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3.4.2. Model Estimation

Here, data of Beijing driver's stated choices of departure time and driving routes under the provision of dynamic travel are adopted, which include 1872 SP responses collected from 624 drivers in 2008. Four alternatives in choice set are trunk road during off-peak hours, ring road, trunk road and branch road during peak hours. SP attributes include travel purpose, error of dynamic travel information prediction, timing constraint for arrival time, travel distance for the three routes, travel time, and probability of arrival time delay during peak hours. For simplicity, only travel time was introduced for representing the alternative-specific context. Therefore, gain here refers to shorter travel time and loss to longer travel time. The regret of alternative i is calculated as , where tni, tnj are the travel times of alternatives i and j, respectively. Following Leong and Hensher (2012), it is assumed that lower values of travel time are perceived as an 'advantage' and higher values of travel time are seen as a 'disadvantage'. The advantage of alternative i over j with respect to travel time is simply the corresponding disadvantage of j over i with respect to the same travel time attribute.

In this case study, the MPRI model was repeatedly estimated by changing the values of prospect parameters (, and ). It was found that the maximum log- likelihood is reached when , and . In this particular case study, respondents showed a linear response to gains and a non-linear response to losses. In case of the original set of prospect parameters ( and ), the MPRI model performs better than the RRM model but worse than the RAM model. When a = 1.0, β = 0.1 and λ = 1.0, the MPRI model performs best. The following conclusions were made.

(1) The MPRI model with a best set of prospect parameters is superior to any other model.

(2) The RURI model performs better than the RRM model without relative interest.

(3) The RAM model without relative interest is not inferior to the RURI model.

(4) Introducing the relative interest parameter into the RRM and RAM models can improve their model accuracy.

As for relative interest, results of the MPRI model with the simulated best set of prospect parameters show that drivers attach the highest importance to the alternative 'trunk road during peak hours', which relative interest parameter is 5.6 times higher, compared to the alternative 'ring road during peak hours' with the lowest relative interest parameter. In contrast, relative interest parameters from the RRM_RI and RAM RI models show different patterns from the MPRI and RURI models. The most important alternative in the RRM_RI model is 'trunk road during off-peak hours' while the alternative 'ring road during peak hours' is regarded as the most important in the RAM RI model, which is the same as the MPRI model.

All six models suggest that the context-dependent travel time is statistically influential to the joint choice behaviour. In addition, signs of travel time parameters are all logical. The RURI model estimated that drivers prefer shorter travel time and the MPRI model estimated that drivers prefer gains to losses. Results of the RRM model suggest that drivers dislike regret and the RAM model confirms that relative advantage of travel time brings positive utility to drivers. The original set of prospect parameters 'α = β = 0.88 and λ = 2.25' suggests that decision-makers are more sensitive to loss than to gain. In contrast, the MPRI with the best set of prospect parameters shows that drivers are almost insensitive to increased travel time (i.e. loss) from competitor alternatives, but significantly sensitive to reduced travel time (i.e. gain).

Significant changes in different models were also found with respect to other explanatory variables. The MPRI/RURI models estimate that the ownership of car navigation system and the familiarity with road network do not significantly affect the joint choice; however, the RRM/RAM models confirm their significant influence. The RRM/RAM models provide logical estimations of the influence of the familiarity with road network in the sense that it is consistent with the survey observation. However, all four models show that the estimated parameter signs are all negative, which is contrary to the survey observations. In the MPRI model with the best set of prospect parameters 'α = 1.0, β = 0.1, and λ = 1.0', the constant term becomes insignificant, but the ownership of car navigation system and familiarity with road network become significant. Other parameters show the same signs and statistical significance as those in the MPRI model with the original set of prospect parameters from Tversky and Kahneman (1992). Introducing relative interest parameters into the RRM and RAM models improved model accuracy, but familiarity with road network is estimated to be inconsistent with the observed SP responses. The constant term in the RAM_RI model becomes positive, which is different from the other models. Other parameters show a consistent trend with the RRM/RAM models without relative interest parameters.

 
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