The results of the Reference Point Model (B) indicate that the marginal utility for savings in travel time of the survey respondents decreases as the difference from the reference point (status quo) becomes larger - diminishing sensitivity. The combination of a positive and a negative suggests that the marginal disutility for losses in travel time of the survey respondents decreases as the difference from the reference point becomes larger. Given the values of , and , the value function curve is concave for gains and convex for loss. This result also suggests that for an equivalent travel time difference (gain or loss), the impact of a loss (travel time difference is presented as a loss) looms larger than the impact of an equivalent gain (which is presented as travel time savings) suggesting that the utility functions are steeper in the losses than in the gains domain. For example for the Reference Point Model (B), the estimates of Travel Time Difference for a gain (= 0.09) and the combination of Travel Time Difference for loss ( = 0.17)
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and (0.92) suggests that the disutility of an additional 10 minutes spent in travel (perceived as a loss) is about twice the utility of a 10 minutes savings in travel time (a gain). The policy implications of this study are that Katy Freeway travelers are more concerned with the damage/disutility caused by being late for work from choosing a route than they are with potential savings in travel time. This is consistent with
expectations as the negative consequences of being late usually outweigh the benefits of being early. Our results from the RP models are in line with previous study by Masiero and Hensher (2010; 2011). Our study and theirs both found significant improvement in the goodness of fit of the model if preferences are specified as asymmetric. Masiero and Hensher (2010) indicated that the asymmetry specification produced a steeper utility function for losses than for gains for the punctuality attribute, while ours is for the travel time attribute (shorter or longer travel time relative to respondents’ most recent trip). Their models suggest nonlinearity and diminishing sensitivity in terms of the marginal disutility of punctuality and ours is for travel time difference. Their WTPs for travel time savings are $6.02 and $9.50 for the unrestricted models, respectively. We also obtained relatively low WTPs for travel time savings from the RP models. However, there are three key differences between our models and theirs: (1) their study investigated loss aversion and diminishing sensitivity in a freight transport framework, while ours is for travelers route choice between MLs and GPLs; (2) Masiero and Hensher (2010; 2011) used a piecewise linear approximation in the utility estimation to model the nonlinearity, and our RP models used two power functions (with loss aversion and risk attitude parameters) for the value function specifications in the domain of gain and losses, respectively; (3) our study examined the efficiency of two survey design methods (Db-
efficient and Adaptive Random) while theirs used a random generation strategy to maintain experiment orthogonality. Additionally, the levels of attributes in their study varied by either 5 or 10 percent, which may not truthfully mimic the actual variation of transport cost and time in the real freight transport industry. Therefore, Masiero and Hensher (2010) indicated that a broader domain (smaller or larger level ranges) of
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attribute levels are needed to establish the validity of the diminishing sensitivity in choice experiments.
The PT-pwf model investigates the significance of the inclusion of probability weighing for both gain and loss by including only the PT proposed probability weighting functions in the utility functions. The results of the PT-pwf model show that when the function is concave low probabilities are over-weighted and when the function is convex high probabilities are under-weighted, which means high probabilities for loss are more under-weighted than probabilities for gain, while low probabilities for loss are more over-weighted than probabilities for gain. This results ( = 0.77 and = 0.81) are close to Tversky and Kahneman's (1992) findings ( = 0.61 and = 0.69) in probability
weighting. The parameter estimates of the probability weighting function for the PT-Full Model (D) ( = 2.73 and = 0.49) indicate that on average, the travelers demonstrate a sense of optimism when the chances of having a longer travel time are high. Parameter estimates ( = 1.93, and = 1.10) for the revised PT-pwf models, however, suggest S- shaped probability weighting curves (see Figure 21 for an example), while the estimates of the base model ( = 0.77 and = 0.81) imply inverted S-shaped curves. The difference between parameter estimates of the base and revised models is primarily because the revised models use smaller samples than the base models and this difference suggests the mix of pessimistic and optimistic beliefs of the sampled respondents. Our results also indicated that when there is a transformation of probabilities (either smaller or larger than 1), medium probabilities (approximately 40 to 60%) always tend to be
underweighted. This suggests that for a given trip the travel time with a medium level of probability would be underweighted, which in turn implies stronger conservative beliefs.
The estimates of Probability Weighting for Loss () and Probability Weighting for Gain () from the PT-pwf ( = 0.77 and= 0.81) and PT-Full ( = 2.73 and = 0.49) models confirm the non-linearity in probability weighting. A value smaller than one implies survey respondents overweight small probabilities and underweight high probabilities. For example a value of 0.49 for , shows that respondents perceive a
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probability of 0.10 as 0.20, i.e. = 0.20 (Equation 3). Additionally, the
difference between estimates (= 0.81vs. = 0.49= 0.77 vs. = 2.73) from the two models (PT-pwf vs. PT-Full) may indicate a significant difference in the way that respondents may perceive objective probabilities presented in the two SP question formats (Format C and D). Remember that in the PT-pwf model, it is the actual travel time (instead of travel time difference) shown to the survey respondent, while in the PT- Full model it is the travel time difference shown to the respondents, and in this format the attribute levels were clearly presented as gain or loss and resulted in much more extreme under- and over-weighting. Considering the close estimates from the PT-pwf model (= 0.81and = 0.77), we then suspect that in this situation respondents may simply use one single probability weighting function, instead of two (one for gain and the other for loss), to translate probability. However, when the attributes are presented in a clear gain/loss format (such as travel time difference instead of travel time) the
respondents are more likely to weight the gain and loss differently (= 2.73 and = 0.49 in the PT-Full model).
6.2 The Value of Travel Time Savings and Travel Time Reliability and Comparison