Characteristics of Premium Transit Services that Affect Choice of Mode (2014)

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H-1 Integrated Choice and Latent Variable Models A p p e n d i x H Contents H-2 Model Formulation H-10 Summary of Latent Variables H-11 Chicago Models H-26 Charlotte Models H-38 Summary of Model Results Underlying attitudes and perceptions are potentially a key driver in explaining respondents’ choices in real-world scenarios as well as in hypothetical settings. The survey work captured respondents’ answers to a number of attitudinal questions. However, it should be clear that attitudes are unobserved (or latent), and that an analyst can only capture indicators of these attitudes. The reasoning is thus that any answers to attitudinal questions provided by a respondent are merely a function rather than a direct measure of the true underlying and unobserved attitudes. Directly incorporating such indicators in the utility function would put the research at risk of measurement error as well as endogeneity bias if the responses to attitudinal questions are correlated with other unobserved components. These issues with measurement error and endogeneity bias can be avoided in a sequential modeling approach such as that discussed this far, in which a number of factors are estimated in a first stage, explaining the answers to the attitudinal questions, and where these factors are then used as explanatory variables in the utility functions of the choice model. However, the estimation of the factors is in this case informed only by the data on attitudinal questions, through calibration of a set of measurement equations that explain the answers to these questions, and not by the observed choices for the respondents. It should be clear that choices in the stated preference component are similarly influenced by these underlying attitudes, and not allowing the data on actual choices to contribute to the estimation of the factors can be seen as a disadvantage (reduced information), not helped by the fact that the researchers have only a single observation per respondent and per attitudinal question. In this stage of the work, the research team makes use of a relatively recent addition to the family of mathematical models for explaining decision making processes. In these models, commonly referred to as hybrid choice models or more specifically integrated choice and latent variable (ICLV) models (Ben-Akiva et al. 1999; Ben-Akiva et al. 2002; Bolduc et al. 2005), the researchers explicitly allow for the impact of underlying attitudes on behavior. The attitudes themselves are treated as latent, and are hypothesized to influence both the observed choices and

H-2 Characteristics of premium Transit Services that Affect Choice of Mode for forecasting purposes. In the ICLV model, the estimation produces parameters for the distribution of the latent variables, and these can then be directly used in model application. If the latent variable has sociodemographic interactions, as is the case in our empirical work, then forecasting can make use of adjusted sociodemographic variables that are in line with likely future population composition, thus producing more reliable measures of the latent attitudes. The fact that answers to attitudinal questions were included in model estimation will have contributed to the specification of the latent variables for use in model application and forecasts will only be produced for the choices. It should be acknowledged that this approach is based on the assumption that the deterministic relationship between any sociodemographic variables and the latent attitudes is stable over time, although the random component does allow for some additional flexibility. Model Formulation In an ICLV model, simultaneous estimation of measurement equations (explaining the observed answers to the attitudinal questions) and the choice model (explaining the stated or revealed choices) means that both components contribute to the estimation of the latent variables that now represent the attitudes. In particular, let n be a set of S different latent variables for respondent n. This establishes that the sth latent variable for respondent n is defined as: where s is a vector of estimated parameters and zn is a vector of characteristics of respondent n. The interaction between these parameters and characteristics forms the deterministic component of the latent variable, with the random component being ns, which can be defined to be a standard Normal variate (i.e., with a mean of zero and a standard deviation of 1). Let LCn( ) be the probability of the observed sequence of choices for respondent n, conditional on a vector of parameters that are to be estimated, where LCn( ) would often be given by a product of separate logit probabilities. This can be rewritten as LCn( , n), to recognise that the choices made by the respondent are influenced not just by the vector of parameters , but also the vector of latent attitudes n. Typically, the role of the latent attitudes will be as interactions with a subset of the parameters in , where in our case, it will be the alternative specific constants for the train and bus alternatives. In other words, whereas the utility of alternative j for respondent n would previously have been given by: where xnj is a vector of attributes of alternative j as faced by respondent n, and where allowance is made for interactions with sociodemographic characteristics zn, the equation can be rewritten as: where is a vector of interaction parameters that explain the influence of n on V. answers to any attitudinal questions. In contrast with the earlier work using separately estimated factors, the estimation of the latent attitudes is thus informed by the choice behavior in addition to the answers to the attitudinal questions. Another advantage of ICLV models is their applicability in forecasting. Indeed, a key shortcoming of any sequential approach is that the factors would need to be modeled separately

integrated Choice and Latent Variable Models H-3 one of the S latent variables is used for a given indicator k, where, typically, a given latent variable is used for more than one indicator. Assume that latent variable ns is used to explain the value for indicator k. In the majority of applications, the responses to the attitudinal questions are treated as continuous variables, that is, writing the value for the kth indicator for respondent n as: where k is a constant that captures the mean value of Ik in the sample population, sk is an estimated parameter capturing the impact of ns on Ik, and kn is an error term, with a mean of zero and a standard deviation of k. It can be noted that by subtracting the sample population mean of Ik from each Ink, the need to estimate k is avoided. With this specification, a positive estimate for sk would mean that an increase in the latent attitude ns leads to a higher value for Ink, which, depending on the data could for example mean stronger agreement with the attitudinal statement. The probability of the observed value for indicator k can then be written as a normal density, as follows: where A(Ink=q) is equal to 1 if Ink=1, Q is the number of possible levels for the indicators, e.g. 5, and it is established that = + and = - , such that the probability for an indicator value of 1 is given by and the probability for an indicator value of Q is given by . The thresholds in an ordered logit specification are increasing by definition. They control for the distribution of the different possible outcomes, in this case the different values for the indicators. With the above specification, the probability of a given outcome is determined not just by the thresholds, but also by where on the distribution of the Q-1 thresholds the value falls. As an example, as the value of increases, it will gradually exceed the values of the individual thresholds, and the probability for a higher value of the indicator will increase. It should be noted that there is a risk of identification issues if all Q-1 thresholds are estimated plus the parameter . In the present work, the researchers make use of a simplified structure in which is constrained to a value of 1 for all k. This means that it is assumed that the impact of latent variable is positive for all the indicators where it is used in the measurement equations. For this reason, it is important that all indicators associated with a given latent variable are specified to act in the same direction, a condition that applies in the present study. The model is still able to allow for the strength of the impact of the latent variable to vary across the different indicators through the spacing of the thresholds. However, it is not possible for the analyst to determine what part of the variance of the thresholds is caused by the observed distribution for the indicators and what part is caused by the differential impacts of the latent variable on different indicators. At the same time, the latent variables are also used to model the answers by respondents to the indicators, typically in the form of attitudinal questions. It is generally assumed that only

H-4 Characteristics of premium Transit Services that Affect Choice of Mode Independently of the specific functional form used for LInk, it is thus established that this probability is a function of n, rewritten as Lnk( n), and the probability of the observed values for the entire set of K indicators is given as follows: where possible additional layers of integration need to be added if random heterogeneity not linked to the latent variables is to be introduced in the model. The estimation of an ICLV model thus entails maximizing the joint likelihood of the observed choices and the observed answers to attitudinal questions. Both are a function of the latent variables, the estimation of which is thus informed by both model components when simultaneous estimation is used. By carrying out the integration jointly over the different model components, correlation is created between the responses to the attitudinal questions and the choices for a given respondent (i.e., this process ensures that the same value for the latent attitudes is used for the different model components for a given individual). Specification of Latent Variables For this set of 20 indicators, a total of seven different latent variables were employed for which a generic specification was used across the four subsets of the data (i.e., Chicago and Charlotte, each time split into commuters and non-commuters). In contrast with the earlier factor analysis, the estimation of the measurement equations was carried out separately for the two purpose segments in each city, rather than using a joint model. An exception to this arises in the case of the non-commute segment for Charlotte (discussed in a later section of this appendix). In each segment, each of the latent variables is also used in an interaction with the constants for bus and train. The specification used is as follows: 1: Level of (Un-)Informedness This latent variable is used to explain the value of a single indicator, namely the stated level of informedness, which has five levels, where an ordered logit specification was used. The use of an ordered logit specification with the required increasing thresholds means that increases in the latent variable correspond to increases in the indicator. Here, it is important to note that a higher value for this indicator corresponds to a lower stated level of informedness (i.e., higher uninformedness). Four threshold parameters were used (Threshold 1 for level of uninformedness, Threshold 2 for level of uninformedness, Threshold 3 for level of uninformedness, Threshold 4 for level of uninformedness). A single sociodemographic characteristic was used in the deterministic component of this latent variable, namely whether a respondent had lived in the area for more than 5 years. In the choice model, this latent variable was interacted with the constants for bus and train. Here, a positive value for these interaction parameters would mean that a higher value for the latent variable also leads to a more positive constant for the transit modes, with the opposite applying for negative estimates.

integrated Choice and Latent Variable Models H-5 2: Willingness to Walk This latent variable is used to explain the value of a single indicator, namely the stated willingness to walk. This is a continuous variable, and a continuous specification was thus used, where, after subtracting the sample mean from the indicator for each person, only two parameters are estimated, namely a parameter capturing the impact of the latent variable on the indicator, and a parameter capturing the standard deviation of the indicator. Eight sociodemographic characteristics were used in the deterministic component of this latent variable, namely: - whether a respondent is a full-time student; - whether a respondent is employed full-time; - whether a respondent is retired; - whether a respondent is female; - whether a respondent is aged over 55 years; - the log of household income; - whether a respondent has lived in the area for more than 5 years; and - whether a respondent has reduced mobility. In the choice model, this latent variable was interacted with the constants for bus and train. 3: Pro-Transit Attitude This latent variable is used to explain the value of the following five indicators: - respondent's agreement with: I am not afraid to ride transit; - respondent's agreement with: I'm the kind of person who rides transit; - respondent's agreement with: I currently make an effort to take public transit whenever I can; - respondent's agreement with: If I wanted to, I could use public transit more frequently; and - respondent's agreement with: It's easy to plan a trip using transit. Each of these has five levels, and an ordered logit specification was used, with four thresholds each. Eight sociodemographic characteristic were used in the deterministic component of this latent variable, namely: - whether a respondent is a full-time student; - whether a respondent is retired;

H-6 Characteristics of premium Transit Services that Affect Choice of Mode - the number of vehicles in the respondent’s household; - the log of household income; - whether a respondent has reduced mobility; and - whether a respondent’s household has more drivers than vehicles. In the choice model, this latent variable was interacted with the constants for bus and train. 4: Pro-Car Attitude This latent variable is used to explain the value of the following six indicators: - respondent's agreement with the statement, For me, car is king! Nothing will replace my car as my main mode of transportation; - respondent's agreement with the statement, Getting to and from transit stations/stops is not pedestrian friendly and is very unpleasant; - respondent's agreement with the statement, I have to drive to get to transit anyway, so I may as well just drive my car the whole way; - respondent's agreement with the statement, Transit is often dirty; - respondent's agreement with the statement, My car reflects who I am; and - respondent's agreement with the statement, My days of taking transit are over. Each of these has five levels, and an ordered logit specification was used, with four thresholds each. Six sociodemographic characteristic were used in the deterministic component of this latent variable, namely: - whether a respondent is retired; - whether a respondent is female; - the number of vehicles in the respondent’s household; - the log of household income; - whether a respondent has reduced mobility; and - whether a respondent’s household has more drivers than vehicles. In the choice model, this latent variable was interacted with the constants for bus and train. - whether a respondent is female; - whether a respondent is aged under 35;

integrated Choice and Latent Variable Models H-7 - respondent's agreement with the statement, If it would save time, I would change my form of travel. Each of these has five levels, and an ordered logit specification was used, with four thresholds each. Two sociodemographic characteristic were used in the deterministic component of this latent variables, namely: - whether a respondent is employed full-time; and - the log of household income. In the choice model, this latent variable was interacted with the constants for bus and train. 6: Environment Attitude This latent variable is used to explain the value of the following three indicators: - respondent's agreement with the statement, Protecting the environment is very important to me; - respondent's agreement with the statement, I am willing to carpool or take public transit more frequently to reduce air pollution and carbon emissions from my vehicle; and - respondent's agreement with: I am willing to pay higher tolls if they are used to reduce congestion. Each of these has five levels, and an ordered logit specification was used, with four thresholds each. Two sociodemographic characteristic were used in the deterministic component of this latent variable, namely: - whether a respondent is aged under 35 years; and - the number of vehicles a respondent’s household owns. In the choice model, this latent variable was interacted with the constants for bus and train. 5: Productivity Attitude This latent variable is used to explain the value of the following two indicators: - respondent's agreement with the statement, More than saving time, I prefer to be productive when traveling; and

H-8 Characteristics of premium Transit Services that Affect Choice of Mode Each of these has five levels, and an ordered logit specification was used, with four thresholds each. Three sociodemographic characteristic were used in the deterministic component of this latent variable, namely: - whether a respondent is female; - the number of vehicles a respondent’s household owns; and - whether children are present in the household. In the choice model, this latent variable was interacted with the constants for bus and train. Model Estimation Procedure The utility specifications from earlier parts of the research were reused for the choice model component of the ICLV model, with the following exceptions: Any coefficients associated with factors were removed, as were coefficients associated with stated high level of informedness and coefficients associated with different levels of stated willingness to walk. The grocery stop variable dropped from the Chicago commuter MNL models was retained. The additional fourteen interaction terms between latent variables and constants were added to the models. The actual estimation consisted of simultaneous maximization of the likelihood from the two model components (i.e., the choice model and the measurement equations). The models were coded in Ox. In contrast with the simple MNL models, the ICLV models directly account for the repeated choice nature of the data. The results presented here make use of robust standard errors (i.e., using the sandwich estimator as opposed to the classical covariance matrix), thus accounting for effects of model mis-specification. Given experience from the MNL analysis highlighting low value of time measures in the RP part of the data, the research team again proceeded by first estimating models on the stated preference data only, and then constraining the value of time in the joint RP/SP models to that from the SP only models. 7: Privacy and Comfort Attitude This latent variable is used to explain the value of the following two indicators: - respondent's agreement with the statement, As long as I am comfortable when traveling, I can tolerate delays; and - respondent's agreement with the statement, Privacy is important to me when I travel.

integrated Choice and Latent Variable Models H-9 Model Exploration for Awareness and Consideration An additional model investigation was carried out as part of this analysis, making use of latent variable models, in which were jointly modeled not just the choices and responses to attitudinal questions, as in the above, but also the responses to the awareness and consideration questions. To this extent, the likelihood of the observed value for awareness for bus for respondent n was modeled as: making it a function of the latent uninformedness attitude ( 1) and the latent pro-transit attitude ( 3). A respondent will indicate that he is aware or not of bus, and this response (AWnb being either 1 or 0) will be modeled as a binary logit model, with the utility for not aware being fixed to zero for normalization. In this utility, is a constant that captures the sample level mean of stated awareness for bus. The two parameters capture the impact of the latent variables on the probability of stated awareness. Similarly, the likelihood of the observed value for consideration for bus for respondent n was modeled as: making it a function of the latent willingness to walk attitude ( 2), the latent pro-transit attitude ( 3), and the latent pro-car attitude ( 4), where CONnb is the observed response to the bus consideration question for respondent n, and where the remainder of the notation follows the same conventions as for awareness. Similar functions were defined for the train option, labeled as LAWnt and LCONnt. The combined likelihood is now written as: Here, the additional exponents on LAW and LCON are needed as the awareness component of the model is only included when the mode in question was actually available (AVnb=1 means that bus was available to respondent 1) while the consideration component is In comparison with the MNL models, the numerical cost of estimating the ICLV models is very high, with models taking on average two days to reach convergence, which is a result of the need for simulation to approximate the value of the multi-dimensional integral, and also as a result of the very large number of parameters. With this in mind, it was not possible to use an iterative approach in which insignificant parameters were gradually removed, and consequently, the results presented here retain all parameters, even if not statistically significant. These will be further refined during model calibration and application to reduce variables to only those that are significant and important for policy purposes.

H-10 Characteristics of premium Transit Services that Affect Choice of Mode Very preliminary work was also conducted to explore the potential for modeling choice set generation in the present context. Specifically, the latent level of consideration of any unchosen RP alternative, say bus, could be written as: noting that the latent consideration is itself a function of other latent variables from the overall model (and a constant), and is in fact equal to the denominator of the above latent consideration probability. This modeled probability of consideration is then used inside a probabilistic choice set generation model, thus no longer relying on the inclusion of an unchosen RP alternative in the model being determined by the stated 0-1 consideration variable. No successful estimations were carried out using this specification to date, but this approach remains an important area for future work Summary of Latent Variables For the present analysis, a set of 20 different indicators were used. In addition to the 18 attitudinal questions that were modeled by the factor analysis earlier in this study, the research team also treated the responses to the willingness to walk and the level of informedness questions as indicators of unobserved underlying attitudes. The researchers thus hypothesize that the actual willingness to walk and the actual perceived level of informedness are not observed by the analyst. Thus, while the earlier multinomial models used a mix between a sequential treatment of attitudes through factor analysis and a deterministic treatment of the stated level of informedness and the stated willingness to walk, all components in the ICLV models are represented through latent variables that are estimated jointly on the choice data and the indicator data. There were seven latent variables included in the integrated choice and latent variable models, and each was represented by demographic characteristics that were significant in model estimation, as shown in TABLE H-1. This table also identifies the type of variable that is included and, for the attitudinal statements, how many levels are represented in each. The level of informedness variable also has five levels, where the willingness to walk variable is continuous. only included when the respondent had indicated previously that he/she was aware of the mode in question (AWnb as previously defined). Modeling Choice Set Generation In all models included in the present report, be they MNL or ICLV, modes are included in the RP component of the choice model as a function of stated consideration. This is common practice and as such is entirely defensible. However, the actual consideration of a mode is arguably not observed but is itself latent, with the stated consideration being merely an indicator of actual consideration.

integrated Choice and Latent Variable Models H-11 TABLE H-1. Description of latent variables. Latent Variable Type* Li ve d 5 y ea rs in a re a Fu ll- tim e st ud en t Em pl oy ed fu ll- tim e R et ire d Fe m al e A ge u nd er 3 5 ye ar s A ge o ve r 5 5 ye ar s Lo g of H ou se ho ld In co m e Ve hi cl es in H ou se ho ld M or e D riv er s Th an Ve hi cl es R ed uc ed M ob ili ty H ou se ho ld s w ith K id s Informed about transit 5 levels Willingness to walk Continuous Pro-transit factor 5 statements with 5 levels each Pro-car factor 6 statements with 5 levels each Productivity factor 2 statements with 5 levels each Environment factor 3 statements with 5 levels each Privacy and comfort factor 2 statements with 5 levels each *The attitudinal statements used in each factor are documented in Appendix G. Chicago Models Separate models were estimated for commuters and non-commuters for the Chicago sample. Each time, the estimation involved the maximization of the joint likelihood for the stated choices and the observed answers to attitudinal questions, with both model components making use of the full set of latent variables. Initial Observations First examined are summary statistics for the two models (TABLE H-2). The overall log-likelihood for the models cannot be compared to that for the simple MNL model as it relates to the joint likelihood of the choice model and measurement equations component. However, it is possible to factor out the part of the log-likelihood relating to the choice component of the model only, conditional on the latent variable specification estimated jointly from the two parts. Here it is noted that in both segments, the log-likelihood for the choice model component is noticeably higher than what was obtained from the simple MNL models, with a difference by 671.5 units for commuters and 376.4 units for non-commuters. No formal tests of significance are possible given the different specification for the choice model component in the ICLV model compared to the simple MNL model, but the differences in fit clearly suggest an improvement in prediction capability.

H-12 Characteristics of premium Transit Services that Affect Choice of Mode between the RP and SP scales are substantially larger than was the case in the simple MNL models. Additionally, both segments show higher scale for SP than for RP, where this was only the case for the commuter segment in the simple MNL model. Furthermore, both scale parameters are different from the base of one (1) at high levels of confidence, where this was not the case in the MNL models. In general, higher scale parameters for SP as opposed to RP are in line with expectations in joint RP/SP modeling, so these results are deemed reasonable and in support of the ICLV structure. TABLE H-2. Summary statistics for the ICLV model in Chicago. Commuters Non-Commuters Individuals 808 693 Choice scenarios 7,272 6,237 Overall log-likelihood -30,082.90 -25,859.40 Overall parameters 156 151 Log-likelihood for choice model component -5,128.00 -4,357.81 Parameters for choice model component 48 43 Estimate Robust t-ratio Estimate Robust t-ratio rho 1.62 2.49 1.98 2.49 Base Utility Parameters Next, those parameters that the choice model component of the ICLV model has in common with the simple MNL model are examined—those not interacted with the latent variables (TABLE H-3). The ICLV models specifically followed the same model specification for the base utility parameters as the MNL models to allow for comparative analysis. Looking first at the commuter results, it is apparent that all parameters retain the same sign, with the following exceptions: The constant for train becomes negative, but it is important to remember that this is now only the mean value which is interacted with a latent variable that does not necessarily have a zero mean given the sociodemographic interactions. The impact of the number of vehicles in a household on the utility of bus and train becomes positive, but is not statistically significant—this effect is now captured by the latent variables. Some differences also are noted in the scale parameter estimated for the SP part of the data when compared to the simple MNL model. Indeed, for both segments, the differences

integrated Choice and Latent Variable Models H-13 A number of changes to significance levels also are noted, with fluctuations for most parameters, but where few of these involve a change from significance to non-significance (or vice versa), with some exceptions, as follows: The fixed mean parameters for both alternative specific constants are no longer statistically significant, most likely as these effects are now captured in the variation in these constants in interaction with the latent variables. The coefficient for parking cost for car is now statistically significant, which is a desirable development. The interaction between travel time sensitivity and the provision of amenities is no longer significant at the higher levels. It is not clear how this can easily relate to the addition of the interaction terms with latent variables. The reliability coefficient for train is now only significant at reduced levels. Reductions in significance for many of the sociodemographic interactions also are observed, with several becoming insignificant. This is to be expected, as these interactions are now also captured in the latent variables. For non-commuters, only two parameters change sign, namely: Having more drivers than vehicles in a household now shows a negative impact on the utility of bus and train, but this is no longer statistically significant, with its effect being captured by the latent variables. The interaction between being retired and the constant for train becomes positive, but is not significant in either model. In terms of significance levels, a number of fluctuations are again observed, and the expected reductions for sociodemographic interactions. A number of key observations are that: The constant for train is now statistically significant. The impact of the number of vehicles on the utility for bus becomes insignificant, with its effect now being captured in the latent variables. The interaction between reduced mobility and the utility for bus and train becomes significant. The interaction between weekend travel and the constant for train becomes positive, but this parameter is not significant in either the MNL model or the ICLV model. Being a long-term resident now has a negative impact on the constant for train, where this effect is possibly now also captured by the latent variables.

TABLE H-3. Base utility parameters for ICLV model in Chicago. Commuters Non-Commuters Auto Bus Train Auto Bus Train Explanatory Variables Est. Rob. t-rat. Est. Rob. t-rat. Est. Rob. t-rat. Est. Rob. t-rat. Est. Rob. t-rat. Est. Rob. t-rat. Alternative specific constant 0.1418 0.14 -1.6677 -1.49 2.5366 2.68 2.1539 2.38 Level of Service Access time (min.)† -0.0348 -3.22 -0.0685 -4.68 -0.0423 -3.56 -0.0423 -3.56 Access time (min.) x Access mode (= walk)† 0.0210 2.45 0.0321 3.86 0.0192 2.66 0.0113 1.76 IVTT (min.) -0.0182 -6.44 -0.0182 -6.44 -0.0182 -6.44 -0.0160 -4.93 -0.0160 -4.93 -0.0160 -4.93 Wait time (min.) -0.0402 -5.40 -0.0294 -4.65 -0.0212 -4.20 -0.0212 -4.20 Fare ($)† -0.5158 -3.80 -0.5158 -3.80 -0.5211 -3.35 -0.3721 -3.20 Auto cost($) -0.2314 -3.69 -0.2437 -3.44 Parking cost ($)† -0.1073 -3.98 -0.0270 -0.54 -0.0123 -0.77 -0.1256 -4.37 -0.0429 -1.37 Access mode (walk over drive)† Span of service (all day v. only peak)† 0.4786 5.80 0.4786 5.80 0.3880 4.26 0.4779 4.92 Reliability (% on time)† 0.0986 2.46 0.0829 1.83 0.0420 0.71 0.0678 1.90 No transfer 0.2556 4.82 0.2556 4.82 0.1375 3.38 0.1375 3.38 Premium on-board (prem. over standard)† 0.1220 2.84 0.1220 2.84 0.1746 2.92 IVTT (min.) x amenities† 0.0024 1.73 Premium stop design (prem. over standard)† 0.0955 2.91 0.0955 2.91 0.0806 2.72 0.0806 2.72

TABLE H-3. (Continued). Commuters Non-Commuters Auto Bus Train Auto Bus Train Explanatory Variables Est. Rob. t-rat. Est. Rob, t-rat. Est. Rob. t-rat. Est. Rob. t-rat. Est. Rob. t-rat. Est. Rob t-rat. Individual Demographics Full-time student 0.2250 0.77 0.2250 0.77 Full-time employed 0.7245 1.02 0.7245 1.02 Homemaker -0.1004 -0.92 Retired 0.2246 1.04 Female -0.0615 -0.09 -0.0788 -0.11 Longtime resident (5+ years) -0.2300 -1.83 -0.1770 -1.85 Has mobility problem 0.3300 1.78 0.6880 2.27 0.6880 2.27 Age less than 35 years 0.1298 0.56 Age between 35 and 55 years -0.1640 -0.73 Age more than 55 years -0.1329 -0.51 Household Demographics Number of vehicles in household 0.0109 0.12 0.0109 0.12 -0.0069 -0.14 Family income (ln Income) -0.1820 -3.10 -0.1388 -1.36 -0.1388 -1.36 More drivers than vehicles -0.5589 -0.77 -0.5589 -0.77 Children (kids) present 0.2734 1.28 0.2734 1.28 0.1912 1.83 Trip Characteristics Group travel -0.1851 -1.59 -0.1851 -1.59 Weekend trip 0.0238 0.20 0.0264 0.39 Makes stop for groceries 0.3258 1.54 0.3258 1.54 -0.3335 -2.48 -0.3335 -2.48 Makes stop for other -0.1774 -0.95 -0.1774 -0.95

H-16 Characteristics of premium Transit Services that Affect Choice of Mode Value of Time Measures As a next step, the estimates from the two models are used to compute value of time measures for the two segments and the three different modes of travel (TABLE H-4). Drops in both segments compared to the MNL results are observed, with reductions in the value of time by around 30% for bus and train in the commuter segment, and by 34% for car, with drops by 30% for car and train in the non-commuter segment, and by 20% for bus. These drops can potentially be explained on the basis of the ICLV model being able to better capture underlying modal preferences (by allowing for heterogeneity) that could otherwise have unduly influenced the generic (across modes) travel time coefficient. As an example, if a large enough share of respondents have a strong dislike of bus and train, and if these modes are slower than car, then this could lead to an overestimation of the travel time sensitivity, and hence higher values of time. TABLE H-4. Value of time ($/hour) for ICLV model in Chicago. Commuters Non-Commuters Estimate Robust t-ratio Estimate Robust t-ratio Auto 4.73 3.20 3.95 2.82 Bus 2.12 3.27 1.85 2.77 Train 2.12 3.27 2.59 2.69 Equivalent Valuations The equivalent valuation is shown in minutes of in-vehicle time TABLE H-5 of various other service characteristics (both desirable and undesirable), where separate relative valuations are shown for train services with and without amenities for commuters (given the impact on in- vehicle time sensitivity). For each mode, the appropriate time coefficient is used. It is also of interest to compare the sensitivity to the different cost components, where results show lower sensitivity to parking costs than to auto cost or fare, where it is important to remember that the sensitivity to parking cost was not statistically significant for bus or train (and was not estimated for bus in the non-commuter segment). Latent Variable Components The key aspect of the ICLV models is the role of the latent variables in explaining both the answers to the attitudinal questions as well as their impact on the constants for bus and train in the choice model component. The different latent variables will be examined in turn. The first latent variable (level of lack of transit information) is interacted with a single indicator where the use of an ordered logit specification means that increases in the indicator correspond to increases in the latent variable (TABLE H-6). Positive impacts on the value of this latent variable for longer term residents are observed. This suggests, maybe rather surprisingly, that respondents who have lived in the area for more than 5 years are more likely to indicate a lower level of transit information about public transit options. This applies to both commuters

integrated Choice and Latent Variable Models H-17 TABLE H-5. Equivalent IVTT (in minutes) for various attributes of ICLV model in Chicago. Commute Non-Commute Explanatory Variables Auto Bus Train Basic Train with Amenities Auto Bus Train Alternative specific constant - (7.78) (91.52) - (158.06) (134.22) Level of service Access time (min.) if walking - 1.91 3.76 4.33 - 2.64 2.64 Access time (min.) if not walking 0.75 2.00 2.00 2.30 1.44 1.94 Wait time (min.) - 2.21 1.62 1.86 - 1.32 1.32 Fare ($) * 2.12 1.85 2.59 Auto cost ($) * 4.73 3.95 - - Parking cost ($) * 10.19 40.46 88.78 7.67 - 22.43 Span of service (all day v. only peak) - (26.26) (26.26) (30.24) - (24.17) (29.78) Reliability (% on time) - (5.41) (4.55) (5.24) (2.62) (4.23) - No transfer - (14.03) (14.03) (16.15) - (8.57) (8.57) Premium on-board (prem. over standard)† - (6.69) (6.69) (7.71) - (10.88) - Premium stop design (prem. over standard) - (5.24) (5.24) (6.04) - (5.02) (5.02) Individual Demographics Full-time student - - - - (14.02) Full-time employed - (39.76) (39.76) - - Homemaker - - - - - Retired - - - - - Female - 3.38 4.33 - - Longtime resident (>5 years) - - 12.62 - 11.03 Has mobility problem - (18.11) - - (42.87) Age less than 35 years - (7.12) - - - Age between 35 and 55 years - - 9.00 - - Age more than 55 years - - 7.29 - - Household Demographics Number of vehicles in household - (0.60) (0.60) - 0.43 Family income (in income) - 9.98 - - 8.65 More drivers than vehicles - - - - 34.83 Children present - (15.00) (15.00) - - Trip characteristics Group travel - - - - 11.53 Weekend trip - - (1.31) - - Makes stop for groceries - (17.88) (17.88) - 20.78 Makes stop for other reasons - 9.73 9.73 - - * In the case of fare, auto cost, and parking cost, the values are in units of $/hour of IVTT.

H-18 Characteristics of premium Transit Services that Affect Choice of Mode and non-commuters. However, no impact of this latent variable is observed for non-commuters for either mode, or for train in the commuter segment. The only significant impact is on the utility of bus in the commuter model, where the effect is negative, suggesting that a lower level of transit information (remembering that a higher value for the indicator means being less informed) leads to a rejection of bus as a commute option. TABLE H-6. 1: Level of lack of transit information. Commuters Non-Commuters 1: Level of Lack of Transit Information Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for level of lack of transit information -0.6426 -5.29 -0.7945 -5.20 Threshold 2 for level of lack of transit information 1.7650 13.46 1.6866 10.38 Threshold 3 for level of lack of transit information 2.4887 17.25 2.3336 13.50 Threshold 4 for level of lack of transit information 3.5295 19.37 3.3753 16.62 Impact on latent variable for respondents who have lived in the area for more than 5 years 0.6792 4.41 0.8023 4.28 Impact of latent variable on bus constant -0.4973 -3.49 0.0883 0.53 Impact of latent variable on train constant 0.0243 0.19 0.0049 0.02 The second latent variable explains the value of the stated duration that a respondent is willing to walk (TABLE H-7). This measurement equation used a continuous specification, where a higher value for the latent variable is seen to be associated with an increase in the indicator, where this effect is stronger for non-commuters. In the commute segment, higher values for the latent variable for full-time students and respondents who have been living in the area for longer than 5 years are observed; however, both interactions are only significant at reduced levels of confidence. In the non-commuter segment, the latent variable is higher for full-time students, while it is lower for retired respondents and respondents with reduced mobility. Both segments show a positive impact of the latent variable on the utility for bus and train, indicating that a greater willingness to walk leads to increased utility for public transport, where this effect is similar for the two modes for commuters, while, for non-commuters, it is much stronger for train than for bus.

integrated Choice and Latent Variable Models H-19 TABLE H-7. 2: Willingness to walk. Commuters Non-Commuters 2: Willingness to Walk Estimate Robust t-ratio Estimate Robust t-ratio Impact of latent variable on stated willingness to walk 1.5860 2.56 3.0835 4.93 Standard deviation of stated willingness to walk 10.3590 11.81 11.9250 11.01 Impact on latent variable for full- time students 0.3804 1.72 0.5634 1.88 Impact on latent variable for respondents in full-time employment -0.1061 -0.21 0.0248 0.16 Impact on latent variable for retired respondents - -0.8362 -2.22 Impact on latent variable for female respondents -0.0081 -0.02 -0.1112 -0.91 Impact on latent variables for respondents aged over 55 years 0.0121 0.08 0.1211 0.69 Impact on latent variable of log of household income -0.0186 -0.34 0.0332 1.25 Impact on latent variable for respondents who have lived in the area for more than 5 years 0.1922 1.75 -0.2312 -1.02 Impact on latent variable for respondents with reduced mobility -0.0667 -0.40 -0.6056 -2.67 Impact of latent variable on bus constant 1.3683 6.13 0.2877 1.61 Impact of latent variable on train constant 1.4634 6.04 0.7218 3.76 The third latent variable (pro-transit attitude) is interacted with five indicators in an ordered logit specification, meaning that increases in the indicators (i.e., stronger agreement with the attitudinal statements) correspond to increases in the latent variable (TABLE H-8). Positive impacts on the latent variable for full-time students in both segments are observed, indicating a stronger pro-transit attitude. The opposite is the case for retired respondents in the non-commuter segment, possibly related to walking issues, as well as for female respondents, where this is only significant at usual levels in the non-commuter segment, and where this could possibly be explained on personal safety grounds. Younger respondents are more pro-transit, although this effect is not highly significant. In both segments, respondents with more vehicles have a more negative value for the latent attitude, with the same applying to respondents with reduced mobility, although this is not highly significant in the non-commute segment. Two additional interactions are significant in the commute segment. A higher value for the pro-transit latent attitude is observed for respondents from households with more drivers than vehicles, which is consistent with intuition. More surprisingly, a positive impact on the latent attitude for higher income respondents is seen. This could possibly be explained on the grounds of higher income commuters having their workplaces located in areas where transit is a good option.

H-20 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-8. 3: Pro-transit attitude. Commuters Non-Commuters 3: Pro-Transit Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 1 -2.7976 -4.08 -5.0266 -6.39 Threshold 2 for Attitudinal Statement 1 -1.3331 -2.01 -3.6149 -4.69 Threshold 3 for Attitudinal Statement 1 -0.2912 -0.44 -2.5739 -3.36 Threshold 4 for Attitudinal Statement 1 1.4676 2.22 -0.7417 -0.98 Threshold 1 for Attitudinal Statement 2 -1.4078 -2.11 -3.4610 -4.48 Threshold 2 for Attitudinal Statement 2 -0.1418 -0.21 -2.2320 -2.93 Threshold 3 for Attitudinal Statement 2 1.4713 2.23 -0.7899 -1.03 Threshold 4 for Attitudinal Statement 2 3.0135 4.53 0.6484 0.84 Threshold 1 for Attitudinal Statement 3 -0.9054 -1.37 -3.1546 -4.07 Threshold 2 for Attitudinal Statement 3 0.2734 0.41 -1.9427 -2.54 Threshold 3 for Attitudinal Statement 3 1.5124 2.30 -0.6794 -0.89 Threshold 4 for Attitudinal Statement 3 3.1649 4.76 0.9070 1.18 Threshold 1 for Attitudinal Statement 4 -0.7827 -1.19 -3.2362 -4.20 Threshold 2 for Attitudinal Statement 4 0.4491 0.68 -1.8392 -2.39 Threshold 3 for Attitudinal Statement 4 1.6248 2.47 -0.8738 -1.14 Threshold 4 for Attitudinal Statement 4 3.2941 4.94 0.8358 1.08 Threshold 1 for Attitudinal Statement 8 -1.7725 -2.68 -4.0429 -5.17 Threshold 2 for Attitudinal Statement 8 -0.2294 -0.35 -2.5545 -3.31 Threshold 3 for Attitudinal Statement 8 1.1191 1.70 -1.2826 -1.67 Threshold 4 for Attitudinal Statement 8 3.0295 4.55 0.8211 1.08 Impact on latent variable for full-time students 0.5203 2.47 0.7730 3.80 Impact on latent variable for retired respondents - -0.7732 -4.60 Impact on latent variable for female respondents -0.1644 -1.48 -0.4332 -3.69 Impact on latent variables for respondents under the age of 35 years 0.2084 1.64 0.2403 1.60 Impact on latent variable of the number of vehicles a household owns -0.4224 -7.86 -0.5015 -7.35 Impact on latent variable of log of household income 0.1512 2.51 -0.0248 -0.34 Impact on latent variable for respondents with reduced mobility -0.4644 -1.95 -0.2886 -1.51 Impact on latent variable if respondent’s household has more drivers than vehicles 0.7005 2.78 0.1255 0.36 Impact of latent variable on bus constant 0.6617 4.71 0.4749 3.98 Impact of latent variable on train constant 0.6440 4.40 0.4020 3.47

integrated Choice and Latent Variable Models H-21 The fourth latent variable (pro-car attitude) is interacted with six indicators in an ordered logit specification, meaning that increases in the indicators (i.e., stronger agreement with the attitudinal statements) correspond to increases in the latent variable (TABLE H-9). The research team notes negative impacts for higher income respondents in the commute segment, consistent with the results for the pro-transit attitude, along with a negative effect for respondents from households with more drivers than vehicles, where this also applies in the non- commute segment, though to a lesser effect. Both segments show an intuitively correct positive effect on the latent attitude if the number of cars in a household is higher, along with positive effects for respondents with reduced mobility, and retired non-commuters. The impact of this latent variable on the bus and train constants in the choice model component is negative as expected, where it is slightly stronger for train than for bus for commuters, with the opposite applying for non-commuters. The productivity latent attitude (TABLE H-10) is used to explain the values of two indicators in an ordered logit specification, once again meaning that higher values for the latent variable correspond to stronger agreement with the attitudinal statements. Neither of the two sociodemographic interactions is significant for commuters, though the positive sign for income is arguably consistent with intuition, with higher income respondents desiring better time-use. For non-commuters, a positive impact on the latent variable for full-time employees is seen. In both segments, the latent variable has the expected positive effect on the utility for bus and train, where there is a stronger effect for train than for bus in the case of commuters, reflecting the greater ability to use time productively when traveling by train. The pro-environment latent attitude (TABLE H-11) is used to explain the values of three indicators in an ordered logit specification, once again meaning that higher values for the latent variable correspond to stronger agreement with the attitudinal statements. Positive impacts on the latent attitude for younger respondents are noted, as are negative impacts (albeit not significant) for respondents from households with more vehicles. For commuters, there is a positive impact of the latent variable on the utility for both bus and train, where this is stronger for bus. For non- commuters, the impact is also positive, but not significant at usual levels of confidence. The privacy and comfort latent attitude (TABLE H-12) is used to explain the values of two indicators in an ordered logit specification, with increases in the latent variable corresponding to increases in the indicator. The only significant interaction is a positive effect for female respondents (i.e. a stronger attitude) in the non-commute segments. For commuters, the expected negative impact of this latent variable on the utility for bus—and to a lesser extent train (where privacy and comfort are maybe less important)—is observed. For non-commuters, the effect is surprisingly positive, and this is possibly caused by the same reasons as the positive effect of the low transit comfort level in the earlier MNL models. In terms of the impact on the choice model, a positive effect of the latent variable on the utility for both bus and train is seen in both segments, consistent with intuition, where this effect is quite similar for the two modes.

H-22 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-9. 4:Pro-car attitude. Commuters Non-Commuters 4: Pro-Car Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 5 -2.7496 -4.07 -1.0568 -1.49 Threshold 2 for Attitudinal Statement 5 -1.4490 -2.16 -0.0312 -0.04 Threshold 3 for Attitudinal Statement 5 -0.1436 -0.21 1.0446 1.48 Threshold 4 for Attitudinal Statement 5 1.2601 1.84 2.3447 3.33 Threshold 1 for Attitudinal Statement 6 -3.3346 -4.93 -1.7270 -2.42 Threshold 2 for Attitudinal Statement 6 -1.7956 -2.66 -0.1576 -0.22 Threshold 3 for Attitudinal Statement 6 -0.2533 -0.37 1.2671 1.78 Threshold 4 for Attitudinal Statement 6 1.5004 2.19 2.8200 3.90 Threshold 1 for Attitudinal Statement 7 -2.3557 -3.49 -0.8605 -1.21 Threshold 2 for Attitudinal Statement 7 -1.3533 -2.00 0.2893 0.41 Threshold 3 for Attitudinal Statement 7 -0.2656 -0.39 1.4004 1.98 Threshold 4 for Attitudinal Statement 7 1.2121 1.77 3.0951 4.32 Threshold 1 for Attitudinal Statement 9 -4.3738 -6.26 -3.0784 -4.10 Threshold 2 for Attitudinal Statement 9 -2.6438 -3.91 -1.0733 -1.51 Threshold 3 for Attitudinal Statement 9 -1.0739 -1.60 0.4469 0.63 Threshold 4 for Attitudinal Statement 9 1.0853 1.60 2.7033 3.79 Threshold 1 for Attitudinal Statement 17 -2.8095 -4.12 -0.8638 -1.21 Threshold 2 for Attitudinal Statement 17 -1.6074 -2.38 0.0948 0.13 Threshold 3 for Attitudinal Statement 17 0.1126 0.17 1.7994 2.53 Threshold 4 for Attitudinal Statement 17 1.8755 2.70 3.5402 4.93 Threshold 1 for Attitudinal Statement 18 -2.0140 -2.97 -0.3131 -0.45 Threshold 2 for Attitudinal Statement 18 -0.8247 -1.22 0.7984 1.14 Threshold 3 for Attitudinal Statement 18 0.6791 1.01 1.9415 2.75 Threshold 4 for Attitudinal Statement 18 1.9281 2.81 3.1040 4.39 Impact on latent variable for retired respondents - 0.2967 1.81 Impact on latent variable for female respondents 0.0927 0.83 0.1366 1.47 Impact on latent variable of the number of vehicles a household owns 0.3319 6.80 0.3303 5.62 Impact on latent variable of log of household income -0.1590 -2.54 -0.0191 -0.29 Impact on latent variable for respondents with reduced mobility 0.7653 3.85 0.3649 2.49 Impact on latent variable if respondent’s household has more drivers than vehicles -0.7390 -2.75 -0.6117 -1.77 Impact of latent variable on bus constant -0.7412 -5.20 -0.8602 -4.74 Impact of latent variable on train constant -0.8211 -5.15 -0.7077 -4.62

integrated Choice and Latent Variable Models H-23 TABLE H-10. 5:Productivity attitude. Commuters Non-Commuters 5: Productivity Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 10 -2.1225 -2.47 -2.5204 -2.64 Threshold 2 for Attitudinal Statement 10 -0.6918 -0.82 -0.9899 -1.05 Threshold 3 for Attitudinal Statement 10 1.2376 1.47 0.9942 1.05 Threshold 4 for Attitudinal Statement 10 3.3041 3.83 3.1192 3.23 Threshold 1 for Attitudinal Statement 11 -1.8626 -2.18 -2.2673 -2.38 Threshold 2 for Attitudinal Statement 11 -0.9276 -1.10 -1.1916 -1.26 Threshold 3 for Attitudinal Statement 11 0.5278 0.63 0.4025 0.43 Threshold 4 for Attitudinal Statement 11 2.5097 2.95 2.3419 2.46 Impact on latent variable for respondents in full-time employment -0.0725 -0.55 0.3360 2.43 Impact on latent variable of log of household income 0.0918 1.18 0.0529 0.61 Impact of latent variable on bus constant 0.3548 1.97 0.4378 2.99 Impact of latent variable on train constant 0.5721 2.95 0.4586 3.24 TABLE H-11. 6: Environment attitude. Commuters Non-Commuters 6: Environment Attitude Estimate Robustt-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 13 -3.6948 -16.59 -3.9488 -15.46 Threshold 2 for Attitudinal Statement 13 -2.6164 -15.56 -2.8520 -15.35 Threshold 3 for Attitudinal Statement 13 -0.5779 -4.33 -0.6616 -4.48 Threshold 4 for Attitudinal Statement 13 1.4916 10.57 1.4324 9.08 Threshold 1 for Attitudinal Statement 14 -2.6839 -15.34 -2.5873 -14.13 Threshold 2 for Attitudinal Statement 14 -1.4966 -10.36 -1.3835 -8.84 Threshold 3 for Attitudinal Statement 14 0.2765 2.06 0.0580 0.40 Threshold 4 for Attitudinal Statement 14 1.9672 12.65 1.9443 11.67 Threshold 1 for Attitudinal Statement 15 -1.3468 -9.59 -1.2308 -8.04 Threshold 2 for Attitudinal Statement 15 -0.0749 -0.57 -0.1462 -0.99 Threshold 3 for Attitudinal Statement 15 1.2892 9.65 1.2312 7.93 Threshold 4 for Attitudinal Statement 15 3.2276 16.67 3.3821 14.87 Age < 35 0.2384 1.97 0.2634 1.93 Impact on latent variable of the number of vehicles a household owns -0.0303 -0.63 -0.0648 -1.07 Impact of latent variable on bus constant 0.3837 3.07 0.1252 1.19 Impact of latent variable on train constant 0.2625 2.07 0.1843 1.48

H-24 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-12. 7: Privacy and comfort attitude. Commuters Non-Commuters 7: Privacy and Comfort Attitude Estimate Robustt-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 12 -2.7560 -14.75 -2.7412 -13.93 Threshold 2 for Attitudinal Statement 12 -1.0573 -6.93 -0.9883 -6.25 Threshold 3 for Attitudinal Statement 12 0.2878 1.92 0.2883 1.86 Threshold 4 for Attitudinal Statement 12 2.6292 13.88 2.8887 13.94 Threshold 1 for Attitudinal Statement 16 -3.5766 -15.68 -3.3760 -14.94 Threshold 2 for Attitudinal Statement 16 -1.8383 -11.57 -1.6515 -10.28 Threshold 3 for Attitudinal Statement 16 -0.0155 -0.11 0.0198 0.13 Threshold 4 for Attitudinal Statement 16 1.8808 11.20 1.8754 10.78 Impact on latent variable for female respondents -0.0701 -0.58 0.2173 2.01 Impact on latent variable of the number of vehicles a household owns -0.0246 -0.48 -0.0263 -0.40 Impact on latent variables if children are present in household 0.1556 1.40 0.0968 0.60 Impact of latent variable on bus constant -0.8685 -4.22 0.9080 4.39 Impact of latent variable on train constant -0.5121 -2.73 0.6854 4.04 Awareness and Consideration Another advantage of the ICLV modeling approach is that awareness and consideration modeling can be jointly modeled with the traveler attitudes in mode choice. An exploration of this was undertaken in this project. While this has theoretical advantages because the choices are estimated jointly, the models were much more complex and were not successful using these specifications. It will be necessary to reduce complexity in some parts of the model to achieve a specification that can be estimated to include awareness and consideration within the model specifications (rather than as an input). This can be a focus of future work. This model was only tested on the Chicago commuter segment. Furthermore, given the additional complexity of the structure, a simplified version of the measurement equations was used, with a continuous specification for all indicators, as opposed to the ordered logit approach. The resulting model produced a log-likelihood for the choice model component of the overall structure of -5,124 units, thus slightly better still than the ICLV model discussed earlier. This suggests that when additionally including the awareness and consideration components in the overall structure, a better explanation of the latent attitudes is obtained, which contributes to better fit for the choice model component. Given the exploratory nature of this part of the work, the research team focused solely on the additional component of this model, rather than presenting all estimates (TABLE H-13). Positive constants are noted which represent the fact that on average, when used, more than 50% of respondents responded positively to the awareness question, with the same applying to the consideration question. For the latter, the response was even more positive on average, with the

integrated Choice and Latent Variable Models H-25 majority of respondents who indicated that they were aware of the mode also indicating that they had considered it. TABLE H-13. Additional components of the ICLV model. Estimate Robust t-ratio Constant for bus awareness 0.6351 1.97 Constant for train awareness 2.2338 2.64 Constant for bus consideration 0.9166 4.71 Constant for train consideration 3.1874 6.02 Impact of latent level of lack of transit information on bus awareness -0.1620 -0.75 Impact of latent pro-transit attitude on bus awareness 0.8161 4.74 Impact of latent level of lack of transit information on train awareness -0.6043 -0.52 Impact of latent pro-transit attitude on train awareness 0.6734 2.92 Impact of latent willingness to walk on bus consideration 0.3054 0.59 Impact of latent pro-transit attitude on bus consideration 0.7358 2.20 Impact of latent pro-car attitude on bus consideration -0.1255 -0.42 Impact of latent willingness to walk on train consideration 0.9032 1.13 Impact of latent pro-transit attitude on train consideration 0.5860 1.30 Impact of latent pro-car attitude on train consideration -0.1238 -0.19 Turning to the interaction parameters, it is notable that while the sign of the interaction terms between the lack of transit information latent variable and the probability of stating awareness is negative as expected (i.e., if a respondent is less well informed, he/she is less likely to be aware), the interaction parameters are not statistically significant. On the other hand, a more positive pro-transit attitude leads to increases in the probability of stated awareness. In the consideration model, increased willingness to walk leads to increased probability of stated consideration for both modes, but the effect is not significant. Increases in the latent pro-transit attitude lead to a higher probability of stating that bus was considered, with the same applying for rail, where the effect is however not statistically significant. Finally, the sign of the impact of a pro-car attitude on the consideration for transit modes is negative as expected, but not statistically significant. From the above discussion, it becomes clear that the inclusion of this additional model component produces reasonable model results, but that the effects are of low statistical significance. The main reason for this is the very high level of stated awareness and consideration. As an example, for Chicago commuters, 68.4% of respondents where bus was available stated to have been aware of it. Even more importantly, of those respondents who stated that they were aware of bus, 81.4% of respondents also stated that they had considered it. For train, the figures are even higher, with 87.7% stating awareness when available, and 97% stating consideration when aware. These high positive response rates mean that the majority of the response patterns are explained through the constants included in the awareness and consideration models. These problems were compounded in other segments, which led to

H-26 Characteristics of premium Transit Services that Affect Choice of Mode abandoning this exploratory research—for example, in the Charlotte non-commuter segment, every respondent who had stated to be aware of train had also stated to have considered it. Furthermore, it should be remembered that the awareness component could only be included when the mode was actually available, where this for example applies to only 38% of Chicago commuters for bus, and 41% for train, leading to small sample sizes. Despite these problems, the above model results are promising. For future research using these datasets, it is suggested that researchers model combined awareness and consideration (i.e., a positive response is when a respondent indicates he or she is aware of a mode and has considered it). This would lead to a less strong positive response overall, and would also avoid the issue of consideration being modeled separately, in which case, with it having to be conditional on awareness, the probability in the data is too close to one (1) to allow for separate analysis, given the above, and the sample size is also affected. Charlotte Models As with the Chicago data, separate models were estimated for commuters and non- commuters for the Charlotte sample. Each time, the estimation involved the maximization of the joint likelihood for the stated choices and the observed answers to attitudinal questions, with both model components making use of the full set of latent variables. Initial Observations Summary statistics are again examined for the two models (TABLE H-14). A comparison of the fits for the choice model component in the ICLV model and the earlier MNL models shows that, for the commuter segment, a substantially higher log-likelihood is again obtained by using the latent variable approach instead of the sequential factor analysis approach, with an increase by around 830 units. The estimated difference in scale between the SP and RP part of the data also is substantially larger than was the case in the MNL models, with a scale parameter of 4.49, compared to the earlier estimate of 1.46. TABLE H-14. Summary statistics for the ICLV model in Charlotte. Commuters Non-Commuters Individuals 1,041 465 Choice scenarios 9,369 4,185 Overall log-likelihood -38,542.70 -18,042.30 Overall parameters 153 150 Log-likelihood for DCM component -6,295.66 -3,577.66 Parameters for DCM component 45 42 Estimate Robust t-ratio Estimate Robust t-ratio rho 4.49 3.38 1.68 0.26 Turning our attention to the results for non-commuters, the findings are more disappointing. The log-likelihood for the choice model component is lower by around 200 units. This means that, with this sample, the sequential approach leads to better performance, where the

integrated Choice and Latent Variable Models H-27 other distinction arises in the deterministic treatment of the stated level of transit information and the stated willingness to walk in the earlier models. A closer study of the ICLV results for the non-commuter segment, which is to follow, shows a lack of impact of the latent variables in the choice model part of the overall structure. An initial hypothesis was that this could be caused by a low level of information contained in the measurement equations part of the overall model. To understand this, it should be remembered that, while the data for the choice model component contains 4,185 observations, only a single observation for each indicator is contained in the data used for the measurement equations (i.e., 465 observations per indicator). In the earlier models, the estimation of the factors was based jointly on the data for commuters and non-commuters (i.e., 1,501 observations per indicator). To test whether this is the source for the difference in performance, an additional model was estimated in which the choice component of the overall structure makes use of data from the 465 non-commuters only, while the measurement equations make use of data from all 1,501 respondents in the Charlotte sample. This thus means that while the link, by way of the latent variables, between responses to attitudinal questions and preferences in the choice model is only made for those respondents (i.e., non-commuters) included in both model components, the estimation of the latent variables themselves is also informed by the attitudinal data from the commuter segment. The results for this new model however revealed no improvement in the ability to link preferences to latent variables, and in fact highlighted a small further drop in the fit for the choice model component. To some extent, this drop in fit is not completely unexpected—the weight of the measurement equations part of the model is increased in this new specification and, in joint estimation of the two components, this can have a detrimental impact on the choice model component. This would be especially the case when there is a lack of correspondence between the two types of data. In the remaining three segments of this study, there seems to be strong correspondence between the choice model and the measurement equations part of the model, and their joint estimation helps both components. This is not the case in the Charlotte non-commuter segment. One possible reason is that the actual specification of the models is at fault here, and that a structure that worked well for the remaining three segments is not as suitable for this segment, e.g. potentially calling for a different specification of the latent variables, in terms of which latent variables are used for which indicators. However, in the earlier MNL models, a generic specification was used for the factor analysis in the commute and non-commute segments, as well as for the impact on the constants in the choice models. The actual reason for the disappointing performance of the models in the non-commuter segment thus remains unclear. The most likely explanation relates to the sample size for the choice model component, where this is smaller by 55% compared to the commuter segment, and 33% compared to the next smallest segment overall in the study, namely the non-commuter segment in the Chicago data. The same differences in sample size clearly also applied in the MNL models. However, a key distinction arises in the estimation procedure used for the models. In the MNL models, the smallest unit of contribution to the log-likelihood function is an individual observation (i.e., one choice). This means that the number of data points is equal to the number of choices. In the estimation of the ICLV models, integration over the distribution of the latent variables is required where this is carried out at the level of an individual respondent. This in turn means that the smallest unit of contribution to the log-likelihood function is the joint probability of the sequence of choices for a given respondent and the answers to all attitudinal

H-28 Characteristics of premium Transit Services that Affect Choice of Mode questions. This thus leads to only 465 individual contributions to the log-likelihood function. This would not be an issue in MNL models, but in the models used here, the integration over the random component means that the distribution of that random component is characterized by only 465 individual ‘data points’. Thus, while the percentage reduction in sample size compared to the other segments is clearly the same for the MNL models as for the ICLV models, the absolute number of points in the log-likelihood functions in the ICLV models seems to go beyond a ‘tipping point’ where it becomes difficult to adequately estimate the role of these random components. Base Utility Parameters Next to be examined are those parameters that the choice model component of the ICLV model has in common with the simple MNL model (i.e., those not interacted with the latent variables as shown in TABLE H-15). Given the obvious issues with the model for non- commuters, the discussion in this section focuses on the results from the commuter segment, with the non-commuter results also included in the table for reference. Note that all parameters retain the same sign, with the following exceptions: The constant for train becomes negative, but is not statistically significant in either model (MNL or ICLV). The impact of being full-time employed on the utility for bus becomes negative, but is not statistically significant in either model. The interaction between being aged over 55 and the utility for bus is now negative, but no longer significant. The impact of income on the utility for bus is now positive, but no longer significant. A number of changes to significance levels occur, with fluctuations for most parameters. Notable observations include: Value of Time Measures As was the case for the Chicago models, substantial drops in the value of time measures are observed, with a drop by 58% for auto, and by 33% for bus and train. For non-commuters, a drop in auto value of time by 20% is observed, but the actual value of time is no longer statistically significant (TABLE H-16). remember that this now relates solely to the mean of the constant. The utility of premium on-board services for bus is now statistically significant. statistically significant. The effect of being female on the utility for train is no longer statistically significant. significant. – – – – – The constant for bus is no longer statistically significant, where it is important to The effect of amenities on the in-vehicle travel time sensitivity for bus is no longer The effect of both age interactions on the utility of bus is no longer statistically

TABLE H-15. Base utility parameters for ICLV model in Charlotte. Commuters Non-Commuters Auto Bus Train Auto Bus Train Explanatory Variables Est. Rob. t-rat. Est. Rob. t- rat. Est. Rob. t- rat. Est. Rob. t- rat. Est. Rob. t- rat. Est. Rob. t- rat. Alternative specific constant 0.4335 0.89 -0.2407 -0.85 2.3925 1.98 0.3334 1.14 Level of Service Access time (min.)† -0.0083 -2.91 -0.0168 -3.32 -0.0227 -1.84 -0.0594 -1.59 Access time (min.) x Access mode (= walk)† -0.0023 -0.42 0.0148 1.50 IVTT (min.) -0.0108 -4.67 -0.0108 -4.67 -0.0108 -4.67 -0.0098 -2.09 -0.0037 -1.93 -0.0037 -1.93 Wait time (min.) -0.0141 -4.38 -0.0141 -4.38 -0.0228 -2.44 -0.0257 -1.95 Fare ($)† -0.1778 -3.76 -0.1778 -3.76 -0.5884 -0.67 -0.3185 -0.66 Auto cost ($) -0.1196 -3.87 -0.0956 -1.50 Parking cost ($)† -0.0512 -3.37 -0.0934 -3.99 -0.0794 -3.84 -0.0905 -2.21 -0.0508 -1.42 -0.0894 -1.55 Access mode (walk over drive)† 0.0358 0.78 Span of service (all day v. only peak)† 0.1450 3.93 0.1450 3.93 0.3849 2.12 0.3849 2.12 Reliability (% on time)† 0.0416 2.51 No transfer 0.0991 3.84 0.0991 3.84 0.0958 1.59 0.0958 1.59 Premium on-board (prem. over standard)† 0.0607 2.16 0.0607 2.16 0.1166 1.94 0.1166 1.94 IVTT (min.) x amenities† 0.0008 0.93 0.0018 2.25 Premium stop design (prem. over standard)† 0.0407 2.38 0.0232 1.43 0.1413 1.56

Commuters Non-commuters Auto Bus Train Auto Bus Train Individual Demographics Full-time student 0.1531 1.72 0.1531 1.72 Full-time employed -0.7927 -0.39 0.1918 1.79 Homemaker -0.3588 -2.00 Retired Female -0.7057 -0.47 -0.0289 -0.53 Longtime resident (5+yrs) -0.0928 -1.13 -0.1057 -1.50 Has mobility problem 0.7207 1.74 Age less than 35 years -0.0926 -1.52 -0.0926 -1.52 Age between 35 and 55 years Age more than 55 years -2.3307 -0.65 0.0168 0.28 0.0168 0.28 Household Demographics Number of vehicles in household Family income(in income) 0.0319 0.12 -0.2073 -1.97 More drivers than vehicles Children present Trip Characteristics Group travel 0.1055 1.89 0.0834 1.25 Weekend trip 0.1176 0.89 -0.0717 -0.68 -0.4350 -1.88 -0.1768 -1.89 Makes stop for groceries -0.0105 -0.20 Makes stop for other -0.0243 -0.26 -0.0105 -0.20 TABLE H-15. (Continued).

Integrated Choice and Latent Variable Models H-31 TABLE H-16. Value of time ($/hour) for ICLV model in Charlotte. Commuters Non-Commuters Estimate Robust t-ratio Estimate Robust t-ratio Auto 5.43 2.98 6.13 1.22 Bus 3.66 2.93 0.38 0.63 Train 3.66 2.93 0.70 0.62 Equivalent Valuations For the equivalent valuations of service characteristics in minutes of in-vehicle time, higher valuations for services with amenities are noted, as would be expected (lower in-vehicle time sensitivity). The relative values for non-commuters are not reliable given the very low implied in-vehicle time for bus and train in this segment (TABLE H-17). For all three modes for commuters, the sensitivity to parking cost is substantially lower than the sensitivity to the main cost components (gas or fares). For non-commuters, the calculations are not reliable given the high associated standard errors. TABLE H-17. Equivalent in-vehicle travel time (in minutes) for various attributes of ICLV model in Charlotte. Commute Non-Commute Explanatory Variables Auto Bus Train Basic Train with Amenities Auto Bus Train Alternative specific constant - (40.02) 22.22 - (642.90) (89.60) Level of Service Access time (min.) if walking 0.77 0.83 1.55 1.87 6.11 15.97 0.77 Access time (min.) if not walking 0.77 0.83 1.76 2.12 6.11 11.99 0.77 Wait time (min.) 1.30 1.40 1.30 1.56 6.14 6.90 1.30 Fare ($) * 3.66 0.38 0.70 Auto cost ($) * 5.43 6.13 - Parking cost ($) * 0.43 0.53 0.45 0.95 0.09 0.28 Span of service (all day v. only peak) 13.39 14.40 13.39 16.08 103.42 103.42 13.39 Reliability (% on time)† 3.84 4.14 0.00 0.00 0.00 0.00 3.84 No transfer 9.15 9.84 9.15 11.00 25.73 25.73 9.15 Premium on-board (prem. over standard)† 5.60 6.03 5.60 6.73 31.33 31.33 5.60 Premium stop design (prem. over standard) 3.76 4.04 2.14 2.57 37.96 0.00 3.76

H-32 Characteristics of premium Transit Services that Affect Choice of Mode Commute Non-Commute Explanatory Variables Auto Bus Train Auto Bus Train Individual Demographics Full-time student - (14.13) (14.13) - - - Full-time employed - 73.18 - - - (51.53) Homemaker - - - - - 96.43 Retired - - - - - - Female - 65.15 2.67 - - - Longtime resident (> 5 years) - - 8.56 - - 28.40 Has mobility problem - - - - (193.66) - Age less than 35 years - 8.55 8.55 - - - Age between 35 and 55 years - - - - - - Age more than 55 years - 215.17 - - (4.52) (4.52) Household Demographics Number of vehicles in household - - - - - - Family income (in income) - (2.94) - - 55.70 - More drivers than vehicles - - - - - - Children present - - - - - - Trip characteristics Group travel - 9.74) - - - (22.40) Weekend trip - (10.85) 6.62 - 116.90 47.50 Makes stop for groceries - - - - - 2.82 Makes stop for other reasons - - - - 6.53 2.82 * In the case of fare, auto cost, and parking cost, the values are in units of $/hour of IVTT. Latent Variable Components Next to be considered are the results relating to the role of the latent variables in the ICLV model. For the latent variable describing the degree of lack of transit information (TABLE H-18), no significant sociodemographic interactions are observed in either segment, albeit an indication exists that long-term residents are more informed (less uninformed) about transit options in the commuter segment. A lower level of information (i.e., a higher value for the latent variable) leads to a lower utility for bus and train in the commuter segment. In the non- commuter segment, the latent variable has no impact in the choice model. TABLE H-17. (Continued).

integrated Choice and Latent Variable Models H-33 TABLE H-18. 1: Level of lack of transit information—Charlotte. Commuters Non-Commuters 1: Level of Lack of Transit Information Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for level of lack of transit information -1.9308 -15.19 -1.4272 -8.63 Threshold 2 for level of lack of transit information 0.7091 6.50 1.0464 7.15 Threshold 3 for level of lack of transit information 1.4226 12.36 1.7584 11.01 Threshold 4 for level of lack of transit information 2.6116 18.40 3.0052 14.31 Impact on first latent variable for respondents who have lived in the area for more than 5 years -0.1491 -1.06 0.0833 0.48 Impact of latent variable on bus constant -0.5153 -4.02 -0.2021 -0.57 Impact of latent variable on train constant -0.5549 -4.22 0.3975 0.61 For the willingness-to-walk latent variable (TABLE H-19), the impact of this latent variable on the indicator (i.e., stated willingness) is not statistically significant in either segment. As a result, it is also not surprising to note that no sociodemographic interactions are significant. The significant and negative interaction term on the utility for bus for commuters simply reflects random variation in the utility for bus across respondents in the sample, where this is however not related to any sociodemographic characteristics, or linked to an underlying heterogeneity in the willingness to walk. TABLE H-19. 2: Willingness to walk—Charlotte. Commuters Non-Commuters 2: Willingness to Walk Robust Robust t-ratio Impact of latent variable on stated willingness to walk 0.1894 0.66 0.5711 0.49 Standard deviation of stated willingness to walk 10.6960 9.26 12.0800 7.92 Impact on latent variable for full-time students -0.12279 -0.47 4.917 0.37 Impact on latent variable for respondents in full-time employment -3.9564 -0.45 -2.7195 -0.34 Impact on latent variable for retired respondents - 0.82955 0.30 Impact on latent variable for female respondents -3.1658 -0.48 -2.5378 -0.38 Impact on latent variables for respondents aged over 55 -10.709 -0.69 -3.2205 -0.52 Impact on latent variable of log of household income 0.61951 0.53 0.42462 0.42 Impact on latent variable for respondents who have lived in the area for more than 5 years 0.099842 0.28 -1.6282 -0.45 Impact on latent variable for respondents with reduced mobility 0.27487 1.03 -5.8419 -0.48 Impact of latent variable on bus constant -0.2293 -4.17 0.0773 0.34 Impact of latent variable on train constant -0.0023 -0.34 0.0588 0.41 Estimate t-ratio Estimate

H-34 Characteristics of premium Transit Services that Affect Choice of Mode Turning to the pro-transit latent attitude (TABLE H-20), a more positive attitude by full- time students is noted in the commuter segment, with negative impacts on the latent attitude (i.e., less pro-transit) in both segments for female respondents, respondents aged under 35 years, and for respondents from households with more vehicles. In addition, non-commuters with reduced mobility are observed to be less pro-transit, while commuters from households with more drivers than vehicles are more pro-transit. In terms of impact on the utilities in the choice model, a lack of impact in the non-commuter segment is again notable, while in the commuter segment the expected positive impact of a more pro-transit attitude on the utility of both bus and train is observed. For the pro-car attitude (TABLE H-21), a more positive attitude is noted for female non- confidence. The impacts on the utilities in the choice model are once again limited to the commuter segment, where it is seen that a more positive pro-car attitude has a negative impact on the utility of bus and train. For the productivity latent attitude (TABLE H-22), no significant sociodemographic interactions are observed for commuters, whereas a positive and almost significant impact is observed for non-commuters who are in full-time employment. In the commuter segments, increases in the latent attitude lead to increases in the utility for bus, with no impacts in the non- commuter segment. No significant sociodemographic interactions are observed for the environment latent attitude for commuters, but a surprising negative effect is noted for non-commuters aged under 35 years. In the non-commuter segment, there is once again no impact by this latent variable in the choice model, whereas for commuters a positive impact is noted on the utility of train. These results are shown in TABLE H-23. Turning finally to the privacy and comfort latent attitude (TABLE H-24), we observe no significant sociodemographic interactions in either segment, and the impact of the latent variable on the utilities in the choice model is not statistically significant for either group. commuters, for respondents from households with more vehicles (in either segment), and for commuters with reduced mobility, albeit that this is not significant at the usual levels of

integrated Choice and Latent Variable Models H-35 TABLE H-20. 3: Pro-transit attitude—Charlotte. Impact on latent variable for respondents with reduced mobility -0.18912 -0.71 -0.76506 -3.61 Impact on latent variable if respondent’s household has more drivers than vehicles 1.1925 1.88 0.25857 0.42 Impact of latent variable on bus constant 0.1243 2.87 0.1021 0.43 Impact of latent variable on train constant 0.1014 2.52 -0.1364 -0.52 Commuters Non-Commuters 3: Pro-Transit Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 1 -3.3085 -4.27 -4.8456 -5.18 Threshold 2 for Attitudinal Statement 1 -1.9353 -2.55 -3.3918 -3.70 Threshold 3 for Attitudinal Statement 1 -1.0229 -1.35 -2.4092 -2.62 Threshold 4 for Attitudinal Statement 1 0.8699 1.15 -0.8247 -0.90 Threshold 1 for Attitudinal Statement 2 -1.8332 -2.41 -3.5054 -3.84 Threshold 2 for Attitudinal Statement 2 -0.4324 -0.57 -2.2199 -2.44 Threshold 3 for Attitudinal Statement 2 1.1152 1.47 -0.7126 -0.78 Threshold 4 for Attitudinal Statement 2 2.4900 3.25 0.7217 0.79 Threshold 1 for Attitudinal Statement 3 -1.0170 -1.34 -3.1551 -3.45 Threshold 2 for Attitudinal Statement 3 0.3576 0.47 -1.6218 -1.77 Threshold 3 for Attitudinal Statement 3 1.4134 1.87 -0.4070 -0.44 Threshold 4 for Attitudinal Statement 3 2.7056 3.52 0.9760 1.06 Threshold 1 for Attitudinal Statement 4 -1.7360 -2.28 -3.6965 -4.03 Threshold 2 for Attitudinal Statement 4 -0.3444 -0.46 -2.2071 -2.39 Threshold 3 for Attitudinal Statement 4 0.6577 0.87 -1.2573 -1.37 Threshold 4 for Attitudinal Statement 4 2.6028 3.40 0.8335 0.90 Threshold 1 for Attitudinal Statement 8 -1.8690 -2.46 -3.7167 -4.07 Threshold 2 for Attitudinal Statement 8 -0.0918 -0.12 -2.1167 -2.31 Threshold 3 for Attitudinal Statement 8 1.3583 1.79 -0.7480 -0.82 Threshold 4 for Attitudinal Statement 8 3.1580 4.10 1.2968 1.39 Impact on latent variable for full-time students 0.36454 1.89 0.2605 1.03 Impact on latent variable for retired respondents - -0.48111 -2.40 Impact on latent variable for female respondents -0.19265 -1.88 -0.53454 -3.52 Age < 35 -0.17112 -1.66 -0.48155 -2.99 Impact on latent variable of the number of vehicles a household owns -0.18601 -3.27 -0.23283 -2.66 Impact on latent variable of log of household income 0.037574 0.56 -0.04146 -0.50

H-36 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-21. 4: Pro-car attitude—Charlotte. Commuters Non-Commuters 4: Pro-Car Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 5 -2.6719 -3.77 -1.8935 -2.16 Threshold 2 for Attitudinal Statement 5 -1.2152 -1.72 -0.3930 -0.45 Threshold 3 for Attitudinal Statement 5 -0.0866 -0.12 0.6863 0.79 Threshold 4 for Attitudinal Statement 5 1.5574 2.20 2.2223 2.53 Threshold 1 for Attitudinal Statement 6 -3.5081 -4.92 -2.5243 -2.90 Threshold 2 for Attitudinal Statement 6 -1.9495 -2.77 -0.9906 -1.16 Threshold 3 for Attitudinal Statement 6 -0.4225 -0.60 0.6352 0.75 Threshold 4 for Attitudinal Statement 6 1.3094 1.85 2.2416 2.60 Threshold 1 for Attitudinal Statement 7 -2.6420 -3.71 -1.4529 -1.67 Threshold 2 for Attitudinal Statement 7 -1.6682 -2.37 -0.3337 -0.38 Threshold 3 for Attitudinal Statement 7 -0.5644 -0.80 0.8318 0.96 Threshold 4 for Attitudinal Statement 7 0.9195 1.30 2.5096 2.84 Threshold 1 for Attitudinal Statement 9 -3.7362 -5.25 -2.6331 -3.01 Threshold 2 for Attitudinal Statement 9 -1.8779 -2.66 -0.7769 -0.90 Threshold 3 for Attitudinal Statement 9 -0.1405 -0.20 0.7638 0.88 Threshold 4 for Attitudinal Statement 9 2.2468 3.20 3.0419 3.51 Threshold 1 for Attitudinal Statement 17 -2.3365 -3.32 -1.2958 -1.50 Threshold 2 for Attitudinal Statement 17 -1.1264 -1.60 -0.3084 -0.36 Threshold 3 for Attitudinal Statement 17 0.5295 0.75 1.2925 1.49 Threshold 4 for Attitudinal Statement 17 2.2033 3.09 3.0842 3.42 Threshold 1 for Attitudinal Statement 18 -2.1006 -2.99 -0.5254 -0.61 Threshold 2 for Attitudinal Statement 18 -0.7701 -1.10 0.6727 0.78 Threshold 3 for Attitudinal Statement 18 1.0743 1.53 2.0947 2.41 Threshold 4 for Attitudinal Statement 18 2.2625 3.19 3.1371 3.57 Impact on latent variable for retired respondents - -0.0114 -0.06 Impact on latent variable for female respondents 0.0692 0.73 0.3733 2.58 Impact on latent variable of the number of vehicles a household owns 0.1762 3.61 0.2429 3.19 Impact on latent variable of log of household income -0.0968 -1.54 -0.0560 -0.70 Impact on latent variable for respondents with reduced mobility 0.3009 1.67 0.2589 1.22 Impact on latent variable if respondent’s household has more drivers than vehicles -0.4731 -1.07 0.5194 1.12 Impact of latent variable on bus constant -0.3327 -4.11 -0.2201 -0.60 Impact of latent variable on train constant -0.2939 -4.03 -0.1470 -0.51

integrated Choice and Latent Variable Models H-37 TABLE H-22. 5: Productivity attitude—Charlotte. Commuters Non-Commuters 5: Productivity Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 10 -2.4332 -2.60 -2.5090 -2.86 Threshold 2 for Attitudinal Statement 10 -0.7589 -0.83 -1.1183 -1.32 Threshold 3 for Attitudinal Statement 10 1.2674 1.38 0.8054 0.95 Threshold 4 for Attitudinal Statement 10 3.4714 3.71 2.8084 3.22 Threshold 1 for Attitudinal Statement 11 -2.1657 -2.34 -2.5231 -2.91 Threshold 2 for Attitudinal Statement 11 -0.9542 -1.03 -1.4256 -1.66 Threshold 3 for Attitudinal Statement 11 0.2570 0.28 0.2148 0.25 Threshold 4 for Attitudinal Statement 11 2.2398 2.41 2.2209 2.58 Impact on latent variable for respondents in full-time employment -0.1076 -0.77 0.3636 1.74 Impact on latent variable of log of household income 0.0813 0.98 0.0439 0.55 Impact of latent variable on bus constant 0.2233 2.99 0.3424 0.68 Impact of latent variable on train constant 0.0604 1.18 -0.1192 -0.60 TABLE H-23. 6: Environment attitude—Charlotte. Commuters Non-Commuters 6: Environment Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 13 -3.9674 -16.34 -4.9790 -11.35 Threshold 2 for Attitudinal Statement 13 -2.7292 -14.86 -3.2648 -12.56 Threshold 3 for Attitudinal Statement 13 -0.7210 -4.90 -1.1803 -5.92 Threshold 4 for Attitudinal Statement 13 1.5011 9.96 0.8799 4.27 Threshold 1 for Attitudinal Statement 14 -2.6962 -15.48 -3.1118 -11.80 Threshold 2 for Attitudinal Statement 14 -1.3384 -8.82 -1.9153 -8.77 Threshold 3 for Attitudinal Statement 14 0.1373 0.94 -0.2571 -1.29 Threshold 4 for Attitudinal Statement 14 2.4069 14.58 1.6972 7.93 Threshold 1 for Attitudinal Statement 15 -1.2691 -8.58 -1.8684 -9.06 Threshold 2 for Attitudinal Statement 15 0.0856 0.61 -0.5387 -2.77 Threshold 3 for Attitudinal Statement 15 1.4409 10.04 0.9351 4.51 Threshold 4 for Attitudinal Statement 15 3.5930 17.70 2.9876 10.80 Age < 35 0.1686 1.56 -0.5378 -3.09 Impact on latent variable of the number of vehicles a household owns 0.0219 0.41 -0.0095 -0.13 Impact of latent variable on bus constant 0.0539 1.17 -0.0618 -0.43 Impact of latent variable on train constant 0.1529 2.57 -0.2538 -0.57

H-38 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-24. 7: Privacy and comfort attitude—Charlotte. Commuters Non-Commuters 7: Privacy and Comfort Attitude Estimate Robust t-ratio Estimate Robust t-ratio Threshold 1 for Attitudinal Statement 12 -2.3907 -13.60 -2.7858 -8.42 Threshold 2 for Attitudinal Statement 12 -0.5756 -3.62 -1.1664 -3.66 Threshold 3 for Attitudinal Statement 12 0.3926 2.47 -0.1027 -0.32 Threshold 4 for Attitudinal Statement 12 3.1125 15.58 2.6669 7.26 Threshold 1 for Attitudinal Statement 16 -3.6148 -17.27 -2.9700 -9.07 Threshold 2 for Attitudinal Statement 16 -1.9117 -11.69 -1.7806 -5.75 Threshold 3 for Attitudinal Statement 16 -0.1660 -1.07 -0.1082 -0.35 Threshold 4 for Attitudinal Statement 16 1.6280 9.67 1.6094 5.09 Impact on latent variable for female respondents -0.0704 -0.71 0.0036 0.02 Impact on latent variable of the number of vehicles a household owns 0.0062 0.11 -0.0201 -0.15 Impact on latent variables if children are present in household -0.0630 -0.58 -0.0559 -0.39 Impact of latent variable on bus constant 0.0876 1.45 -0.1686 -0.53 Impact of latent variable on train constant 0.0619 1.29 0.0818 0.29 Summary of Model Results We have demonstrated that ICLV models are possible and offer the following benefits compared to a more traditional multinomial or nested logit choice modeling structure: The use of the ICLV approach leads to a better statistical fit (demonstrated by the higher log-likelihood) for the choice model component of the hybrid structure (with the exception of the non-commuter segment of the Charlotte data). This is because the model obtains information on the underlying attitudes jointly from the observed choices and the answers to attitudinal questions and, to a smaller degree, because the model allows for sociodemographic interactions in the specification of the latent variables. The ICLV models provide further insights about the role of attitudes in the decision making, and also the key sociodemographic drivers behind these attitudes. The traditional multinomial or nested logit modeling structure requires that a separate model be developed to forecast traveler attitudes or latent variables, where the ICLV model forecasts these variables within the modeling structure from key sociodemographic drivers. The primary reason not to use an ICLV model is the added complexity it contains for the latent variables of interest. In this context, the five attitudinal factors could have been limited to two or three factors and the latent variables could have been reduced as well. The use of ICLV in this study was as a proof of concept rather than a final solution for coefficients on latent variables.

integrated Choice and Latent Variable Models H-39 The key findings relate to the role of the latent variables in the models, as shown in TABLE H-25. In this brief summary, we present the results in simplified table form, where +++/- -- represent positive/negative effects that are significant at the 99% level of confidence, using ++/-- for the 95% level, and +/- for the 90% level. Any effects that are not significant above the 90% level are not shown in the tables. For the impact of the latent variable in ordered logit specifications, +* is used to indicate that the effect is positive, but it is not possible to determine the size or significance of the effect. In comparison with the MNL models, the ICLV models now provide further insights about the role of attitudes in the decision making, and also the key sociodemographic drivers behind these attitudes. For the level of lack of transit information, we find that longer term residents in Chicago are likely to be less well informed about transit, which may indicate that people are set in their ways over time and do not seek out transit information. We also show that a lower level of information (i.e. higher value for the latent variable) leads to a lower utility for bus for Chicago commuters and for both transit modes for Charlotte commuters, which is quite intuitive. For willingness to walk, we find a significant impact of the latent variable on the stated willingness only in the Chicago models, where increases in the willingness to walk variable lead to increased utility for both transit modes for commuters and for train for non- commuters. In the Charlotte models, there is no link between the latent variable and the indicator, and the negative interaction with the utility for bus simply captures random heterogeneity in the data. The ICLV models demonstrate a number of significant interactions between sociodemographic variables and the latent pro-transit attitude, which is associated with higher levels of agreement with five attitudinal statements, and which leads to increased utility for both transit modes in all segments except Charlotte non-commuters, where there is no effect. For the pro-car attitude, there are again a number of significant interactions, and the latent variable is associated with increases in the level of agreement with six attitudinal statements, and leads to reductions in the utility for the two transit options in all segments except Charlotte non-commuters, where there is no effect. For the productivity latent attitude, we find weak positive effects for full-time employees in both non-commute segments, where the latent variable is associated with increases in the level of agreement with two attitudinal statements, and leads to increases in the utility for the two transit options for both Chicago segments, and for bus in the Charlotte commute segment. The pro-environment latent variable is higher for younger respondents in Chicago, and lower for younger Charlotte non-commuters. It is associated with increases in the level of agreement with three attitudinal statements, and leads to increases in the utility for the two transit options for Chicago commuters, and for train for Charlotte commuters. Female non-commuters in Chicago have a higher value for the latent privacy and comfort attitude, which is associated with increases in the level of agreement with two attitudinal statements, and which leads to reductions in the utility for the two transit options for Chicago commuters, but increases for both options for Chicago non-commuters.

H-40 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-25. Summary of latent variable findings. Chicago Charloe Commuters NonCommuters Commuters Non Commuters 1: Level of Lack of Transit Information Lived in the area for more than 5 years +++ +++ Stated level of lack of transit information +* +* +* +* Impact on utility of bus --- --- Impact on utility of train --- 2: Willingness to Walk Full-time student + + Retired -- Lived in the area for more than 5 years + Has reduced mobility --- Stated willingness to walk ++ +++ Impact on utility of bus +++ --- Impact on utility of train +++ +++ 3: Pro-Transit Attitude Full-time student ++ +++ + Retired --- -- Female --- - --- Aged under 35 years - --- Number of vehicles --- --- --- --- Log of income ++ Has reduced mobility - --- More drivers than vehicles +++ + Respondent's agreement with statement “I am not afraid to ride transit” +* +* +* +* Respondent's agreement with statement “I'm the kind of person who rides transit” +* +* +* +* Respondent's agreement with statement “I currently make an effort to take public transit whenever I can” +* +* +* +* Respondent's agreement with statement “If I wanted to, I could use public transit more frequently” +* +* +* +* Respondent's agreement with statement “It's easy to plan a trip using transit” +* +* +* +* Impact on utility of bus +++ +++ +++ Impact on utility of train +++ +++ ++

integrated Choice and Latent Variable Models H-41 TABLE H-25. (Continued). Chicago Charloe Commuters NonCommuters Commuters Non Commuters 4: Pro-Car Attitude Retired + Female +++ Number of vehicles +++ +++ +++ +++ Log of income -- Has reduced mobility +++ ++ + More drivers than vehicles --- - Agreement with statement “For me, car is king! Nothing will replace my car as my main mode of transportation” +* +* +* +* Agreement with statement “Getting to and from transit stations/stops is not pedestrian friendly and is very unpleasant” +* +* +* +* Agreement with statement “I have to drive to get to transit anyway, so I may as well just drive my car the whole way” +* +* +* +* Agreement with statement “Transit is often dirty” +* +* +* +* Agreement with statement “My car reflects who I am” +* +* +* +* Agreement with statement “My days of taking transit are over” +* +* +* +* Impact on utility of bus --- --- --- Impact on utility of train --- --- --- 5: Productivity Attitude Employed full-time ++ + Agreement with statement “More than saving time, I prefer to be productive when traveling” +* +* +* +* Agreement with statement “If it would save time, I would change my form of travel” +* +* +* +* Impact on utility of bus ++ +++ +++ Impact on utility of train +++ +++ 6: Environment Attitude Aged under 35 years ++ + --- Agreement with statement “Protecting the environment is very important to me” +* +* +* +*

H-42 Characteristics of premium Transit Services that Affect Choice of Mode TABLE H-25. (Continued). Commuters Non Commuters Commuters Non Commuters Agreement with statement “I am willing to carpool or take public transit more frequently to reduce air pollution and carbon emissions from my vehicle” +* +* +* +* Agreement with statement “I am willing to pay higher tolls if they are used to reduce congestion” +* +* +* +* Impact on utility of bus +++ Impact on utility of train ++ ++ 7: privacy and comfort attitude Female ++ Agreement with statement “As long as I am comfortable when traveling, I can tolerate delays” +* +* +* +* Agreement with statement “Privacy is important to me when I travel” +* +* +* +* Impact on utility of bus --- +++ Impact on utility of train --- +++ There are many similarities in the base utility parameters between the ICLV and traditional multinomial logit choice models. One comparison that is different is that value of time estimates are smaller in the ICLV models than in the multinomial logit models, ranging from a 20% to a 58% reduction by market segment and city. This may be explained because the ICLV model can better capture modal preferences by allowing for heterogeneity that would otherwise have been captured in the travel time coefficient. Chicago Charlotte