, 1994). Survey conducted in the New York metropolitan area indicated that if people are able to obtain more timely and reliable trac information, they are more likely to use it (Harris and Konheim, 1995). Abdel-Aty et al. (1994) found that commuters might value and use pre-trip information more than en-route, because it gives them the situation on their routes in advance, which enables them to change route and/or departure time. Abdel-Aty et al. (1997) further investigated the factors that in¯uence route choice with particular emphasis on the eect of trac information and travel time variability on route choice, and found that receiving pre-trip trac information was a signi®cant factor in the model. Khattak et al. (1995) proposed a combined revealed and SP model to explore how driversÕ pre-trip decisions are aected by ATIS in the context of unexpected congestion. Jha et al. (1998) developed a Bayesian updating model to capture the mechanism by which travelers update their travel time perceptions from one day to next in light of information provided by ATIS and their previous experience. In Taiwan, most of the pre-trip information is provided to commuters through radio service (Jou et al., 1997). Studies showed that commuters are willing to change their departure time,
890
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
route, and transportation mode under a well-developed route guidance system. Although a very signi®cant amount of eort has been invested in US, Europe, and Japan to promote an ATIS industry, in Taiwan only recently have researchers started to address some of the issues associated with analyzing and modeling commutersÕ reactions to ATIS (Jou et al., 1997). 2.2. Dynamic modeling and related econometric issues Heckman (1981) presented a general dynamic model for the analysis of discrete panel data that can be used to analyze the structure of discrete choices made over time. Dynamic models are typically estimated with repeated observations for each respondent. Under these conditions, the estimation gives rise to an obvious correlation of disturbances, or heterogeneity, which refer to variations in unobserved contributing factors across behavioral units. If unobserved factors are correlated with the measured explanatory variables, then estimated coecients will be biased if the heterogeneity is not properly taken into account. Abdel-Aty et al. (1997) had a more extensive and thorough review of discrete choice models with repeated measurement data and the correction procedures. For example, Abdel-Aty et al. (1997) assumed a parametric functional form for the pattern of the heterogeneity to account for unobserved heterogeneity. This approach is introduced hereinafter for the illustration purpose. Let the probabilities that the event occurs and does not occur, respectively, as: 0 Xit b a ; P occurs P dit 1=a; b; Xit P Hit P 0=a; b; Xit U ru 1 Xit0 b a ; P not occur P dit 0=a; b; Xit P Hit < 0=a; b; Xit U ru where Hit Vit uit Xit0 b a uit ; a is a constant, b is a vector of parameters, and Xit is a vector of exogenous variables. The distribution of the dit is generated by the distributions of uit and Vit . This model is similar to the multivariate probit model if the uit is assumed to be jointly normally distributed with mean zero and variance r2u . The in¯uence of the unobserved variables in Eq. (1) is captured by the constant term a. The probability of observing di di1 ; di2 ; di3 ; di4 ; . . . ; diTi given Ti in this speci®cation is: dit Ti 0 Y Xit b a Xit0 b U U P di =a; b; Ti ; Xit ru ru t1
a
1
dit
:
2
To investigate the heterogeneity, Eq. (1) is rewritten as Eq. (3) by assuming the probabilities are conditional on both Xit and an individual speci®c error term, ti , which represents all the other in¯uences. 0 Xit b a ti P occurs P dit 1=a; b; Xit ; ti P Hit P 0=a; b; Xit ; ti U ; ru 3 Xit0 b a ti : P not occur P dit 0=a; b; Xit ; ti P Hit P 0=a; b; Xit ; ti U ru
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
891
The ti : i 1; . . . ; I are assumed to be identically distributed with density function f ti independent of the Xi , so that Eq. (2) becomes dit 1 dit Z 1Y Ti 0 Xit b a Xit0 b a P di =a; b; Ti ; Xit ; f ti U U f ti d ti : 4 ru ru 1 t1 Eq. (4) is a marginal likelihood function. The unknown variables, ti , are integrated out. The distribution of ti is called a mixing continuous distribution. The log-likelihood function is dit 1 dit Z 1Y Ti 0 I X Xit b a Xit0 b a L ln U U f ti d ti : 5 ru ru 1 t1 i1 The parametric form of ti can be assumed to be normally distributed with mean zero and variance r2t . The maximum likelihood estimates can then be obtained by general MLE packages such as the one provided with GAUSS statistical software (Aptech Systems, 1992). Alternative structural framework gives rise to a variety of interesting and important models useful in the analysis of discrete panel data. Mahmassani and Chang (1987) initially developed a boundedly rational model formulation of departure time and route switching in day-to-day commute. Jou and Mahmassani (1998) extended the previous work by combining early and late side indierence bands of tolerable schedule delay (de®ned as the dierence between the preferred arrival time and the actual arrival time for a given commute). The boundedly rational mechanism governing day-to-day departure time and route switching decisions postulates that commuter does not switch his/her next dayÕs departure time and/or route so long as the corresponding schedule delay on current day remains within the commuterÕs indierence bands for departure time and route choices. Based on the literature review, the following comments can be made: 1. To test for the heterogeneity presented in the model, the procedures proposed by Abdel-Aty et al. (1997) are applied in this paper. A parametric functional form for the pattern of the heterogeneity is assumed to account for unobserved heterogeneity. 2. A joint model, conceptually similar to the one proposed by Jou and Mahmassani (1998), for route and departure time decisions with and without pre-trip information is applied in this paper. 3. Several assumptions in conjunction with the model speci®cations made in Section 3.3 are based on the empirical evidence highlighted in Section 2.1. 3. Model development This section discusses the development for modeling the decisions of route and departure time, taken jointly, and incorporating pre-trip information. The eect of pre-trip information on commutersÕ choice behavior is presented ®rst, followed by model framework, and model speci®cation. 3.1. Role of pre-trip information The role that pre-trip information plays in the process of commuterÕs decision making is shown in Fig. 1. Fig. 1 shows that whether a commuter receives pre-trip information depends on his/her
892
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
Fig. 1. The eect of pre-trip information on commutersÕ choice behavior.
socioeconomic characteristics, working place characteristics, and experienced trac system characteristics. These three characteristics and whether receiving pre-trip information together form a fundamental mechanism of commuterÕs decision making, that is, whether accept or switch his/her departure time and route. Sid in Fig. 1 is an indicator variable of departure time (d) switch
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
893
for commuter i, Sid 1, if commuter i switches his/her departure time; Sid 0, otherwise. Sir is an indicator variable of route (r) switch for commuter i. Sir is de®ned similarly as Sid . As such, commuter i has four possible combinations, i.e., (1,1), (1,0), (0,1), (0,0). For example, (1,1) represents that commuter i changes his/her departure time and route, and (0,0) represents commuter i does not change his/her departure time and route. 3.2. Model framework In this study, latent variable, internal to each individual, is part of the mechanism underlying the switching, and therefore can neither be observed nor measured directly. Commuters switch departure times and routes as long as the corresponding latent variable is greater than a certain threshold (set to zero in this study). Given actual observations of commutersÕ decisions to switch or not to switch their departure times and routes in response to exogenous information and experienced trac conditions, the functional structure can be derived. Observations can be either cross section data or times series data depending on limitations of time and ®nancial consideration. In this study, cross section data is applied ®rst. Further studies can conduct diary survey to capture the dynamics of the commuterÕs decision process. The objective of this study is to investigate the eects of pre-trip information on commuterÕs decision including departure time and route. Two scenarios, with and without pre-trip information, are analysed. Instead of performing estimations for these two scenarios (models) separately and then comparing the dierence and similarity between these two models, a joint latent variable incorporating with and without pre-trip information is introduced and derived for simplifying the estimation procedures. Because of the assumption of normal distributed error term in the latent variable, probit framework is applied in this study. The probit model is well known for the allowance of more ¯exible model speci®cation through parameters in the variance±covariance matrix. Two scenarios, with and without pre-trip information, are introduced to theoretically model the choice of commuterÕs departure time and route in this section. A joint model incorporating these two scenarios is further derived to facilitate the estimation procedures. The various terms incorporated in the following expressions are de®ned in Table 1. Table 2 lists the parameters and de®nitions of variance±covariance matrix in latent variables. Table 1 De®nitions of latent variable elements Element
De®nition
I N f() h() Xi Zid Zir hid and hir eid sir wi
With pre-trip information Without pre-trip information Systematic component of departure time Systematic component of route Socioeconomic characteristics for commuter i Attribute vectors of departure time for commuter i Attribute vectors of route for commuter i Parameters to be estimated Error term of departure time for commuter i Error term of route for commuter i A binary indicator variable; 1, if with pre-trip information; 0, otherwise
894
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
Table 2 Parameters and de®nitions of variance±covariance matrix in latent variables Parameter
De®nitions
r21 r22 r23 r24
Variance of departure time latent variable with pre-trip information Variance of route latent variable with pre-trip information Variance of departure time latent variable without pre-trip information Variance of route latent variable without pre-trip information Covariance of departure time and route latent variables with pre-trip information Covariance of departure time and route latent variables without pre-trip information
c1 c2
1. Separate models: (scenarios one and two). As described before, the latent variables of departure time and route for commuter i with and without pre-trip information can be expressed as Eq. (6). These latent variables consist of systematic and random components. YidT f T Xi ; Zid ; hid eTid ;
YirT hT Xi ; Zir ; hir sTir ;
6
where T: if T I, scenario one (with pre-trip information); if T N , scenario two (without pretrip information); f T and hT are the systematic components of departure time and route, Xi the socioeconomic vector for commuter i, Zid and Zir the alternative-speci®c vector for commuter i, hid and hir the parameters to be estimated, eTid and sTir are the random terms. The random terms eIid and sIir , are also assumed to be multivariate normal with zero means and general covariance matrices and can be expressed as 2 r1 c 1 I R : 7 c1 r22 c1 is the covariance of departure time and route with pre-trip information. It assumes a contemporaneous correlation between departure time and route choices for a certain commuter, re¯ecting dependence on the same set of experienced trac conditions. r21 and r22 are the variance of departure time and route latent variables, respectively, with pre-trip information. Similarly, general covariance matrix RN can then be expressed as follows: 2 r3 c2 N R : 8 c2 r24 c2 is the covariance between departure time and route choices without pre-trip information. r23 and r24 are the variance of departure time and route latent variables, respectively, without pre-trip information. 2. Joint model (with and without pre-trip information). The latent variables of departure time and route for a commuter w/o pre-trip information can be further developed from Eq. (6) and expressed as Eq. (9). Yid wi YidI 1
Yir wi YirI 1
wi YidN ;
wi YirN :
9
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
895
For illustration purpose, Yid in Eq. (9) can be derived as Eq. (10). Yid wi f I Xi ; Zid ; hid eIid 1 wi f I Xi ; Zid ; hid 1
wi f N Xi ; Zid ; hid eNid
wi f N Xi ; Zid ; hid wi eIid 1
10
wi eNid ;
wi is an indicator variable, equals to 1 when commuter i receives pre-trip information, with wi 0, otherwise. Let eid wi eIid 1
wi eNid ;
f Xi ; Zid ; hid wi f I Xi ; Zid ; hid 1
wi f N Xi ; Zid ; hid ;
11
then Eq. (10) can be rewritten as follows: Yid f Xi ; Zid ; hid eid : Similarly Yir h Xi ; Zir ; hir sir :
12
R (joint) can then be derived as Eq. (13). 2 rD cDR ; R cDR r2R
13
where r2D wi r21 1
wi r23 ;
r2R wi r22 1
wi r24 ;
cDR wi c1 1
wi c2 :
Since the probability distribution of Sid can be assumed to be related to probability density of Yid by Pr Sid 1 Pr Yid > 0 and the probability distribution of Sir can be assumed to be related to probability density of Yir by Pr Sir 1 Pr Yir > 0, the sample strata for the choice of commuter i Sid ; Sir can then be de®ned as follows: (1) S1 : Sid 1 and Sir 1; (2) S2 : Sid 1 and Sir 0; (3) S3 : Sid 0 and Sir 1; (4) S4 : Sid 0 and Sir 0. The likelihood for the entire sample can be derived as Eq. (14) (Maddala, 1983). " Z #" Z # Y 1 Z 1 Y 1 Z h : W e; s de ds W e; s de ds L f :
S1
"
YZ S3
h :
f : 1
Z
S2
1 h :
#" W e; s de ds
f :
YZ S4
1
f : 1
Z
h : 1
#
14
W e; s de ds ;
where W is the standard bivariate normal density function, and can be expressed as Eq. (15) (Daganzo, 1979): xR 1 xT 1 W 2pjRj exp ; 15 2 where R is de®ned as Eq. (13), and x eid ; sir .
896
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
To test for the heterogeneity presented in the model, the procedures proposed by Abdel-Aty et al. (1997) (as described in Section 2.2) are applied in this paper. The likelihood function is then rewritten as Eq. (16). #" Z # Z 1 "Y Z 1 Z 1 Y 1 Z h : W e; s de ds W e; s de ds L 1
"
f :
S1
YZ S3
f :
Z
1
h :
1 h :
f :
S2
#" Z Y W e; s de ds S4
f : 1
Z
1
h : 1
#
16
W e; s de ds f ti d ti :
The parametric form of ti is assumed to be normally distributed with mean zero and variance r2t . 3.3. Model speci®cation The latent variable is assumed to include the following components: (1) initial component, (2) commuter characteristics component, (3) dynamic component, and (4) myopic component. The myopic component captures the short-term dynamic eect while the long-term dynamic eect is captured by the dynamic component. In addition, as noted previously, the latent variable speci®cations must re¯ect dierent behaviors for a commuter with pre-trip information vs. without pre-trip information. This is achieved through the indicator variable wi 1 for commuter i receives pre-trip information, and wi 0 otherwise. The detailed departure time model speci®cation can then be expressed as: f Xi ; Zid ; hid wi f I Xi ; Zid ; hid 1
wi f N Xi ; Zid ; hid
wi a0 a1 AGEi a2 GENDERi a3 NFAILid a4 SDi 1
17
wi a5 a6 AGEi a7 GENDERi a8 NFAILid a9 SDi :
The route model speci®cation can be expressed as: h Xi ; Zir ; hir wi hI Xi ; Zir ; hir 1 wi hN Xi ; Zir ; hir wi b0 b1 AGEi b2 GENDERi b3 NFAILir b4 SDi 1
18
wi b5 b6 AGEi b7 GENDERi b8 NFAILir b9 SDi :
The de®nitions of the variables included in Eqs. (17) and (18) are given in Table 3. Several assumptions are made in conjunction with the above model speci®cations. First, an initial component exists for both departure time and route, this initial band is asymmetric for a commuter with pre-trip information vs. without pre-trip information. Second, a commuterÕs age may aect departure time and route switching decisions, with older commuters less likely to switch than younger ones. Third, a commuterÕs gender may in¯uence departure time and route switching decisions, with female commuters generally less likely to switch than males. Fourth, the latent variables may increase in response to more switches over a period of time, re¯ecting the relaxation of aspiration levels due to the uncertainty of experienced trac conditions. Fifth, a variable ``SD'' is de®ned as the dierence of actual arrival time and work starting time in absolute value. This variable re¯ects inherent preferences and risk attitudes of each commuter, as well as the characteristics of the working place. The latent variables may increase with a greater SD value.
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
897
Table 3 De®nitions of latent variable elements Element
De®nition
AGEi
Age of commuter i; 1 if age < 18; 2 if age 2 18; 30; 3 if age 2 31; 40; 4 if age 2 41; 60; 5 if age > 61 Gender of commuter i; 1, if male; 0, otherwise Number of unacceptable arrivals (number of departure time changes) for commuter i in the most recent week Number of unacceptable arrivals (number of route changes) for commuter i in the most recent week Average absolute schedule delay of commuter i in the most recent week; abs(actual arrival time±work start time)
GENDERi NFAILid NFAILir SDi
4. Model estimation 4.1. Data Three hundred households in the Taichung metropolitan area in Taiwan were randomly selected and interviewed in April of 1996. All commuters in the household were requested to complete separate questionnaires. A total of 296 households accepted the survey and 925 questionnaires were completed. The total valid sample size of auto commuters was 671. This survey comprised two main parts: personal characteristics and commuting behavior characteristics. The survey was designed to collect the necessary SP data because the focus of this paper is to investigate the attributes that in¯uence urban commutersÕ choice behavior with and without pre-trip information. This type of information can only be obtained through hypothetical questioning using the SP approach. A detailed description of the survey can be found in JouÕs work (1997). To learn how commuters adjust their decisions in response to supplied information, there is a need to identify the factors that lead commuters to alter their choice behavior with and without the pre-trip information. Building a model that predicts commutersÕ choice behavior will aid in evaluating the development of pre-trip information and assessing its impact. The model described here was developed to relate commuter behavior to personal and travel behavior characteristics. In this section, only departure time and route decisions of commuters are investigated. It is also important to note that the dependent variable in the switching models is not an actual decision to switch for a particular commuter but a response to the survey of whether the commuter switches departure time or route. A commuter is considered as departure time or route switching whenever he/she switches departure time or route 3 out of 5 weekdays per week. This current commuter is considered as a departure time switch from the previous day whenever the absolute value of the dierence between two departure times is greater than or equal to 10 min, and is considered as a route switch whenever the chosen route is dierent from the previous day. Thus, these models describe the factors behind the tendency or likelihood to make a switch rather than an actual switch. A commuter is de®ned as receiving pre-trip information if he/she normally listens to trac reports before leaving their homes.
898
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
4.2. Estimation results Two separate models for departure time and route were speci®ed in Eqs. (17) and (18). Each model consists of two scenarios, with and without pre-trip information. The full model with a more general variance±covariance matrix that includes correlation, as speci®ed in Eq. (13), is estimated. Likelihood ratio tests are then performed to examine the equality of parameters between two scenarios, with and without pre-trip information, both for departure time and route. A ®nal model speci®cation is obtained following this procedure. By maximizing the likelihood function, parameters h; r, and c can be estimated. The statistical signi®cance of the coecient c will indicate the presence of correlation between departure time and route choice. The heterogeneity is also investigated by the signi®cance of rt . The estimation results are presented in Table 4. The log-likelihood value at convergence (obtained from the maximization of the joint maximum likelihood function in Eq. (16)) for the joint model system is )535.82. The log-likelihood when all the parameters are zero is )930.21. A loglikelihood ratio test clearly rejects the null hypothesis that all variable parameters and error correlations are zero. An informal goodness-of-®t index q2 , which is most useful in comparing two speci®cations developed on the exact same data, is used to examine the performance of the joint model system. This value is on the high side at 0.42 indicating a good explanatory power of the model. In addition, the signi®cance of rt con®rms the existence of unobserved heterogeneity and the need to capture it in the estimation process. The results of likelihood ratio test for pre-trip information eects on departure time and route, separately and jointly, are summarized in Table 5. The results of ®rst two rows in Table 5 indicate that one can reject the null hypotheses that the coecients of attributes (with pre-trip information) are respectively equal to the corresponding coecients (without pre-trip information) for both departure time and route. The results of last two rows also indicate that one can reject the null hypotheses that the coecients of attributes (departure time) are respectively equal to the corresponding coecients (route) for both scenarios (w/o pre-trip information). The results indicate that the coecients associated with pre-trip information dier signi®cantly from those associated with the no pre-trip information scenario, implying that pre-trip information has a dierent in¯uence on both departure time and route latent variables. On the other hand, the coecients associated with departure time also signi®cantly dier from the one associated with route in both scenarios, implying the dierent switching behavior between departure time and route decisions for a given scenario. The behavioral interpretation and discussion are based on the results in Table 4, as Eqs. (17) and (18) are considered as the ®nal models. The results in Table 4 reveal that the initial latent variable with pre-trip information is larger than that without pre-trip information. This is shown by the respective values of a0 and a5 for departure time, and b0 and b5 for route. The socio-economic variable coecients, a1 ; a2 ; a6 , and a7 for departure time and b1 ; b2 ; b6 , and b7 for route, have the correct signs. The results suggest that younger commuters tend to switch than older ones for both departure time and route switching decisions. Male commuters are more likely to switch than females for both departure time and route switching decisions. These results indicate that male and younger commuters are more risk prone as found in a previous work (Abdel-Aty et al., 1997). The dynamic component parameters are a3 and a8 for departure time switching decisions and b3 and b8 for route. These parameters capture the dynamic eect of commutersÕ learning through
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
899
Table 4 Estimation results for the joint model Component
Attributes/parameter
Estimates
t
DT initial (I) DT initial (N) DT Socio-economic 1 (I) DT Socio-economic 1 (N) DT Socio-economic 2 (I) DT Socio-economic 2 (N) DT Dynamic (I) DT Dynamic (N) DT Myopic (I) DT Myopic (N) R initial (I) R initial (N) R Socio-economic 1 (I) R Socio-economic 1 (N) R Socio-economic 2 (I) R Socio-economic 2 (N) R Dynamic (I) R Dynamic (N) R Myopic (I) R Myopic (N) DT standard deviation (I) DT standard deviation (N) R standard deviation (I) R standard deviation (N) Covariance for the con-temporaneous correlation of R and DT (I) Covariance for the con-temporaneous correlation of R and DT (N)
a0 I a5 N AGEi I=a1 AGEi N =a6 GENDERi I=a2 GENDERi N=a7 NFAILi I=a3 NFAILi N =a8 SDi I=a4 SDi N =a9 b0 I b5 N AGEi I=b1 AGEi N =b6 GENDERi I=b2 GENDERi N=b7 NFAILi I=b3 NFAILi N =b8 SDi I=b4 SDi N =b9 r1 r3 r2 r4 c1
)3.91 )4.49 )1.30 )2.50 1.75 1.28 )1.52 )2.75 1.45 0.81 )11.31 )13.50 )5.78 )6.95 1.15 0.75 )3.78 )4.05 0.89 0.30 15.12 12.32 14.98 10.56 5.99
)10.21 )5.36 )2.05 )6.36 6.02 3.92 )2.69 )4.63 8.06 6.45 )3.54 )3.62 )5.78 )4.90 3.03 2.19 )3.64 )5.12 3.08 9.30 4.60 5.97 2.98 3.45 5.21
c2
5.10
3.45
Standard deviation of t Log-likelihood at convergence Log-likelihood at zero Likelihood ratio index
rt
2.48 )535.82 )930.21 0.42
5.92
Table 5 Log-likelihood ratio test for pre-trip information eects on departure time and route (separately and jointly) Restricted on
L U
L R
Test statistics
Signi®cant
DT w/o pre-trip information R w/o pre-trip information DT and R w pre-trip information DT and R o pre-trip information
)535.82
)554.12 )555.32 )551.79 )560.12
36.60 39.00 31.94 48.60
Yes Yes Yes Yes
previous experience. The results indicate that commuters tend to engage in less departure time or route switching after experiencing conditions that require them to switch in the most recent week. Jou and Mahmassani (1998) observed a similar ®nding in a ®eld survey where pre-trip information is not available. The parameters for the myopic component are a4 and a9 for departure
900
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
time and b4 and b9 for route. The results imply that if commutersÕ actual arrival time is substantial early or late with respect to their working start time, they will be more likely to switch departure time and route decisions. The presence of both correlation and state dependence is one of the concerns in the model speci®cation. The latter, to a large extent, is captured by speci®cation of the modelÕs systematic components, such as the dynamic and myopic components. Correlation is re¯ected in the covariance matrix of the random terms, As expected, the r's and c's in Table 4 are signi®cant at a reasonable level, which con®rms the need to incorporate the respective correlation term for departure time and route. The covariance terms are smaller than the main variance terms. As expected, all the correlation terms exhibit positive signs indicating positive correlation between the unobserved disturbances. Comparing the results for scenario one with those for scenario two, the coecients of socioeconomic variables for scenario one are greater than those for scenario two for both departure time and route switching, re¯ecting the dierence in in¯uence of commuter characteristics (AGE and GENDER) on the two scenario latent variables. This is also true for the dynamic and myopic components, implying that the number of unacceptable arrivals (NFAIL) and absolute schedule delay (SD) have dierent eect on latent variables of scenarios one and two for both departure time and route switching. The parameters of scenario one are greater than those of scenario two which suggests that commuters are indeed more likely to switch with pre-trip information than without pre-trip information. Comparing the results for route with those for departure time, the estimated values for the departure time latent variable are usually greater than those for route switching, with respect to the same attributes, both for scenarios one and two. These results are consistent with earlier ®ndings (Jou and Mahmassani, 1998) con®rming a commuter is very likely to switch departure time whenever s/he switches route. 5. Concluding comments This paper establishes the model framework to investigate the eects of pre-trip information on commuterÕs decision including departure time and route. Two scenarios, with and without pre-trip information, are analysed. Instead of performing estimations for these two scenarios (models) separately and then comparing the dierence and similarity between these two models, a joint latent variable incorporating with and without pre-trip information is introduced and derived for simplifying the estimation procedures. Because of the assumption of normal distributed error term in the latent variable, probit framework is applied to take advantage of the allowance of more ¯exible model speci®cation through parameters in the variance±covariance matrix. In addition, this paper also addresses unobserved heterogeneity with individual-speci®c random error components in binary probit models with a normal mixing distribution. The results of log-likelihood ratio test clearly rejects the null hypothesis that all variable parameters and error correlations are zero. The high value of q2 indicates a good explanatory power of the model. In addition, the signi®cance of rm con®rms the existence of unobserved heterogeneity. The results of likelihood ratio test indicate that the coecients associated with pre-trip information do signi®cantly dier from the one associated without pre-trip information, implying that pre-trip information has a dierent in¯uence on both departure time and route latent vari-
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
901
ables. On the other hand, the coecients associated with departure time also signi®cantly dier from the one associated with route in both scenarios, implying that there exists dierent switching behavior between departure time and route for a given scenario. The behavioral interpretation and discussion of ®nal models reveal that the initial latent variable with pre-trip information is larger than that without pre-trip information. The socio-economic variable coecients have the correct signs. The results suggest that younger commuters tend to switch than older ones for both departure time and route switching decisions. Male commuters are more likely to switch than females for both departure time and route switching decisions. The dynamic component parameters capture the dynamic eect of commutersÕ learning through previous experience. The results indicate that commuters tend to engage in less departure time or route switching after experiencing conditions that require them to switch in the most recent week. The estimated parameters for the myopic component imply that if commutersÕ actual arrival time is substantial early or late with respect to their working start time, they will be more likely to switch departure time and route decisions. The estimates of the variance and covariance terms are all signi®cant at a reasonable level, which con®rms the need to incorporate the respective correlation term for departure time and route. The parameters of scenario one are greater than those of scenario two suggesting that commuters with pre-trip information are more likely to switch than those without pre-trip information. The estimated values for the departure time are usually greater than those for route, with respect to the same attributes, both for scenarios one and two, con®rming that a commuter is very likely to switch departure time whenever s/he switches route. Although this study has generated valuable insights into the eect of pre-trip information on commuter choice behavior, possible further research directions suggested by the ®ndings of this study are discussed hereafter. 1. Only whether receiving pre-trip information (yes or no) was investigated in this study. Future study could extend the developed model to examine the impacts of amount and accuracy of trac information on commuter behavior. As such, the results will be more useful to oer insights into the eects of information strategies on the system's performance. 2. The data obtained from home interview was cross-sectional in this study. A detailed diary survey could provide suciently rich and ¯exible database for analyzing the impacts of trac information on day-to-day dynamics of commuter decisions of departure time and route. 3. Dierent survey strategies and alternative model-®tting techniques could lead more naturally to the work in the remainder of the paper, e.g. contrasting those where before/after chosen routes need to be explicitly observed against those using latent variables. 4. The signi®cance of the standard deviation of the error components shows clearly the need for some formal statistical correction to account for heterogeneity. The non-parametric approach can be used in the future to compare with the results presented in this paper. Acknowledgements This paper is based on research at FCU which was funded by the National Science Council of Taiwan. The cooperation of the participants and the numerous research assistants conducting the survey and coding data is particularly appreciated. The quality of this paper was enhanced by three anonymous referees' comments and suggestions.
902
R.-C. Jou / Transportation Research Part B 35 (2001) 887±902
References Abdel-Aty, M.A., Vaughn, K.M., Kitamura, R., Jovanis, P.P., Mannering, F., 1994. Models of commuters information use and route choice: Initial results based on a southern california commuter route choice survey. Transportation Research Record 1453, 46±55. Abdel-Aty, M.A., Kitamura, R., Jovanis, P.P., 1997. Using stated preference data for studying the eect of advanced trac information on drivers' route choice. Transportation Research C 5 (1), 39±50. Aptech Systems Inc., 1992. Gauss Version 3.0 User's, Manual, Kent, Washington. Beaton, W.P., Sadana, A., 1994. The demand for and the change in commuting behavior attributed to the use of a corridor speci®c ATIS pre-trip incident alert system. In: Proceedings of the IVHS America 1994 Annual Meeting. Atlanta, GA, pp. 814±822. Daganzo, C.F., 1970. Multinomial Probit: The Theory and its Application to Demand Forecasting. Academic Press, New York. Harris, P., Konheim, C.S., 1995. Public interest in, and willingness to pay for enhanced traveler information as provided by IVHS in the New York metropolitan area. In: Proceedings of the ITS America 1995 Annual Meeting. Washington, DC, pp. 247±252. Heckman, J.J., 1981. Statistical models for discrete panel data. In: Manskiv, C.F., McFadden, D. (Eds.), Structural Analysis of Discrete Data with Econometric Applications. pp. 114±175 (Chapter 3). Jha, M., Madanat, S., Srinivas, P., 1998. Perception updating and day-To-day travel choice dynamics in trac networks with information provision. Transportation Research C 6, 189±212. Jou, R.C., Mahmassani, H.S., 1998. Day-to-day dynamics of urban commuter departure time and route switching decisions: joint model estimation. In: de Dios Ortuzar, J., Hensher, D., Jara-Diaz, S. (Eds.), Travel Behaviour Research: Updating the State of Play. pp. 365±384 (Chapter 20). Jou, R.C., Hu, T.Y., Lin, C.W., 1997. Empirical results from Taiwan and their implications for advanced travelers' pretrip information systems. Transportation Research Record 1607, 126±133. Khattak, A., Polydoropoulou, A., Ben-Akiva, M., 1995. Commuter normal and shift decisions in unexpected congestion: pretrip response to ATIS. Presented at the 74th Annual Meeting of Transportation Research Board, Washington, DC. Kikuchi, S., Aneja, S., Chakroborty, P.A., Hofmann, J., Machida, M., Perincherry, V., 1994. Advanced traveler aid systems for public transportation ± the intelligent transit mobility system (ITMS). Final report prepared for Federal Transit Administration, US DOT. Maddala, G.S., 1983. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press, Cambridge, MA. Mahmassani, H.S., 1997. Dynamics of commuter behaviour: Recent research and continuing challenges. In: Stopher, P., Martin Lee-Gosselin, (Eds.), Understanding Travel Behaviour in an Era of Change. Pergamon Press, Oxford, pp. 279±313. Mahmassani, H.S., Chang, G.L., 1987. On boundedly-rational user equilibrium in transportation systems. Transportation Science 21 (2), 89±99. Mahmassani, H.S., Liu, Y.S., 1997. Models of user pre-trip and en-route switching decisions in response to real-time information. In: Proceedings of the Eighth IFAC Symposium on Transportation Systems'97. Chania, Greece. Polak, J.W., Jones, P.M., 1992. The acquisition of pre-trip information: a stated preference approach. Presented at the 71st Annual Meeting of the Transportation Research Board, Washington, DC. Stephanedes, Y.J., Zografos, K.G., 1994. Modeling the impact of pre-trip freeway delay advisories on commuter departure time and route choices. Presented at the 73rd Annual Meeting of the Transportation Research Board, Washington, DC. Vaughn, K.M., Abdel-Aty, M.A., Kitamura, R., Jovanis, P.P., Yang, H., Kroll, Neal E.A., Post, R.B., Oppy, B., 1993. Experimental analysis and modeling of sequential route choice under ATIS in a simplistic trac network. Presented at the 72nd Annual Meeting of the Transportation Research Board, Washington, DC.