Bibliography and Technical Appendices to Intercity Passenger Rail in the Context of Dynamic Travel Markets (2016)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Technical Appendix: The ICLV/Hybrid Model Development 71 TECHNICAL APPENDIX: ICLV AND HYBRID MODEL DEVELOPMENT This technical appendix provides a full description of the NCRRP ICLV/Hybrid Model summarized in Chapter 5 of NCRRP Report 4. This text was significant shortened for use in Chapter 5 and this version should be used by those wanting a more complete description of the model. Introduction The gap between discrete choice models and behavioral theory has encouraged different developments that attempt to enrich behavioral realism by explicitly modeling one or more components of the respondents' decision-making process (e.g., accounting for attitudes and perceptions). The most general framework proposed is the integrated choice and latent variable (ICLV) methodology (Ben-Akiva et al., 1999a; Ashok et al., 2002; Ben-Akiva et al., 2002; Bolduc et al., 2005), with some examples of recent applications given in Abou-Zeid et al. (2010), Glerum et al. (2014) and Hess et al. (2013). This hybrid modeling approach integrates latent variable and latent class models with discrete choice methods to model the influence of latent variables and classes on the choice process. Latent variable models capture the formation and measurement of latent psychological factors, such as attitudes and perceptions, which explain unobserved individual heterogeneity. In other words, hybrid choice models allow the joining of models that can analyse both “hard” concepts like travel times, costs, comfort, frequency, etc. with “softer” concepts like how attitudes and values influence choice making. Most of the work to date has been academic with small samples and little effort on understanding important policy implications. In this study for NCRRP, we demonstrate how attitudes and values (beyond simply times and costs) can influence demand and mode choice for two major US intercity corridors: the Northeast Corridor (NEC) and the Cascade Corridor. The NEC in particular is the biggest intercity corridor in the US and is in desperate need for infrastructure investment, which will costs many billions of dollars (NY Times). In this study, we obtained over 6,000 respondents—a very large dataset for such an effort—to use hybrid choice models to better understand the demand for these two major US intercity rail corridors. As far as we know from the literature, this is the largest scale study of its kind using hybrid choice techniques. This is important due to the immense needs of the NEC, in particular, and the necessary investment that needs to be made. Billions will need to be spent, so understanding demand for intercity rail and what influences is critical to spend wisely to maximize the value of the investments being considered (Northeast Corridor Commission). For this NCRRP study, respondents live in the larger metropolitan area of Boston, New York, Philadelphia, or Washington, D.C. (for NEC participants) or Portland, Seattle, or Vancouver (for Cascade participants) and made at least one intercity trip to other cities within their respective corridor. The total sample size is roughly 5,500 respondents from the NEC recruited through an online sample and a previous study of auto users in the NEC. And 500 respondents obtained from an online sample for the Cascade sample. Not only is this sample size much larger than in most typical studies using ICLV studies, but we also work extensively on disentangling pure random heterogeneity from that which can be linked to underlying latent attitudes. This takes into account the criticisms in Daly et al. (2012) and Vij & Walker (2015), and should at least in part avoid issues where the overall degree of heterogeneity is understated and/or the share of heterogeneity that can be linked to latent attitudes is overstated. The remainder of this technical appendix is organized as follows. We first look at the survey work and model specification, before turning to model results, application and finally present some conclusions.

Technical Appendix: The ICLV/Hybrid Model Development 72 Survey Work and Data Processing The survey work comprised an online stated preference questionnaire that was designed to reduce respondent burden and increase respondent participation (Dillman). An example stated preference scenario is shown below. Note that party costs were calculated versus individual costs. Costs and times were developed based on respondent’s previous answers as well as network data on the two corridors. The scenarios tested concepts of different future expected times and costs on both the NEC and Cascade. FIGURE 1 Stated Preference Experiment from the Survey. The field of experimental design has seen substantial developments over recent years, moving away from the use of orthogonal designs, and turning to efficient designs which rely on prior information about the likely sensitivities of respondents to the individual attributes (see e.g., Rose and Bliemer, 2014). Making use of this prior information leads to more meaningful trade-offs that increase the information content in the data. In practice, this leads to substantially lower standard errors. The designs produced for this study allowed for uncertainty in our priors by using Bayesian D-efficient designs. We worked with wide regions, using normally distributed priors, with standard deviations that are 50% of the mean values. The priors were based on an extensive review of values obtained in past studies. Different designs were produced across purposes and for different journey lengths (i.e., different reference values), with a total of 108 designs produced for this study. In addition to the stated preference experiments, a number of attitudinal batteries were included in the questionnaire to understand the attitudes and values of respondents. These attitudinal statements were based on the Theory of Planned Behaviour (TPB) (Aizen, 1991) to understand the responses that were used as the indicator variables in the hybrid choice model described below. The TPB aims to understand behavioral beliefs (i.e., one’s attitude toward intercity rail), normative beliefs (i.e., how friends and family and those one respects feel about intercity rail), and perceived behavioral control (i.e., the ability for the respondent to take intercity rail). Responses were collected online. Nearly all responses were used, though about 600 overall were eliminated for a variety of reasons (inability to generate a valid trip time from google maps, speed- through respondents, straight-line answers to all attitude questions, and any radically large/small rail and bus and air access times and costs). After data cleaning, a final sample of 6,564 respondents was retained for modeling (this is slightly more than the 6,000 responses above due to the ability to model some respondents across different trip purposes, as they could choose more than one). Data coding and model building was undertaken by the Research Team using Ox, a software package (Doornik, 2001).

Technical Appendix: The ICLV/Hybrid Model Development 73 Model Specification Separate models were estimated for four different segments: • work, composed of business and attending a conference, with a total of 1,043 respondents; • vacation, with a total of 2,062 individuals; • visiting friends and relatives (VFR), with a total of 2,724 individuals; and • other purposes, with a total of 735 individuals. A common specification was used as the starting point for all segments, and this was the refined by excluding attributes that did not show a significant and meaningful influence in a given segment. We will now describe the individual components of the overall model structure, looking in turn at the role of explanatory variables, latent attitudes, modal constants and attitudinal indicators. Key Explanatory Variables We focus first on the components of utility related to explanatory variables, which are travel time (access time, in-vehicle time, and egress time), and travel cost. For air, bus and rail, travel cost was defined as the per person cost, while, for car, we recognized that the driver often pays a larger share, and thus multiplied the total cost by 1 1+𝑙𝑙𝑙𝑙𝑙𝑙(1+𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑠𝑠𝑖𝑖𝑧𝑧𝑧𝑧). For car, access time and egress time were set to zero. To capture random heterogeneity in sensitivities across respondents, we defined the individual coefficients to follow a log-uniform distribution, i.e., allowing for different time and cost sensitivities across respondents. This distribution has a similar shape to a lognormal distribution (being the exponential of a uniform rather than a normal distribution), but with a less extreme tail, and initial tests showed it to obtain not only more meaningful results, but also slightly better fit. Separate coefficients were used for travel time on different modes and also for access and egress time, allowing us to capture differences in the perceived onerousness of different time components. Using the example of car in- vehicle time, we would have that the sensitivity for respondent n is given by:𝛽𝛽𝑐𝑐𝑝𝑝𝑝𝑝−𝐼𝐼𝐼𝐼𝐼𝐼,𝑛𝑛 = −𝑒𝑒𝑝𝑝𝑙𝑙𝑙𝑙𝑙𝑙�−𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐−𝐼𝐼𝐼𝐼𝐼𝐼�+𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙�−𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐−𝐼𝐼𝐼𝐼𝐼𝐼�𝜍𝜍𝑐𝑐𝑐𝑐𝑐𝑐−𝐼𝐼𝐼𝐼𝐼𝐼,𝑛𝑛 (1) where 𝜍𝜍𝑐𝑐𝑝𝑝𝑝𝑝−𝐼𝐼𝐼𝐼𝐼𝐼,𝑛𝑛 is a standard Uniform variate (between 0 and 1), distributed across respondents, where 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐−𝐼𝐼𝐼𝐼𝐼𝐼) and 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽𝑐𝑐𝑐𝑐𝑐𝑐−𝐼𝐼𝐼𝐼𝐼𝐼) relate to the lower bound and spread of the uniform distribution for the logarithm of the negative of the car in-vehicle time coefficient. For cost, we used a similar approach, but additionally captured interactions with income. A complication arises as a share of respondents does not report income. Rather than making an arbitrary assumption that these respondents had an average income, we used a separate mean effect for the random cost coefficient for these respondents, but kept the level of the underlying heterogeneity for the uniform distribution (i.e., the log of the negative of the coefficient) the same. In this way, we have: 𝛽𝛽𝑐𝑐𝑙𝑙𝑠𝑠𝑝𝑝,𝑛𝑛 = −𝑥𝑥𝑝𝑝𝑧𝑧𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝𝑧𝑧𝑝𝑝 ∙ 𝑒𝑒𝑝𝑝𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽𝑐𝑐𝑙𝑙𝑐𝑐𝑐𝑐),𝑐𝑐𝑟𝑟𝑟𝑟𝑙𝑙𝑐𝑐𝑐𝑐𝑟𝑟𝑐𝑐+𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽𝑐𝑐𝑙𝑙𝑐𝑐𝑐𝑐)∙𝜍𝜍𝑐𝑐𝑙𝑙𝑐𝑐𝑐𝑐,𝑛𝑛 �𝑖𝑖𝑖𝑖𝑐𝑐𝑛𝑛𝚤𝚤𝑖𝑖𝑐𝑐���� �𝜆𝜆𝑖𝑖𝑛𝑛𝑐𝑐 −𝑥𝑥𝑛𝑛𝑙𝑙𝑛𝑛−𝑝𝑝𝑧𝑧𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝𝑧𝑧𝑝𝑝 ∙ 𝑒𝑒𝑝𝑝𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽𝑐𝑐𝑙𝑙𝑐𝑐𝑐𝑐),𝑛𝑛𝑙𝑙𝑛𝑛−𝑐𝑐𝑟𝑟𝑟𝑟𝑙𝑙𝑐𝑐𝑐𝑐𝑟𝑟𝑐𝑐+𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽𝑐𝑐𝑙𝑙𝑐𝑐𝑐𝑐)∙𝜍𝜍𝑐𝑐𝑙𝑙𝑐𝑐𝑐𝑐,𝑛𝑛 (2) where 𝑥𝑥𝑝𝑝𝑧𝑧𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝𝑧𝑧𝑝𝑝 and 𝑥𝑥𝑛𝑛𝑙𝑙𝑛𝑛−𝑝𝑝𝑧𝑧𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝𝑧𝑧𝑝𝑝 are dummy variables to identify income reporters and income non-reporters, and where 𝜍𝜍𝑐𝑐𝑙𝑙𝑠𝑠𝑝𝑝,𝑛𝑛 is again a Uniform variable, distributed between 0 and 1. The additional parameter 𝜆𝜆𝑖𝑖𝑛𝑛𝑐𝑐 is an estimated income elasticity on the cost sensitivity.

Technical Appendix: The ICLV/Hybrid Model Development 74 Latent Attitudes The latent attitude specification used in these models follows on from earlier factor analysis work carried out on the same data. In particular, we define four latent variables 𝛼𝛼𝑙𝑙, with l=1,…,L, where L=4. These are hereafter referred to as: • attitude toward cars; • attitude toward information technology; • attitude toward urbanism/sociability; and • attitude toward privacy. Each of these latent attitudes is defined to have a deterministic and a random component, with latent attitude l for person n being: 𝛼𝛼𝑙𝑙,𝑛𝑛 = 𝛾𝛾𝑙𝑙𝑧𝑧𝑛𝑛 + 𝜉𝜉𝑙𝑙,𝑛𝑛 (3) where the estimates of 𝛾𝛾𝑙𝑙 capture the impact of a range of sociodemographic characteristics of person n (𝑧𝑧𝑛𝑛) on the latent attitude, and where 𝜉𝜉𝑙𝑙 is a standard Normal variate (mean of 0, standard deviation of 1), distributed across respondents, capturing the random element of the latent attitude. The sociodemographic terms tested for effects on the latent attitudes were: • gender (female dummy); • age (using 5 categories of which 35-45 served as base); • education: dummy for respondents without a graduate degree; and • employment: dummy for respondents who are not employed. Modal Constants The mode specific constants for respondent n were specified to follow a Normal distribution across respondents, allowing for differences across individual travelers in their baseline preferences for different modes. We then have: 𝛿𝛿𝑗𝑗,𝑛𝑛 = 𝜇𝜇𝛿𝛿𝑗𝑗 + 𝛾𝛾𝑗𝑗𝑧𝑧𝑛𝑛 + ωj𝑤𝑤𝑛𝑛 + 𝜎𝜎𝛿𝛿𝑗𝑗𝜉𝜉𝑗𝑗,𝑛𝑛 + ∑ 𝜏𝜏𝑗𝑗,𝑙𝑙𝛼𝛼𝑙𝑙,𝑛𝑛𝐿𝐿𝑙𝑙=1 , (4) We will initially focus on the three first components above, before turning our attention to the ∑ 𝜏𝜏𝑗𝑗,𝑙𝑙𝛼𝛼𝑙𝑙,𝑛𝑛𝐿𝐿𝑙𝑙=1 component. In the above specification, we have that 𝜇𝜇𝛿𝛿𝑗𝑗 is an estimated mean, 𝜎𝜎𝛿𝛿𝑗𝑗 is an estimated standard deviation, 𝜉𝜉𝑗𝑗,𝑛𝑛 is a standard Normal variate (mean of 0, standard deviation of 1) distributed across respondents, and 𝛾𝛾𝑗𝑗 and ωj are vectors of estimated parameters that measure the impact of respondent (𝑧𝑧𝑛𝑛) and trip (𝑤𝑤𝑛𝑛) characteristics captured in 𝑧𝑧𝑛𝑛, which are specified in the paragraphs below. For identification purposes, the mean and standard deviation were set to zero for bus, on the basis of tests showing that the level of random heterogeneity was lowest for bus. Identification was also ensured for the effects of sociodemographic and trip characteristics by setting, for a given characteristic 𝑧𝑧𝑛𝑛,𝑘𝑘𝛾𝛾𝑗𝑗,𝑘𝑘 to zero for at least one j. The same applies to 𝑤𝑤𝑛𝑛 and ωj,k. The characteristics included in the vector 𝑧𝑧𝑛𝑛 for interactions with constants included: • gender (female dummy): tested for the non-car modes; • age (using 5 categories of which 35-45 served as base): interacted with the non-car modes; • education: dummy for respondents without a graduate degree, interacted with the constant for non-car modes (with degree as base);

Technical Appendix: The ICLV/Hybrid Model Development 75 • employment: dummy for respondents who are not employed, interacted with the constant for non-car modes (employed as base); • households with fewer cars than adults: dummy interacted with the car constant (one or fewer cars per adult); and • households with more cars than licenses: dummy interacted with the car constant (one or fewer cars per license); while, for 𝑤𝑤𝑛𝑛, they were: • frequency: daily service frequency, interacted with the constant for non-car modes. Note that this was included here as opposed to being listed as an explanatory variable above as it was not included as a variable in the survey, i.e., it was not explicitly shown to respondents. The aim behind including this is to test whether respondents in corridors with higher frequency of service for a given mode are more likely to choose that mode also in the hypothetical scenarios; • West Coast dummy: interacted with the constant for non-car modes (East Coast as base); • party size: terms for one other person and two plus other people, interacted with the constant for non-car modes (single person as base); • trip length: terms of overnight, two nights and three plus nights, interacted with the constant for non-car modes (day trip as base); and • distance effects for air: dummy terms for trips under 200 miles and trips over 400 miles, interacted with the air constant (200-400 miles as base); The combined utility specification now includes: • the impacts of the explanatory variables, with randomly distributed time and cost coefficients, where the latter is also interacted with income; • the mode specific constants, which include a deterministic component as well as a random part; and • an impact on the modal constants by the latent attitudes, which again include a deterministic and random component. Two important points need to be made here. Firstly, the sociodemographic terms included in the modal constants explained above relate to person as well as trip characteristics, while those sociodemographic terms mentioned earlier for the latent attitudes related only to person characteristics. This reflects the assumption that attitudes are stable for each person across different trips. Secondly, all respondent characteristics included in the deterministic component of the latent attitude have also been included in the modal constant as well, thus avoiding a situation where a sociodemographic effect is erroneously captured as relating to attitudes when it may just relate to underlying modal preferences, or vice versa. As an example, it may well be the case that younger respondents travel less by car for reasons unrelated to their attitude toward cars. If age was included as a covariate only on the latent attitude toward cars but not separately on the modal constants, this inherent modal preference may erroneously be captured as an attitudinal differences. In very much the same way, the modal constants now include a random component that relates to the latent attitudes (through the inclusion of ∑ 𝜏𝜏𝑗𝑗,𝑙𝑙𝛼𝛼𝑙𝑙,𝑛𝑛𝐿𝐿𝑙𝑙=1 in Equation [4]) while a separate random component (𝜎𝜎𝛿𝛿𝑗𝑗𝜉𝜉𝑗𝑗,𝑛𝑛) relates to random variations in preferences for modes which cannot be linked to latent attitudes, for example due to uncaptured journey specific effects.

Technical Appendix: The ICLV/Hybrid Model Development 76 This brings us to an important point. The specification of an alternative specific constant (except for bus) now includes two separate random terms, both following a Normal distribution, and both with deterministic interactions on the mean, some of which relate to the same underlying sociodemographic variables. In the current form, this would be an overspecification, with two parameters capturing the same effect. What allows us to separately identify the two components is that one of them, namely the latent variable component, is also used in a separate measurement model, which we will turn our attention to next. Measurement Model We have four latent attitudes in our model, and these are used in the measurement model component of our overall framework to explain the answers that respondents give to a number of attitudinal questions and one question about their habits. In particular, we follow the segmentation developed in the earlier factor analysis work, with the groupings summarized in Table 1. With the exception of the smart technology ownership question, all questions use a 7-level Likert scale. We now use the four latent attitudes to explain the answers to the attitudinal questions. With 𝐼𝐼𝑠𝑠 used to refer to a given attitudinal question, and letting 𝛼𝛼𝑙𝑙 be the associated latent attitude, we use an ordered logit model to explain the likelihood of the actual observed value of 𝐼𝐼𝑠𝑠 for respondent n as: 𝐿𝐿𝐼𝐼𝑠𝑠,𝑛𝑛 = ∑ 𝑥𝑥𝐼𝐼𝑐𝑐,𝑛𝑛,𝑝𝑝 � 𝑧𝑧𝑐𝑐𝐼𝐼𝑐𝑐,𝑟𝑟−𝜁𝜁𝑙𝑙,𝑐𝑐𝛼𝛼𝑙𝑙,𝑛𝑛1+𝑧𝑧𝑐𝑐𝐼𝐼𝑐𝑐,𝑟𝑟−𝜁𝜁𝑙𝑙,𝑐𝑐𝛼𝛼𝑙𝑙,𝑛𝑛 − 𝑧𝑧𝑐𝑐𝐼𝐼𝑐𝑐,𝑟𝑟−1−𝜁𝜁𝑙𝑙,𝑐𝑐𝛼𝛼𝑙𝑙,𝑛𝑛1+𝑧𝑧𝑐𝑐𝐼𝐼𝑐𝑐,𝑟𝑟−1−𝜁𝜁𝑙𝑙,𝑐𝑐𝛼𝛼𝑙𝑙,𝑛𝑛�7𝑝𝑝=1 (5) where 𝑥𝑥𝐼𝐼𝑐𝑐,𝑛𝑛,𝑝𝑝=1 if and only if respondent n chooses answer p for question s. The 𝑡𝑡𝐼𝐼𝑐𝑐,𝑝𝑝 parameters are thresholds that are to be estimated, with the normalisation that 𝑡𝑡𝐼𝐼𝑐𝑐,0 = −∞ and 𝑡𝑡𝐼𝐼𝑐𝑐,7 = +∞. The estimated parameter 𝜁𝜁𝑙𝑙,𝑠𝑠 measures the impact of the latent variable 𝛼𝛼𝑙𝑙 on 𝐼𝐼𝑠𝑠. A significant estimate for 𝜁𝜁𝑙𝑙,𝑠𝑠 thus shows us that the latent attitude 𝛼𝛼𝑙𝑙 has a statistically significant impact on the answers provided to the attitudinal question 𝐼𝐼𝑠𝑠. The above specification is used directly with the latent car attitude, the latent urbanism attitude and the latent privacy attitude on the three indicators associated with each one (cf. Table 1). For the latent information technology attitude, this specification is used for the two associated attitudinal questions. For the question relating to ownership of smart technology, the binary nature of the answer to that question means that a binary response model is used instead, specified as: 𝐿𝐿𝐼𝐼6,𝑛𝑛 = 𝑥𝑥𝐼𝐼6,𝑛𝑛,0 11+𝑧𝑧𝑐𝑐𝐼𝐼6+𝜁𝜁2,6𝛼𝛼2,𝑛𝑛 + 𝑥𝑥𝐼𝐼6,𝑛𝑛,1 𝑧𝑧𝑐𝑐𝐼𝐼6+𝜁𝜁2,6𝛼𝛼2,𝑛𝑛1+𝑧𝑧𝑐𝑐𝐼𝐼6+𝜁𝜁2,6𝛼𝛼2,𝑛𝑛 (6) where 𝑥𝑥𝐼𝐼6,𝑛𝑛,0 is 1 if respondent n does not own smart technology (and 0 if he/she does), with the opposite applying for 𝑥𝑥𝐼𝐼6,𝑛𝑛,1. This indicator is explained through the second latent variable, and 𝑡𝑡𝐼𝐼6 is an estimated constant that explains the average rate of respondents owning smart technology in our data, while 𝜁𝜁2,6 captures the impact of the latent attitude on ownership of smart technology. Joint Specification The four latent variables are a function of the respondent characteristics 𝑧𝑧, while the utilities of the four alternatives are a function of respondent characteristics z, trip characteristics w and mode characteristics x. The four latent attitudes are used to explain the values of twelve indicators and also contribute to the utility of the modal alternatives in the choice model (with a normalization). These utilities are then used to explain the choices observed in the data. With 𝑖𝑖𝑛𝑛,𝑝𝑝 being the alternative chosen by respondent n in task t (out of T=8), we have that the likelihood of the observed choices and answers to attitudinal questions for respondent n is given by:

Technical Appendix: The ICLV/Hybrid Model Development 77 𝐿𝐿𝑛𝑛 = ∫ ∫ ∫ ∏ 𝑧𝑧𝐼𝐼𝑖𝑖𝑛𝑛,𝑐𝑐 ∑ 𝑧𝑧 𝐼𝐼𝑗𝑗,𝑐𝑐4 𝑗𝑗=1 𝐼𝐼 𝑝𝑝=1𝛿𝛿𝛽𝛽𝛼𝛼 ∏ 𝐿𝐿𝐼𝐼𝑠𝑠,𝑛𝑛12𝑠𝑠=1 𝑓𝑓(𝛼𝛼)𝑓𝑓(𝛽𝛽)𝑓𝑓(𝛿𝛿)𝑑𝑑𝛿𝛿𝑑𝑑𝛽𝛽𝑑𝑑𝛼𝛼 (7) where we use a Logit kernel for the choice model component, and where 𝐿𝐿𝐼𝐼𝑠𝑠,𝑛𝑛 is defined as above. Both the component relating to the choices (i.e. the Logit kernel) and the component relating to the attitudinal questions are a function of the vector of latent variables 𝛼𝛼, while the choice model component is also a function of the random components used in the marginal utility coefficients (𝛽𝛽) and the random components used in the alternative specific constants (𝛿𝛿). This is why the entire likelihood function is integrated over the distribution of 𝛼𝛼, 𝛽𝛽 and 𝛿𝛿. For estimation, we work with the log-likelihood function (the logarithm of Equation 7) and approximate this using numerical simulation, i.e. maximizing the simulated log-likelihood. In this process, we need to take draws (where we rely on 250 MLHS draws per person, see Hess et al., 2006) for 7 normally distributed random terms (the random components for the car, rail and air constants, and the random components for the four latent attitudes), as well as 7 uniformly distributed random terms (the random components for the log-uniformly distributed access time, egress time, travel cost, and four mode specific in-vehicle time coefficients). All models were coded in Ox (Doornik, 2001), and the standard errors reported in the results are obtained with the sandwich method (Huber, 1967). The above likelihood is a function of a large number of parameters to be estimated, namely: • the lower bounds (a) and ranges (b) for the underlying Uniform distributions used for the log-uniformly distributed time and cost coefficients • the means (𝜇𝜇) and standard deviations (𝜎𝜎) for the mode specific constants • the impact of income (𝜆𝜆𝑖𝑖𝑛𝑛𝑐𝑐) on the cost sensitivity • the impact (𝛾𝛾) of the sociodemographic characteristics on: o the mode constants; and o the latent variables • the impact (𝜔𝜔) of the trip characteristics on the mode constants • the threshold parameters (t) for the eleven ordered logit measurement model and the constant for the binary logit measurement model • the impacts of the latent variables on the indicators (𝜁𝜁) Model Results The modeling effort undertaken for this work was substantial, with a total of 160 different parameters used across the different models. The results are in turn very detailed and are presented across a number of different tables at the end of this Appendix. We will now look at the different parts of the results in turn. Model Fit Statistics and Headline VTT Measures The overall model fit statistics and headline value of travel time (VTT) are presented in Table 2, where we present the VTT measures for a mean income of $125K per year (this is a high mean, but is not surprising due to the fact these are intercity travelers in two major US corridors making discretionary or business trips), and where we report the mean and standard deviation of the distribution resulting from the ratio between the negative log-uniform distributions for the time and cost coefficients. The overall model fits are not directly comparable across purposes, not only given the differences in sample size, but also due to the use of different numbers of indicators across segments in the measurement models (details on this are given later on). After estimation, it is possible to factor out the component of the overall log-likelihood relating to the stated choices alone, and the calculation of the ρ2 measures shows very similar performance across segments, where the high values show the relative ease

Technical Appendix: The ICLV/Hybrid Model Development 78 of explaining mode choices for intercity travel, especially after accounting for random heterogeneity and the role of attitudes. (These measures are unadjusted for the number of parameters as it is not immediately clear how many degrees of freedom should be used, but with the overall data size, any adjustment would have a very minor impact only.) Turning to the VTT measures, we can see that, with the exception of access time (where VFR is very similar to work), the measures are higher for work trips than for all other purposes. Even when remembering that these are calculated for a given income of $125K, this is still not surprising given the different time pressures faced on work trips. Egress time is valued substantially lower than access time for all purposes except work trips, where the opposite applies, potentially as a result of these trips being presented as outbound and respondents being more sensitive to the part of their journey relating to getting to their work location after exiting the main-mode station. Major differences exist across modes in the way travel time is valued, and the orderings differ across purposes. We see that, while for work trips, car IVT is valued the least highest, this is not the case for the three remaining purposes, where the least onerous type of IVT applies to air for vacation, and rail for VFR and other purposes. The highest VTT generally applies to bus, which is clearly a comfort factor, except for other purposes, where the VTT for air is marginally higher than that for bus. Overall, rail IVT is valued the least highest. Finally, the standard deviations show that there exists extensive variation across individual travellers in how they value travel time. The actual values of time are calculated from the results in Table 2 which show that, with a few exceptions (access time for work, egress time, car travel time for work and air travel time for work), the estimates for the variance parameters are statistically significant, showing substantial heterogeneity, especially for the travel cost sensitivity. We also see that, across all four purposes, the sensitivity to travel cost is higher for income non-reporters than for a respondent at the mean income of $125K. The impact of income on cost sensitivity is strongest for work travel, and lowest for vacation and VFR travel. Mode Constants We next move to the constants for the four modes, with results shown in Table 3 where this excludes the impacts of the latent attitudes, which are looked at later on. We start by looking at the mean values of the modal constant, i.e., studying the underlying preference for different modes, all else being equal (i.e., same time, cost, etc.). Remembering that these estimates relate to a respondent in the base sociodemographic group (aged between 35 and 44, with a degree and in employment, traveling alone on an East Coast day trip between 200 and 400 miles), we see that: • male respondents on work trips prefer rail ahead of air, car and then bus (the base), where, for female respondents, the difference between car and bus becomes negligible; • male respondents on vacation trips prefer rail, ahead of bus, air and car, where, for female respondents, air is ranked second; • both male and female respondents on VFR trips prefer rail, ahead of air, car and bus; and • both male and female respondents with other purposes prefer rail, ahead of car, bus and air. Numerous shifts in the modal constants are also observed, as follows: • Age has impacts for bus and air, where: o on vacation trips, the likelihood of traveling by bus is higher for respondents under 35; and o the likelihood of traveling by air reduces for VFR purposes in the two highest age groups, but increases in the highest age group for other purposes.

Technical Appendix: The ICLV/Hybrid Model Development 79 • Having more vehicles than licenses in a household increases the probability of traveling by car for work trips. • Compared to respondents with a graduate degree, those without are: o more likely to use bus on VFR and other trips; and o more likely to use air on VFR trips than those with a degree • Compared to respondents in firm employment, those not are: o more likely to travel by bus for work reasons; o less likely to travel by air for other reasons. • Compared to respondents on day trips, we see that: o those with an overnight stay are less likely to use bus or rail for VFR trips; o those with one or more nights away are less likely to use bus for other trips; and o those with three or more nights away are more likely to use air for vacation trips and less likely to use rail for other trips. • Compared to respondents traveling alone, we see that: o those traveling with one other person are less likely to use bus, air or rail for vacation trips, less likely to use rail or air for VFR trips, or air for work trips; and o those traveling with two or more people are more likely to use bus for work trips, less likely to use air or rail for vacation and VFR trips, and less likely to use air for other trips. • Increases in service frequency increases the likelihood of choosing bus for vacation and VFR trips, and air for VFR and other trips. • Compared to the East Coast, travellers on the West Coast are less likely to travel by bus for vacation, air for other purposes, or rail for work and vacation. • Across all purposes, respondents on trips below 200 miles are less likely to use air, than those traveling between 200 and 400 miles, where, above 400 miles, they are even more likely to travel by air. Attitude Toward Cars The results in Table 3 relate to the latent attitude toward cars. Looking first at the signs of the 𝜁𝜁 parameters, we see that those respondents with a more positive latent attitude are more likely to agree with the statements “Rather than owning a car, I would prefer to borrow, share, or rent a car just for when I need it” and “I feel I am less dependent on cars than my parents are/were”, and to disagree with the statement “I love the freedom and independence I get from owning one or more cars”. This thus identifies this latent attitude as an anti-car attitude, or at the very least as a reduced car lover attitude. Looking at the 𝛾𝛾 parameters, we can see that these anti-car respondents are less likely to be female for non-work trips (perhaps due to personal security issues), are more likely to be young (as expected given the changes in car attitudes across generations), are more likely to be less educated (other than for vacation trips where there is no effect) and are less likely to be employed (for VFR trips only), where this is likely to be an income effect too, which the main income effect on cost fails to capture completely. Looking finally at the impacts of this latent attitude on mode choice behavior, the 𝜏𝜏 parameters show us that respondents with a less positive car attitude (i.e., a more positive value for this latent attitude) are less likely to choose car (not surprisingly), but there is also a reduced probability of choosing air for work and VFR trips, possibly due to environmental considerations, though again possibly also due to some confounding with income effects. We finally also see a reduced probability of choosing rail for VFR trips (with bus being the base), reinforcing the earlier point that for VFR, there are possibly confounding effects with income for this latent attitude.

Technical Appendix: The ICLV/Hybrid Model Development 80 Attitude Toward Information Technology The results in Table 3 relate to the latent attitude toward information technology, where this was only included for VFR and other purposes after no impact on mode choice behavior was found for work and vacation. This may be seen as surprising for work especially, but could be the result of a relatively homogeneous group of work travelers, who all have a heightened use of information technology, making it hard to find an impact on mode choice. Looking first at the signs of the 𝜁𝜁 parameters, we see that those respondents with a more positive latent attitude are more likely to agree with the statements “It would be important to me to receive e-mail or text message updates about my bus or train trip” and “Being able to freely perform tasks, including using a laptop, tablet, or smartphone is important to me”. This thus identifies this latent attitude as a pro- information technology attitude. Looking at the 𝛾𝛾 parameters, we can see that, for VFR trips, these respondents are more likely to be female, highly educated, or employed and are more likely to be younger (for both VRT and other purposes). Looking finally at the impacts of this latent attitude on the mode choice behavior, the 𝜏𝜏 parameters show us that respondents with a more positive attitude toward information technology are less likely to choose car for VRT and other purposes, while, for other trips, they are also more likely to choose air. While the former effect is as expected, the latter is somewhat surprising as the use of information technology is less easy during air travel than for bus or rail, although that is starting to change with more abundant in-plane Wi-Fi, the ability to keep devices on during take-off and landing, etc. Attitude Toward Urbanism The results in Table 3 relate to the latent attitude toward urbanism, which was found to have an effect only for the other purposes segment. Looking first at the signs of the 𝜁𝜁 parameters, we see that those respondents with a more positive latent attitude are more likely to agree with the statements “I enjoy being out and about and observing people”, “I like to live in a neighborhood where I can walk to a commercial or village center” and “If everyone works together, we could improve the environment and future for the earth”, identifying them as more sociable respondents. Looking at the 𝛾𝛾 parameters, we can see that these respondents are more likely to be female and to have a graduate degree. Looking finally at the impacts of this latent attitude on the mode choice behaviour, the 𝜏𝜏 parameters show us that respondents with a more positive social latent attitude are more likely to choose air and rail than those with a less positive attitude, compared to car and bus. Attitude Toward Privacy The results in Table 3 relate to the latent attitude toward privacy, where this has an effect on mode choice behavior in all four trip-purpose segments. Looking first at the signs of the 𝜁𝜁 parameters, we see that those respondents with a more positive latent attitude are more likely to agree with the statement “I don't mind traveling with people I do not know” and less likely to agree with the statements “The idea of being on a train or a bus with people I do not know is uncomfortable” and “The thought of sharing a car with others for such a trip seems unpleasant to me”. This thus shows that respondents with a more positive value for this latent attitude are less concerned about privacy. Looking at the 𝛾𝛾 parameters, we can see that these respondents are more likely to be female for other purposes, are more likely to be older and less likely to be less educated (for work, vacation and VFR) or to be unemployed (for all purposes other than work). Looking finally at the impacts of this latent attitude on the mode choice behavior, the 𝜏𝜏 parameters show us that respondents who are less concerned about privacy are less likely to choose car or air (for all purposes other than work), while, for work trips, they are more likely to choose rail. The negative coefficient of the latent attitude on the probability of choosing rail for other purposes needs to be

Technical Appendix: The ICLV/Hybrid Model Development 81 put into the context that the impact is even more negative on car and air, showing simply that these respondents are more likely to choose bus than others, which is a reasonable result. Strength of Impact of Latent Attitudes A key aspect of our modeling approach was to include pure random heterogeneity not linked to the latent attitudes in addition to that attributed to the latent attitudes. This means that the total random variation in the mode constants for car, air and rail is a combination of the random heterogeneity in the constants and the random heterogeneity introduced by the latent attitude. It is then of interest to see what share of this random heterogeneity can be linked to the latent attitudes. This is the approach used in Table 4 , where we compute the total random variance in a modal constant (given by 𝜎𝜎𝛿𝛿𝑗𝑗 2 + ∑ 𝜏𝜏𝑗𝑗,𝑙𝑙2𝐿𝐿𝑙𝑙=1 ) and then report the share of that variance that can be attributed to the different subparts. Looking first at car, we can see that the share of random heterogeneity that can be attributed to the latent attitudes is only one-fifth for work trips and one quarter for vacation. However, for VFR and other, it is more than half, with the biggest share, in line with expectations, due to the attitude toward cars. For rail, the share of random heterogeneity linked to the latent attitudes is small except for other purposes, where the vast majority of the random heterogeneity can be attributed to the latent variables. For air, the picture is more varied, showing for the first time a case where, for work, the latent attitudes contribute the largest part to the random variation in the mode constants. For vacation, there is no impact by any of the latent variables, while, for VFR and other, the share is around one-third and one-fifth, respectively. Finally, Table 5 looks at the role of key sociodemographic variables in influencing mode choice, comparing the direct impact (i.e., through inclusion in the definition of mode constants) with the indirect impact through the latent variables. The latter are calculated in interaction with the 𝜏𝜏 parameters and summed across latent variables, while, for the former, we renormalized the values to use bus as the base for all effects, in common with the latent variable impacts. An interesting picture emerges when studying these results. Firstly, we can see that overall, more of the sociodemographic characteristics are able to manifest an impact on mode choice through the latent variables than through direct inclusion in the definition of the mode choice constants. This in itself is not surprising as the latent attitude effects benefit from calibration on more observations, including not just choice data but also the indicator variables. Additionally, however, and with no exception, where a sociodemographic variable has both a direct and an “indirect” impact on the mode constants, the former is always larger, sometimes substantially so. No immediate reason arises for this, but overall, our extensive exercise has been much more successful than previous studies in capturing an effect of socio-demographics on behavior through the latent variables. This is somewhat contrary to the statement in Ben-Akiva et al. (1999b) that it can be difficult to find good causal variables for the latent variables. A possible reason is that much of the previous work on latent variables has failed to follow the guidance in Vij & Walker (2015) to attempt to disentangle the role of heterogeneity caused by latent variables from that unrelated to latent variables, which we do. One important aspect of the project that made it unique from most academic efforts to date is that once the model was estimated, we then applied it to understand the impacts of various demographic and policy shifts. This is important to allow the model to actually become useful for decision-making and policy work. To apply the model, we used sample enumeration, meaning we took the 6,000 respondents in our sample and applied the model to each of them. Once we implemented the model and checked that it accurately reported base mode shares from the sample (it does), then we used the application to play with a number of what-if scenarios and the resulting changes in mode shares.

Technical Appendix: The ICLV/Hybrid Model Development 82 There is debate in the academic literature about endogeneity and causality in hybrid choice models. For example, there is concern about assuming that attitudes toward urbanism increase by 10%, as it is hard to tell whether an urban attitude is developed which causes the choice in mode or if by choosing a particular mode it affects your attitude toward urbanism due to “cognitive dissonance,” meaning the way we rationalize our decisions. Therefore, the table below simply shows potential demographic shifts by saying, “What if all the males in the sample were female, etc.” and the resulting changes in share for the rail mode based on these changes. We are not presenting here direct shifts in attitudes, which can also be played with, as the demographic shifts are more tangible and less prone to endogeneity concerns. Note that in Table 6, the biggest changes affecting rail share is when the sample is assumed to be all young people under 35. You can see that the anti-car attitude of young people has a major effect on the rail share. Also interesting is the privacy variable. Young people have MORE concern about privacy than older people; thus when everyone is made young, some of the rail increase is mitigated by young people’s desire for more privacy (thought the car attitude is still much stronger). The reverse is true for those over 65. Summary and Conclusions The Technical Appendix for ICLV/Hybrid Model Development demonstrates that the results obtained in this study have the ability to help formulate real policy implications using advanced (and formerly only academic) modeling techniques in a real-world setting. The results have been applied in a way to make them easy to interpret and use for policy makers. This indicates that studies that can obtain a significant sample and which can then estimate and apply complex models in reasonable ways to the policy implications clear to decision makers is a worthwhile and possible outcome. As shown in the paper, to measure and estimate both hard and soft attributes means that a relatively complex model is necessary to describe these complex behaviours. Yet, as demonstrated in the model application section, this complexity can then be simplified to generate good clear policy implications that are useful and tangible. This example shows how this can be accomplished for hybrid choice models, but the study is also a model of how this could be done for other applications where the state of the art is put into the state of the practice.

Technical Appendix: ICLV/Hybrid Choice Model Development 83 TABLE 1 Attitudinal Indicators car attitude “Rather than owning a car, I would prefer to borrow, share, or rent a car just for when I need it” “I love the freedom and independence I get from owning one or more cars” “I feel I am less dependent on cars than my parents are/were” technology attitude “It would be important to me to receive e-mail or text message updates about my bus or train trip” “Being able to freely perform tasks, including using a laptop, tablet, or smartphone is important to me” Respondent owns smart technology (at least one smartphone, tablet, GPS device or laptop) urbanism attitude “I enjoy being out and about and observing people” “I like to live in a neighborhood where I can walk to a commercial or village center” “If everyone works together, we could improve the environment and future for the earth” privacy attitude “The idea of being on a train or a bus with people I do not know is uncomfortable” “I don't mind traveling with people I do not know” “The thought of sharing a car with others for such a trip seems unpleasant to me”

Technical Appendix: ICLV/Hybrid Choice Model Development 84 TABLE 2 Model Fit Statistics, VTT Measures at Income of $125k per Year, Impact of Explanatory Variables and Mode Constants WORK VACATION VFR OTHER Respondents 1,043 2,062 2,724 735 Log-likelihood (total) -15,827.00 -30,867.10 -48,659.70 -20,354.90 Log-likelihood (choice) -5,065.95 -9,803.58 -12,041.90 -2,879.41 ρ2 for choice model only 0.56 0.57 0.60 0.65 mean std. dev. mean std. dev. mean std. dev. mean std. dev. value of access time ($/hr) 50.10 39.37 38.71 50.73 49.19 102.06 41.60 84.31 value of egress time ($/hr) 58.37 98.27 25.86 28.70 14.75 47.36 18.02 45.89 value of car IVT ($/hr) 44.15 34.61 23.48 28.75 27.39 32.15 27.93 32.19 value of bus IVT ($/hr) 61.33 61.81 48.28 54.84 40.24 47.94 34.02 37.03 value of air IVT ($/hr) 49.35 130.69 20.72 58.81 29.01 34.30 36.65 38.72 value of rail IVT ($/hr) 46.08 43.81 22.96 21.96 23.96 23.58 26.31 29.20 est t-rat est t-rat est t-rat est t-rat access time 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -3.9150 -10.13 -2.8467 -22.11 -2.8057 -19.56 -7.9529 -10.32 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -0.1875 -0.20 -3.0618 -7.71 -2.4337 -4.74 6.0773 6.79 egress time 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -6.9454 -2.84 -5.7072 -6.89 -6.6600 -3.08 -2.3157 -9.06 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) 4.6302 1.95 2.1882 1.69 3.6599 1.48 -9.0141 -1.60 IVT (car) 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -4.0950 -10.85 -3.4560 -55.37 -5.3063 -19.14 -3.1642 -38.99 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -0.0784 -0.12 -2.6874 -8.63 1.5739 3.36 -2.2307 -6.44 IVT (bus) 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -4.8138 -35.11 -5.1620 -40.62 -5.0798 -40.00 -5.0285 -24.46 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) 1.7660 4.16 2.3066 14.20 2.1105 14.66 1.9725 6.95 IVT (air) 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -11.7700 -1.20 -13.5680 -6.67 -3.6075 -9.74 -3.0383 -14.21 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) 10.0540 0.97 11.3470 5.08 -2.2287 -2.52 -1.8133 -2.85 IVT (rail) 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -3.4296 -26.15 -3.8837 -42.42 -3.6779 -28.87 -3.2838 -13.47 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) -1.5006 -10.27 -1.4875 -8.22 -1.4840 -6.27 -2.0560 -4.35

Technical Appendix: ICLV/Hybrid Choice Model Development 85 cost 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) (income reporters) -4.9485 -19.87 -4.7051 -48.61 -4.3928 -51.55 -4.4786 -24.89 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) (income non-reporters) -5.6919 -5.98 -4.8481 -23.44 -5.1859 -23.68 -4.7184 -9.44 𝑏𝑏𝑙𝑙𝑙𝑙𝑙𝑙(−𝛽𝛽) 2.8859 11.02 2.9076 20.95 2.4727 18.45 3.0380 10.48 income elasticity (𝜆𝜆𝑖𝑖𝑛𝑛𝑐𝑐) -0.3200 -3.25 -0.1027 -2.35 -0.1251 -2.63 -0.1810 -3.80 car constant 𝜇𝜇𝛿𝛿𝑗𝑗 mean 0.8204 1.00 -0.8155 -1.39 1.7003 3.67 1.7623 2.99 𝜎𝜎𝛿𝛿𝑗𝑗 standard deviation -2.8398 -10.48 -2.7435 -19.92 -2.1138 -9.29 -2.4398 -9.55 𝛾𝛾𝑗𝑗 more vehicles than licenses in household 1.2058 2.10 bus constant 𝜇𝜇𝛿𝛿𝑗𝑗 mean 0 - 0 - 0 - 0 - 𝜎𝜎𝛿𝛿𝑗𝑗 standard deviation 0 - 0 - 0 - 0 - 𝛾𝛾𝑗𝑗 female 0.7791 1.91 0.3534 1.78 1.4077 2.96 aged under 35 0.8485 2.10 no graduate degree 1.6069 8.22 1.0314 2.33 not employed 0.9090 1.20 𝜔𝜔𝑗𝑗 overnight trip -0.7617 -2.22 one or more nights away -1.2603 -3.85 one or more other people in party -1.8521 -3.66 two or more other people in party 1.0473 3.33 frequency of service 0.0096 2.80 0.0091 3.43 West coast -1.6929 -4.70 air constant 𝜇𝜇𝛿𝛿𝑗𝑗 mean 2.1196 2.03 -0.7797 -0.92 2.2816 3.25 -0.3916 -0.37 𝜎𝜎𝛿𝛿𝑗𝑗 standard deviation 1.5479 1.45 2.1333 9.68 2.3069 9.87 1.4371 5.42 𝛾𝛾𝑗𝑗 female 1.3593 3.29 aged between 55 and 64 -0.5811 -1.11 aged 65 or over -0.8950 -2.28 2.9667 4.85 no graduate degree 1.0246 3.26 not employed -1.2695 -2.77 𝜔𝜔𝑗𝑗 three or more nights away 0.9820 2.27 one other person in party -0.6674 -1.47 -2.2473 -5.03 -0.9228 -3.27 two or more other people in party -2.8939 -5.06 -1.8685 -5.56 -1.1443 -2.49

Technical Appendix: ICLV/Hybrid Choice Model Development 86 distance under 200 miles -1.3584 -3.38 -1.5424 -2.65 -1.6538 -4.78 -1.5062 -3.17 distance over 400 miles 2.2162 2.29 2.1668 4.46 1.0978 2.51 0.5217 0.63 frequency of service 0.0325 1.41 0.1325 4.07 West coast -2.8008 -3.70 rail constant 𝜇𝜇𝛿𝛿𝑗𝑗 mean 2.4121 4.09 0.7658 1.71 2.6482 7.44 1.8148 2.95 𝜎𝜎𝛿𝛿𝑗𝑗 standard deviation 1.6040 8.78 -0.4448 -1.94 0.9862 5.55 1.6237 7.28 𝛾𝛾𝑗𝑗 female 0.1405 0.88 𝜔𝜔𝑗𝑗 overnight trip -0.5962 -1.67 three or more nights away -1.6014 -3.74 one other person in party -1.6532 -4.14 -0.5459 -2.79 two or more other people in party -2.2215 -5.56 -1.1882 -6.10 West coast -0.5172 -1.06 -0.7450 -2.09

Technical Appendix: ICLV/Hybrid Choice Model Development 87 TABLE 3 Formation and role of attitudes ATTITUDE TOWARDS CARS WORK VACATION VFR OTHER est t-rat est t-rat est t-rat est t-rat 𝛾𝛾𝑙𝑙 female -0.2193 -3.44 -0.1639 -2.68 -0.2075 -2.32 aged under 35 0.5038 1.95 0.2325 1.63 0.9432 5.73 aged between 45 and 54 -0.3996 -2.15 -0.4035 -4.44 -0.3929 -5.24 aged between 55 and 64 -0.5256 -2.95 -0.5740 -5.11 -0.7531 -9.27 aged 65 and over -0.5715 -2.78 -0.7918 -7.03 -0.8867 -8.34 -0.2905 -2.02 not a graduate -0.2466 -2.25 -0.1382 -2.11 -0.3530 -3.25 not employed 0.1972 2.69 𝜏𝜏𝑗𝑗,𝑙𝑙 impact on utility of car -1.4274 -3.82 -0.9658 -6.25 -2.1502 -9.76 -2.0074 -7.58 impact on utility of air -0.4972 -1.04 -1.0998 -5.76 impact on utility of rail -0.7620 -5.99 “Rather than owning a car, I would prefer to borrow, share, or rent a car just for when I need it” 𝜁𝜁𝑙𝑙,𝑠𝑠 1.4209 9.12 1.2817 14.91 1.2889 18.06 1.0385 7.92 𝑡𝑡𝐼𝐼𝑐𝑐,1 -2.8212 -10.56 -2.7423 -18.40 -2.9712 -21.67 -2.1196 -13.10 𝑡𝑡𝐼𝐼𝑐𝑐,2 -1.3212 -5.41 -1.2173 -9.63 -1.4694 -12.83 -0.5597 -4.32 𝑡𝑡𝐼𝐼𝑐𝑐,3 -0.5792 -2.43 -0.4568 -3.75 -0.6748 -6.29 0.1011 0.82 𝑡𝑡𝐼𝐼𝑐𝑐,4 0.3791 1.58 0.5171 4.26 0.2937 2.89 1.1651 8.78 𝑡𝑡𝐼𝐼𝑐𝑐,5 0.9369 3.84 1.2863 10.26 0.9754 9.54 1.6324 11.50 𝑡𝑡𝐼𝐼𝑐𝑐,6 2.2262 8.45 2.3445 16.61 2.1557 19.65 2.6352 14.60 “I love the freedom and independence I get from owning one or more cars” 𝜁𝜁𝑙𝑙,𝑠𝑠 -1.3647 -9.39 -1.1748 -14.04 -1.2836 -15.55 -1.7967 -9.37 𝑡𝑡𝐼𝐼𝑐𝑐,1 -3.7261 -13.07 -3.7698 -20.90 -3.5752 -23.40 -4.5916 -11.88 𝑡𝑡𝐼𝐼𝑐𝑐,2 -3.1936 -12.17 -3.0738 -20.21 -2.6962 -21.75 -3.9447 -11.60 𝑡𝑡𝐼𝐼𝑐𝑐,3 -2.5118 -10.22 -2.5962 -18.68 -2.2404 -19.84 -3.3174 -11.33 𝑡𝑡𝐼𝐼𝑐𝑐,4 -1.5595 -6.89 -1.5760 -13.04 -1.2376 -12.38 -2.0700 -9.30 𝑡𝑡𝐼𝐼𝑐𝑐,5 -0.2125 -0.96 -0.3931 -3.51 -0.1820 -1.91 -0.8658 -4.65 𝑡𝑡𝐼𝐼𝑐𝑐,6 1.5275 6.32 1.4001 11.39 1.5926 14.90 1.0509 5.72 “I feel I am less dependent on cars than 𝜁𝜁𝑙𝑙,𝑠𝑠 1.7313 9.32 1.8284 14.11 1.6630 17.02 1.7576 9.45 𝑡𝑡𝐼𝐼𝑐𝑐,1 -2.0500 -6.42 -1.8646 -9.44 -2.1162 -15.12 -1.0587 -5.42

Technical Appendix: ICLV/Hybrid Choice Model Development 88 My parents are/were” 𝑡𝑡𝐼𝐼𝑐𝑐,2 -0.3465 -1.19 -0.2243 -1.31 -0.4727 -3.85 0.4023 2.21 𝑡𝑡𝐼𝐼𝑐𝑐,3 0.5098 1.78 0.6788 4.02 0.4302 3.51 1.2695 6.84 𝑡𝑡𝐼𝐼𝑐𝑐,4 1.2436 4.34 1.4735 8.68 1.2988 10.15 2.0399 9.72 𝑡𝑡𝐼𝐼𝑐𝑐,5 2.1221 7.20 2.4754 13.77 2.2659 16.15 2.8938 11.60 𝑡𝑡𝐼𝐼𝑐𝑐,6 3.1273 9.95 3.8838 17.54 3.4159 20.15 4.0424 12.39 ATTITUDE TOWARDS INFORMATION TECHNOLOGY WORK VACATION VFR OTHER est t-rat est t-rat 𝛾𝛾𝑙𝑙 female 0.1741 2.63 aged between 45 and 54 -0.2133 -2.65 -0.1977 -1.42 aged between 55 and 64 -0.5013 -5.18 -0.4943 -3.73 aged 65 and over -0.8184 -7.41 -0.8722 -5.09 not a graduate -0.0956 -1.32 not employed -0.1308 -1.72 𝜏𝜏𝑗𝑗,𝑙𝑙 impact on utility of car -0.5772 -2.12 -1.2915 -6.74 impact on utility of air 2.1968 9.15 “It would be important to me to receive e-mail or text message updates about my bus or train trip” 𝜁𝜁𝑙𝑙,𝑠𝑠 1.3723 11.70 1.0909 7.85 𝑡𝑡𝐼𝐼𝑐𝑐,1 -4.9150 -23.08 -4.3277 -14.93 𝑡𝑡𝐼𝐼𝑐𝑐,2 -3.7676 -21.39 -3.3221 -13.66 𝑡𝑡𝐼𝐼𝑐𝑐,3 -3.2105 -19.94 -2.8478 -13.17 𝑡𝑡𝐼𝐼𝑐𝑐,4 -1.8515 -14.02 -1.5464 -8.79 𝑡𝑡𝐼𝐼𝑐𝑐,5 -0.3459 -3.09 -0.2304 -1.50 𝑡𝑡𝐼𝐼𝑐𝑐,6 1.6264 13.24 1.5908 9.93 “Being able to freely perform tasks, including using a laptop, tablet, or smartphone is important to me” 𝜁𝜁𝑙𝑙,𝑠𝑠 1.3627 12.48 1.3074 8.91 𝑡𝑡𝐼𝐼𝑐𝑐,1 -5.2905 -23.71 -5.5909 -12.86 𝑡𝑡𝐼𝐼𝑐𝑐,2 -3.9949 -21.85 -4.0694 -13.36 𝑡𝑡𝐼𝐼𝑐𝑐,3 -3.2259 -19.88 -3.0776 -11.87 𝑡𝑡𝐼𝐼𝑐𝑐,4 -1.8991 -14.29 -1.7347 -8.22 𝑡𝑡𝐼𝐼𝑐𝑐,5 -0.5586 -4.88 -0.5008 -2.80 𝑡𝑡𝐼𝐼𝑐𝑐,6 1.3549 11.65 1.2747 7.22 ATTITUDE TOWARD URBANISM WORK VACATION VFR OTHER est t-rat

Technical Appendix: ICLV/Hybrid Choice Model Development 89 𝛾𝛾𝑙𝑙 female 0.3617 3.26 not a graduate -0.2253 -2.06 𝜏𝜏𝑗𝑗,𝑙𝑙 impact on utility of air 1.2629 4.83 impact on utility of rail 0.5292 2.99 “I enjoy being out and about and observing people” 𝜁𝜁𝑙𝑙,𝑠𝑠 1.1813 8.48 𝑡𝑡𝐼𝐼𝑐𝑐,1 -5.0410 -13.48 𝑡𝑡𝐼𝐼𝑐𝑐,2 -4.1311 -15.44 𝑡𝑡𝐼𝐼𝑐𝑐,3 -3.1033 -14.95 𝑡𝑡𝐼𝐼𝑐𝑐,4 -2.0236 -12.96 𝑡𝑡𝐼𝐼𝑐𝑐,5 -0.4778 -3.83 𝑡𝑡𝐼𝐼𝑐𝑐,6 1.5659 11.01 “I like to live in a neighborhood where I can walk to a commercial or village center” 𝜁𝜁𝑙𝑙,𝑠𝑠 0.9229 7.45 𝑡𝑡𝐼𝐼𝑐𝑐,1 -3.8221 -15.60 𝑡𝑡𝐼𝐼𝑐𝑐,2 -2.8778 -15.58 𝑡𝑡𝐼𝐼𝑐𝑐,3 -2.0316 -13.82 𝑡𝑡𝐼𝐼𝑐𝑐,4 -1.2632 -9.88 𝑡𝑡𝐼𝐼𝑐𝑐,5 -0.0810 -0.74 𝑡𝑡𝐼𝐼𝑐𝑐,6 1.3224 11.05 “If everyone works together, we could improve the environment and future for the earth” 𝜁𝜁𝑙𝑙,𝑠𝑠 1.4226 7.59 𝑡𝑡𝐼𝐼𝑐𝑐,1 -4.8139 -12.74 𝑡𝑡𝐼𝐼𝑐𝑐,2 -4.1706 -14.31 𝑡𝑡𝐼𝐼𝑐𝑐,3 -3.7071 -14.05 𝑡𝑡𝐼𝐼𝑐𝑐,4 -2.7650 -12.87 𝑡𝑡𝐼𝐼𝑐𝑐,5 -1.3056 -8.08 𝑡𝑡𝐼𝐼𝑐𝑐,6 0.6032 4.05 ATTITUDE TOWARDS PRIVACY WORK VACATION VFR OTHER est t-rat est t-rat est t-rat est t-rat 𝛾𝛾𝑙𝑙 female 0.2065 1.86 aged between 55 and 64 0.2962 2.62 0.1913 2.20 0.2462 1.49 aged 65 and over 0.5004 3.19 0.4041 4.00 0.3524 4.60 0.5450 3.50 not a graduate -0.5850 -4.36 -0.3099 -4.40 -0.1688 -2.53

Technical Appendix: ICLV/Hybrid Choice Model Development 90 not employed -0.0865 -1.10 -0.1947 -2.91 -0.4732 -3.60 𝜏𝜏𝑗𝑗,𝑙𝑙 impact on utility of car -1.1976 -6.25 -0.7277 -4.73 -1.6770 -6.45 impact on utility of air -1.0411 -4.89 -0.5819 -2.65 -2.5531 -7.65 impact on utility of rail 1.4259 7.33 -0.5487 -2.14 “The idea of being on a train or a bus with people I do not know is uncomfortable” 𝜁𝜁𝑙𝑙,𝑠𝑠 -1.4550 -7.93 -1.7859 -14.49 -1.7989 -15.61 -1.6129 -8.51 𝑡𝑡𝐼𝐼𝑐𝑐,1 -2.2301 -12.06 -2.7850 -18.98 -2.4584 -21.02 -2.7330 -10.88 𝑡𝑡𝐼𝐼𝑐𝑐,2 -0.1512 -1.28 -0.4803 -4.94 -0.1746 -2.24 -0.5418 -2.76 𝑡𝑡𝐼𝐼𝑐𝑐,3 0.6267 5.29 0.5066 5.02 0.8564 10.30 0.4542 2.36 𝑡𝑡𝐼𝐼𝑐𝑐,4 1.7855 11.97 1.7337 14.03 2.0993 19.87 1.6867 8.04 𝑡𝑡𝐼𝐼𝑐𝑐,5 2.9063 14.87 3.0485 19.66 3.4794 24.39 3.1367 12.38 𝑡𝑡𝐼𝐼𝑐𝑐,6 4.2639 15.24 4.5268 21.51 4.6240 25.56 4.1860 13.49 “I don't mind traveling with people I do not know” 𝜁𝜁𝑙𝑙,𝑠𝑠 1.0128 8.13 1.1832 13.65 1.4419 15.93 1.5671 8.32 𝑡𝑡𝐼𝐼𝑐𝑐,1 -3.5739 -18.10 -3.6891 -24.50 -3.9863 -27.70 -3.9006 -12.29 𝑡𝑡𝐼𝐼𝑐𝑐,2 -2.5355 -17.32 -2.3661 -22.08 -2.8443 -26.27 -2.6732 -10.86 𝑡𝑡𝐼𝐼𝑐𝑐,3 -1.5207 -13.28 -1.3536 -15.46 -1.7684 -20.36 -1.5305 -7.53 𝑡𝑡𝐼𝐼𝑐𝑐,4 -0.5239 -5.48 -0.2703 -3.65 -0.6019 -8.55 -0.2730 -1.50 𝑡𝑡𝐼𝐼𝑐𝑐,5 0.4945 5.23 0.8456 11.27 0.6204 8.93 1.0450 5.46 𝑡𝑡𝐼𝐼𝑐𝑐,6 2.4524 16.64 2.9431 25.26 2.8805 26.80 3.2882 12.50 “The thought of sharing a car with others for such a trip seems unpleasant to me” 𝜁𝜁𝑙𝑙,𝑠𝑠 -0.5084 -5.49 -0.6565 -9.51 -0.6797 -10.95 -0.5455 -4.56 𝑡𝑡𝐼𝐼𝑐𝑐,1 -2.6219 -20.85 -2.5018 -28.28 -2.4289 -32.24 -2.3753 -15.92 𝑡𝑡𝐼𝐼𝑐𝑐,2 -1.2451 -15.02 -1.1030 -18.16 -1.0356 -20.53 -0.8579 -8.49 𝑡𝑡𝐼𝐼𝑐𝑐,3 -0.5286 -7.13 -0.3937 -7.03 -0.3023 -6.47 -0.2227 -2.32 𝑡𝑡𝐼𝐼𝑐𝑐,4 0.3628 4.93 0.4967 8.76 0.6163 12.76 0.7708 7.99 𝑡𝑡𝐼𝐼𝑐𝑐,5 1.2602 14.81 1.3513 20.62 1.5306 26.78 1.6225 14.54 𝑡𝑡𝐼𝐼𝑐𝑐,6 2.6287 21.14 2.6230 28.08 2.8671 33.24 3.0780 17.28

Technical Appendix: ICLV/Hybrid Choice Model Development 91 TABLE 4 Different Sources of Random Heterogeneity in Mode Constants (Share of Variance) WORK VACATION VFR OTHER ca r pure random variation 0.80 0.76 0.45 0.41 car attitude 0.20 0.09 0.47 0.28 information technology attitude 0.03 0.12 privacy attitude 0.15 0.05 0.19 ai r pure random variation 0.91 0.81 0.77 0.14 car attitude 0.09 0.18 information technology attitude 0.32 urbanism 0.11 privacy attitude 0.19 0.05 0.43 ra il pure random variation 0.56 1.00 0.63 0.82 car attitude 0.37 urbanism 0.09 privacy attitude 0.44 0.09

Technical Appendix: ICLV/Hybrid Choice Model Development 92 TABLE 5 Comparison of Direct and Indirect Impact of Socio-Demographics (Impacts of Socio-Demographics on Modal Constants) WORK VACATION VFR OTHER direct through LV direct through LV direct through LV direct through LV CA R female -0.78 -0.21 -0.35 -0.25 -1.41 -0.07 aged under 35 0.72 -0.85 0.22 1.89 age between 45 and 54 -0.57 -0.39 -0.97 -0.26 aged between 55 and 64 -0.75 -0.33 -1.91 -0.23 aged 65 and over -0.82 -0.28 -2.12 -0.80 no graduate degree -0.35 -0.37 -1.61 -0.48 -1.03 -0.71 not in employment -0.91 -0.10 0.21 -0.79 AI R female -0.78 1.36 -0.35 -0.18 -1.41 0.98 aged under 35 0.25 -0.85 age between 45 and 54 -0.20 -0.43 -0.43 aged between 55 and 64 -0.26 0.20 -0.58 -0.83 -0.46 aged 65 and over -0.28 0.42 -0.90 -0.77 -0.52 no graduate degree -0.12 -0.32 -0.58 -0.25 -1.03 -0.28 not in employment -0.91 -0.09 0.10 -1.27 -1.21 RA IL female -0.78 0.14 -0.35 -0.12 -1.41 0.30 aged under 35 -0.85 age between 45 and 54 -0.30 aged between 55 and 64 0.42 -0.57 0.14 aged 65 and over 0.71 -0.68 0.30 no graduate degree -0.83 -1.61 -0.11 -1.03 -0.12 not in employment -0.91 0.15 -0.26

Technical Appendix: ICLV/Hybrid Choice Model Development 93 TABLE 6 How Demographics affect the share of Rail Trips in the Model % change in rail trips Anti-car Pro Pro Urbanism Less concerned privacy All at once Technology Shift female to male attitude 2.30% -0.41% -0.30% -0.40% 1.20% Shift male to female attitude -1.80% 0.30% 0.20% 0.40% -1.00% Shift age groups to under 35 attitude 17.95% 2.50% 0.00% -3.40% 16.40% Shift under 35 to 35-44 attitude -1.70% 0.00% 0.00% 0.00% -1.70% Shift age groups to over 65 attitude -11.90% -3.40% 0.00% 10.40% -5.70% Shift no college to college attitude 1.20% 0.10% 0.10% 2.70% 4.20% Shift college to no college attitude -3.60% -0.30% -0.20% -7.50% -11.40% Shift no job to employed attitude -0.60% 0.20% 0.00% 1.30% 0.90% Shift employed to no job attitude 1.20% -0.40% 0.00% -2.50% -1.70%

Technical Appendix: ICLV/Hybrid Choice Model Development 94 REFERENCES Abou-Zeid, M., Ben-Akiva, M., Bierlaire, M., Choudhury, C. and Hess, S. (2010). Attitudes and Value of Time Heterogeneity. In Applied Transport Economics - A Management and Policy Perspective (Van de Voorde, E. and Vanelslander, T. eds.). De Boeck Publishing, pp. 523–545. Ajzen, I. (1991). The theory of planned behavior. Organizational Behavior and Human Decision Processes, 50(2): 179–211. Ashok, K., Dillon, W.R., and Yuan, S. (2002). Extending discrete choice models to incorporate attitudinal and other latent variables. J Mark Res, 39(1):31–46. Ben-Akiva, M., McFadden, D., Gärling, T., Gopinath, D., Walker, J., Bolduc, D., Börsch- Supan, A., Delquié, P., Larichev, O., Morikawa, T., Polydoropoulou, A., and Rao, V. (1999). Extended framework for modeling choice behavior. Mark Lett, 10(3):187–203. Ben-Akiva, M., Walker, J., Bernardino, A.T., Gopinath, D.A., Morikawa, T., Polydoropoulou, A. (1999). Integration of Choice and Latent Variable Models. Massachusetts Institute of Technology, Cambridge, MA Ben-Akiva, M., McFadden, D., Train, K., Walker, J., Bhat, C., Bierlaire, M., Bolduc, D., Börsch-Supan, A., Brownstone, D., Bunch, D.S., Daly, A., De Palma, A., Gopinath, D., Karlstrom, A. and Munizaga, M.A. (2002). Hybrid choice models: progress and challenges. Mark Lett, 13(3):163–75. Bolduc, D., Ben-Akiva, M., Walker, J, and Michaud, A. (2005). Hybrid choice models with logit kernel: applicability to large scale models. In Integrated Land-use and Transportation Models: Behavioural Foundations, (Lee-Gosselin, M. and Doherty, S., eds.) Oxford: Elsevier, pp. 275–302. Chorus, C.G. and Kroesen, M. (2014) On the (im-) possibility of deriving transport policy implications from hybrid choice models, Transport Policy, 36:217–222 Critical Infrastructure Needs on the Northeast Corridor. (2013). Northeast Corridor Commission. Daly, A.J., Hess, S., Patruni, B., Potoglou, D. and Rohr, C. (2012), Using ordered attitudinal indicators in a latent variable choice model: A study of the impact of security on rail travel behaviour, Transportation, 39(2), pp. 267–297. Dillman, D.A., Smyth, J.D., and Christian, L.M. (2014). Internet, Phone, Mail, and Mixed-Mode Surveys: The Tailored Design Method 4th Edition Doornik, J.A. (2001). Ox: An Object-Oriented Matrix Language. Timberlake Consultants Press, London.

Technical Appendix: ICLV/Hybrid Choice Model Development 95 Glerum, A., Atasoy, B. and Bierlaire, M. (2014). Using semi-open questions to integrate perceptions in choice models. The Journal of Choice Modelling, Vol. 10, pp. 11–33. DOI 10.1016/j.jocm.2013.12.001 Hess, S., Train, K.E. and Polak, J.W. (2006), On the use of a Modified Latin Hypercube Sampling (MLHS) approach in the estimation of a Mixed Logit model for vehicle choice, Transportation Research Part B, 40(2), pp. 147–163. Hess, S., Shires, J. and Jopson, A. (2013). Accommodating underlying pro-environmental attitudes in a rail travel context: Application of a latent variable latent class specification, Transportation Research Part D: Transport and Environment, Vol. 25, pp. 42–48. Huber, P.J. (1967). “The Behavior of Maximum Likelihood Estimates under Nonstandard Conditions,” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, pp. 221–33. Mueller, B. (2015). On Day 3 of Delays, New Jersey Transit’s Shortfalls Are Painfully Clear. New York Times. http://mobile.nytimes.com/2015/07/23/nyregion/new-jersey- transit-service-again-disrupted-by-electrical-problems.html?_r=2 Rose, J.M. and Bliemer, M.C.J. (2014) Stated choice experimental design theory: The who, the what and the why. In Handbook of Choice Modelling (Hess, S. and Daly, A., eds.) Edward Elgar, Cheltenham, pp. 152–177. Vij, A. and Walker, J. (2015), Statistical properties of Integrated Choice and Latent Variable models, working paper.