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109 CHAPTER 11. THE HYBRID CHOICE MODEL 11(A) INTRODUCTION AND STRUCTURE Advanced hybrid choice models, also often referred to as Integrated Choice and Latent Variable (ICLV) models were used to analyze the data from the stated choice survey. These models account for the differences across individual respondents in their preferences in terms of their baseline preferences for given modes of transport. We also allowed for further heterogeneity in these modal constants that is linked to attitudinal constructs. These latent attitudes vary both deterministically (e.g., as a function of age) and randomly (i.e., due to unobserved factors) across individuals. At the same time as explaining a share of the heterogeneity in modal preferences across respondents, they are also used to explain the answers that these same respondents give to a set of attitudinal questions. 11(B) MODEL SPECIFICATION ATTITUDINAL CONSTRUCTS In our model, we have five separate latent attitudes. Let ð¼ , be the first such latent construct for respondent n. It is defined to have both an observed and a random component, with: where ð¾ is a vector of estimated parameters that explain the impact of respondent characteristics ð§ (e.g., age) on the latent attitude, and where ð is a random error term which follows a standard normal distribution. The preceding equation is a structural equation for the first latent variable, where one such equation is used for each latent attitude. MEASUREMENT MODEL The data used in our analysis contains responses to a large number of attitudinal statements. Let ð¼ , give the answer that respondent n gives to the kth such question, commonly referred to as an indicator. The ICLV structure hypotheses that the answers to these questions are driven by the latent attitudes. If for example ð¼ is used to explain the value of ð¼ , , then we would write: In our analysis, we rely on a continuous treatment of the indicators and further center them on zero, meaning that the estimation of ð¿ is no longer required. We make the assumption that the indicators are normally distributed and estimate the standard deviation of the error term ð as ð . The likelihood of the observed value for ð¼ , is then given by a normal density, say ð ð¼ , . ð¼ð,1 ð¾1ð§ð ð1 ð¼ð,ð ð¿ð ðð,1ð¼ð,1 ð1
110 CHOICE MODEL The choice model explains the preferences expressed by respondents between car and air in the stated choice survey. The choice model explains the deterministic component of utility of a given mode i for respondent n in choice situation t as: ð , , ð¿ ð½ , ð¥ , , ð ð¼ In this expression, ð¿ is a mode specific constant (normalized to zero for car), ð½ , is a vector of coefficients representing the sensitivities to explanatory variables (such as time and cost) of mode i for respondent n and ð is a vector of parameters explaining the impact of the five latent attitudes on the utility of mode i (normalized to zero for air). We allow for both deterministic and random heterogeneity in the mode specific constants (ð¿) but the marginal utility coefficients (ð½) are deterministic. For the mode specific constants, we specify the baseline constant for air to follow a normal distribution, estimating a mean and a standard deviation. In addition, we estimate shifts on the means of these constants in several cases). Finally, we estimate an income elasticity on the cost sensitivity. MODEL ESTIMATION Model estimation jointly maximizes the likelihood of the observed choices and observed answers to the attitudinal questions for a given respondent. This creates the link between the two parts of the data. Separate models were estimated for business and leisure trip purposes. 11(C) RESULTS OUTPUTS FOR MEASUREMENT MODEL AND STRUCTURAL MODEL We first look at the outputs of the model estimation process for the structural equations and measurement model. This helps us to clarify the role and meaning of the five attitudinal constructs which we use to explain the answers respondents provide to 13 separate attitudinal questions. The grouping used relies on the insights of the Structural Equation Model described earlier. We use the groupings that had the largest effect in the SEM as long as they were based on the attitudinal questions (for example the cost factor in the SEM is ignored even though it had the largest effect in the SEM because cost is dealt with in the choice model part of the ICLV). The five latent variables then are referred to as: Auto Orientation, Values Information/Technology, Multiday Trips Unpleasant, Car Stress, and Airport Stress.
111 LV1: Auto Orientation Our first latent construct is used to explain the answers to three separate attitudinal statements. Below, we show the estimates for the ð parameters (measuring the impact of the latent variable on the indicator), the ð parameters (measuring the variance of the indicators in the sample) and the ð¾ parameters (measuring the role of socio-demographics in explaining the value of the latent attitudes). The ð measure the impact of the latent variable (LV) on the attitudinal statements. The positive signs show that a higher value for this LV means stronger agreement with the attitudinal statement, identifying this LV as pro-car. Four sociodemographic characteristicsâage, number of household vehicles, household size, and household incomeâwere used to explain the value of the LV. We see that having no household vehicles indicates an anti-car attitude, pro-car attitude increases as household size increases, and pro-car attitude decreases as income increases. TABLE 11-1: AUTO ORIENTATIONâATTITUDINAL STATEMENT ATTITUDINAL STATEMENT BUSINESS LEISURE Î Î£ Î Î£ EST T-RAT EST T-RAT EST T-RAT EST T-RAT It is important to me to control the radio and the air conditioning in the car 0.57 10.33 1.25 40.60 0.15 2.38 1.39 70.14 I love the freedom and independence I get from owning one or more cars 0.77 13.62 1.32 37.23 0.54 6.92 1.41 41.00 I need to drive a car to get where I need to go 0.89 15.39 1.51 43.04 0.51 6.90 1.61 56.89 TABLE 11-2: AUTO ORIENTATIONâDEMOGRAPHICS DEMOGRAPHICS BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Auto Orientation: Age under 35 (base=45+) 0.14 1.36 -- -- Auto Orientation: Age 35-44 (base=45+) 0.33 3.02 -- -- Auto Orientation: No vehicles in household (base=1,2) -1.75 -4.53 -3.19 -4.21 Auto Orientation: 3+ vehicles in household (base=1,2) 0.10 0.98 0.66 4.36 Auto Orientation: Household size of 1 person (base = 2,3) -0.22 -1.65 0.36 1.87 Auto Orientation: Household size of 4+ people (base = 2,3) 0.28 2.48 -- -- Auto Orientation: Income -0.001 -2.84 -0.002 -2.68
112 LV2: Values Information/Technology Our second latent construct is used to explain the answers to two separate attitudinal statements. This LV was only included in the leisure model, due to insignificant effect when tested in the business model. The positive signs of the ð show that a higher value for this LV means stronger agreement with the attitudinal statement, identifying this LV indicates a value for access to information and technology. We see, unsurprisingly, that younger age groups and females put a greater value on technology while smaller households put lesser value on technology. Value placed on technology increases with household income. TABLE 11-3: VALUES INFORMATION/TECHNOLOGYâATTITUDINAL STATEMENT ATTITUDINAL STATEMENT BUSINESS LEISURE Î Î£ Î Î£ EST T-RAT EST T- RAT EST T-RAT EST T-RAT Being able to freely perform tasks, including using a laptop, tablet, or smartphone is important to me. -- -- -- -- 0.72 13.71 1.21 38.81 It would be important to me to receive email or text message updates about my plane trip. -- -- -- -- 0.62 10.88 1.23 42.06 TABLE 11-4: VALUES INFORMATION/TECHNOLOGYâDEMOGRAPHICS DEMOGRAPHICS BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Values Information Tech: Female (base=Male) -- -- 0.34 4.55 Values Information Tech: Age under 35 (base=45-64) -- -- 0.19 1.52 Values Information Tech: Age 35-44 (base=45-64) -- -- 0.13 1.20 Values Information Tech: Age over 65 (base=45-64) -- -- -0.42 -4.50 Values Information Tech: Household size of 1 (base = 3+) -- -- -0.16 -1.47 Values Information Tech: Household size of 2 (base = 3+) -- -- -0.23 -2.60 Values Information Tech: Income -- -- 0.001 3.09
113 LV3: Multiday Trips Unpleasant Our third latent construct is used to explain the answers to three separate attitudinal statements. The positive signs of the ð show that a higher value for this LV means stronger agreement with the attitudinal statement, identifying this LV indicating aversion to multiday car trips. We see that younger people and people traveling alone find longer multiday car trips more unpleasant. TABLE 11-5: MULTIDAY TRIPS UNPLEASANTâATTITUDINAL STATEMENT ATTITUDINAL STATEMENT BUSINESS LEISURE Î Î£ Î Î£ EST T-RAT STD.DEV T-RAT EST T-RAT STD. DEV T-RAT To me, the basic idea of driving for more than a day is unpleasant 1.49 34.50 1.12 27.22 1.57 45.81 1.08 36.34 The thought of driving for several days with family/friends is unpleasant 1.41 30.50 1.23 30.04 1.47 40.55 1.14 37.77 The level of uncertainty associated with a multiday auto trip tends to make me choose the plane 1.20 24.01 1.32 37.52 1.39 37.82 1.22 42.93 TABLE 11-6: MULTIDAY TRIPS UNPLEASANTâDEMOGRAPHICS DEMOGRAPHICS BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Multiday Trips Unpleasant: Age under 35 (base=45-64) 0.31 3.12 0.28 3.22 Multiday Trips Unpleasant: Age 35-44 (base=45-64) 0.34 3.17 0.18 2.12 Multiday Trips Unpleasant: Age over 65 (base=45-64) -0.19 -1.83 -- -- Multiday Trips Unpleasant: Party size of 1 -0.27 -2.58 -- -- Multiday Trips Unpleasant: Income 0.001 2.12 -0.000 -1.11
114 LV4: Car Stress Our fourth latent construct is used to explain the answers to two separate attitudinal statements. The positive signs of the ð show that a higher value for this LV means stronger agreement with the attitudinal statement, identifying this LV as an anti-car LV. We see that younger respondents feel more stressed with automobile travel than older respondents. People in larger households (4+) find car travel to be more stressful than those in smaller households. Finally, car travel becomes less stressful as income increases. TABLE 11-7: CAR STRESSâATTITUDINAL STATEMENT ATTITUDINAL STATEMENT BUSINESS LEISURE Î Î£ Î Î£ EST T-RAT EST T-RAT EST T-RAT EST T-RAT To me, getting stuck in traffic congestion on a long trip is a big concern 0.90 16.01 1.23 32.80 0.84 16.74 1.25 40.87 I feel really stressed when driving for a long time in congestion in and around big cities 1.05 15.43 1.51 33.16 1.00 18.46 1.46 41.90 TABLE 11-8: CAR STRESSâCOEFFICIENT COEFFICIENT BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Car Stress: Age under 35 (base=35-64) 0.12 1.48 0.13 1.43 Car Stress: Age over 65 (base=35-64) -0.21 -2.14 -- -- Car Stress: Household size of 4+ people (base = 1,2,3) 0.34 3.53 -- -- Car Stress: Income -0.001 -1.94 -- --
115 LV5: Airport Stress Our fifth and final latent construct is used to explain the answers to three separate attitudinal statements. The positive signs of the ð show that a higher value for this LV means stronger agreement with the attitudinal statement, identifying this LV as an anti-air travel LV. Females and younger age groups are less stressed about air travel while stress with air travel decreases as income increases. TABLE 11-9: AIRPORT STRESSâATTITUDINAL STATEMENT ATTITUDINAL STATEMENT BUSINESS LEISURE Î Î£ Î Î£ EST T-RAT EST T-RAT EST T-RAT EST T-RAT Having people so close to me in an airline seat is unpleasant to me 1.11 23.33 1.21 35.77 0.99 28.04 1.21 54.24 Dealing with the crowds of people at the airports is uncomfortable for me 1.49 32.77 0.91 20.52 1.24 36.11 1.02 38.60 For me, the process of going through airport security is stressful 1.32 30.01 1.16 34.24 1.13 29.65 1.24 46.56 TABLE 11-10: AIRPORT STRESSâCOEFFICIENT COEFFICIENT BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Airport Stress: Female (base=male) -0.23 -3.42 -- -- Airport Stress: Age under 35 (base=45-64) 0.31 4.06 -- -- Airport Stress: Age 35-44 (base=45-64) 0.40 4.77 -0.23 -2.92 Airport Stress: Age over 65 (base=45-64) -0.08 -1.04 -0.11 -2.27 Airport Stress: Household size of 4+ people (base = 1,2,3) 0.15 1.96 -- -- Airport Stress: Income -0.001 -3.24 -0.001 3.94
116 IMPACT OF LVS ON UTILITIES IN CHOICE MODEL We next look at the impact of the five LVs on the mode specific utilities in the choice model. Each time, the ð for air is normalized to zero, meaning that we see the impact on car relative to air. For the Auto Orientation LV we see that a positive value for this latent attitude increases the utility (and hence probability) for car. For the Values Information/Technology LV we see a negative impact on car in the leisure model. This LV was not included in the business model. For the Multiday Trips Unpleasant LV and the Car Stress LV we observe a negative impact car in both the business and leisure models. Finally, for the Airport Stress LV, we observe, as expected, a positive impact on car. TABLE 11-11: IMPACT OF LVS ON UTILITIES IN CHOICE MODEL OTHER DETERMINISTIC AND RANDOM HETEROGENEITY IN MODE SPECIFIC CONSTANTS We next look at the baseline mode constants which indicate a preference for air or car assuming all other characteristics of the trip are equal. The air constant includes a base constant and several shifts, including shifts for access modes and different departure airports. The base constant shows that air is preferred to car overall. This effect is even stronger in the business travel model, which shows that air is even more preferred for business travel. The access mode shift for being dropped off at the airport is positive in the leisure model (although insignificant in the business model) implying that those who are able to be dropped off at the airport have an even greater preference for air. However, the shift for taking another mode, such as a taxi, is negative, which indicates that taxi access is less preferred than driving. This negative shift can be explained because taxi costs were not included in the SP data and were not included in the model. TAU BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Impact of Auto Orientation LV on car utility 1.19 6.80 0.80 2.69 Impact of Values Information/Tech LV on car utility -- -- -0.38 -1.61 Impact of Multiday Trip Unpleasant LV on car utility -1.25 -7.24 -1.77 -7.58 Impact of Car Stress LV on car utility -0.87 -2.94 -0.73 -5.01 Impact of Airport Stress LV on car utility 0.97 3.53 1.03 5.45
117 The model also includes shifts on the air constant for all the large departure airports included in the study. These are best understood regionally, as there are slightly different factors affecting each region. For example, business travelers in the Washington, DC region have a negative shift to flights from the Dulles airport, meaning that if all other things were equal, they would prefer to travel out of any other airport in the region. Finally, the model includes a random component for the air constant, indicating that there is significant heterogeneity across respondents that is not explained by the shifts included in the model. TABLE 11-12: OTHER DETERMINISTIC AND RANDOM HETEROGENEITY IN MODE SPECIFIC CONSTANTS COEFFICIENT BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Air constant 3.90 11.11 1.35 4.78 Shift if access mode is "Dropped off" 0.00 -- 0.33 3.19 Shift if access mode is "Taxi" or "Other" -0.26 -2.70 -0.22 -2.04 Shift for Dulles (IAD) -0.40 -5.90 -- -- Shift for Logan (BOS) 0.36 4.17 0.26 3.62 Shift for Denver (DEN) 1.19 10.07 0.83 8.97 Shift for Philadelphia (PHL) -- -- 0.76 1.52 Shift for O'Hare (ORD) -- -- 0.34 3.23 Shift for Midway (MDW) -- -- 0.19 1.81 Standard deviation for random component of air utility 2.75 12.68 3.58 28.23 The model normalizes the car constant to zero as compared to the air constant; however, two shifts are applied to the car constant. The rental car shift is negative, indicating that, all things being equal, the need to use a rental car makes driving less attractive than it would be if a personal vehicle were available. In addition, business travelers over 65 years have more of a preference for car. TABLE 11-13: DETERMINISTIC AND RANDOM HETEROGENEITY IN MODE SPECIFIC CONSTANTSâ RENTAL CAR COEFFICIENT BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Shift in car constant for rental car -1.49 -4.56 -1.82 -3.21 Age 65 and over (vs. under 64) 0.83 1.14 -- --
118 ESTIMATES RELATING TO EXPLANATORY VARIABLES We finally look at the parameters explaining the sensitivities to the explanatory variables, namely costs, access time, in-vehicle time, frequency as well as direct or indirect flight itineraries and whether or not autonomous vehicles were used for the driving trip. All cost and time coefficients are negative, indicating that increased cost or time to a travel option would be a deterrent to that option. Flight frequency is split into frequency for direct flights and frequency for indirect flights. Both coefficients are positive, indicating that more flights in a day are better, as expected. Adding frequency for connecting flights is a bit more valuable than adding frequency to direct flights, likely because this might lessen the burden of missing a connection. The autonomous vehicle attribute was insignificant in the business model and negative in the leisure model, likely indicating that leisure travelers felt uncertainty about this option and were thus less likely to choose it. A connecting flight was much less attractive to respondents than a direct flight and a flight itinerary with two stops was less attractive than one stop. Finally, we see strong income elasticity, showing that for a 10% increase in income, we see a reduction in cost sensitivity of 3.0% in the business model and 1.9% in the leisure model. TABLE 11-14: ESTIMATES RELATING TO EXPLANATORY VARIABLES COEFFICIENT BUSINESS LEISURE ESTIMATE T-RATIO ESTIMATE T-RATIO Air fare ($) -0.01 -13.10 -0.01 -16.87 Gas cost for access ($) -0.04 -2.42 -0.06 -4.37 Parking cost for access ($) -0.01 -5.46 -0.02 -7.28 Gas cost for driving ($) -0.01 -3.22 -0.02 -12.44 Rental cost ($) 0.00 -0.79 0.00 -1.09 Flight time (min) 0.00 -8.69 0.00 -13.06 Access time (min) -0.02 -16.81 -0.03 -26.06 Car drive time (min) 0.00 -6.03 0.00 -11.46 Log of frequency of direct flights 0.16 6.82 0.16 7.81 Log of frequency of connecting flights 0.12 5.55 0.15 7.64 Driving trip made by an autonomous vehicle 0.00 -- -0.40 -4.70 One-stop itinerary (vs. direct) -0.74 -10.60 -0.74 -11.66 Two-stop itinerary (vs. one stop) -0.40 -2.98 -0.22 -1.68 Income elasticity -0.30 -3.31 -0.19 -3.72
119 IMPLIED MONETARY VALUATIONS While not a core focus of this study, one way to evaluate the sensitivities that are estimated in the model is to calculate the marginal rates of substitution for different attributes of interest. In basic economic theory, the marginal rate of substitution is the amount of one good (e.g., money) that a person would exchange for a second good (e.g., travel time), while maintaining the same level of utility, or satisfaction. Table 10-22 shows the resulting values of time for each of the three models. These values are shown for respondents with the median household income of $87,500. Value of time will change with income based on the income elasticity coefficient. We see that business travelers place a higher value on all attributes than leisure travelers indicating that they are more willing to play for a faster or more comfortable trip. These results imply that business travelers would be willing to spend $17 to save an hour of driving time but would be willing to spend $36 to save an hour of flying time. Leisure travelers would be willing to spend $10 to save an hour of driving time and $26 to save an hour of flight time. With regards to frequency, the log construction of this variable becomes apparent here. If a direct itinerary currently only has one flight per day, we see that business travelers would be willing to pay $32 more for an additional flight added per day, but if a direct itinerary already has a frequency of 10, adding an additional flight is only worth $3.16 to a business traveler. Finally, in terms of number of stops, these results imply that a business traveler would be willing to pay $143 for a direct flight over a one-stop flight and that that same person would be willing to pay $220 for a direct flight over a two-stop flight. We see that business travelers are willing to pay nearly twice as much as leisure travelers for a direct itinerary. TABLE 11-15: IMPLIED MONETARY VALUATIONS WILLINGNESS TO PAY BUSINESS LEISURE Value of in-vehicle time for car ($/hr) $17.19 $10.41 Value of access time ($/hr) $36.03 $32.77 Value of in-vehicle time for air ($/hr) $35.86 $25.95 WTP for one additional flight per day for direct flights as base freq of 1 $31.63 $17.20 WTP for one additional flight per day for connecting flights as base freq of 1 $22.93 $16.16 WTP for one additional flight per day for direct flights as base freq of 5 $6.33 $3.44 WTP for one additional flight per day for connecting flights as base freq of 5 $4.59 $3.23 WTP for one additional flight per day for direct flights as base freq of 10 $3.16 $1.72 WTP for one additional flight per day for connecting flights as base freq of 10 $2.29 $1.62 WTP for one additional flight per day for direct flights as base freq of 20 $1.58 $0.86
120 WILLINGNESS TO PAY BUSINESS LEISURE WTP for one additional flight per day for connecting flights as base freq of 20 $1.15 $0.81 WTP for direct vs 1 stop $143.15 $76.85 WTP for direct vs 2 stops $220.54 $99.87 .