Relative utility can be also used to endogenously represent choice set generation. Zhang et al. (2005) made such an attempt in the context of shopping destination and parking place choices. Data were collected from 765 shoppers who parked their cars at seven parking places in the central area of Hiroshima City, Japan, in October 2003. In this case study, an NL model was built to jointly represent shoppers'

choices of destinations (seven shopping areas) and parking places (seven places). Because after a shopper visits the first destination, he/she has to decide whether to go back to home or to continue shopping by visiting other destination(s) (i.e. making a tour), the authors defined the destination choice set as combinations of the seven shopping areas and whether to go back home directly or to make a tour after visiting the first destination. To simplify the discussions, they only focused on the choice set generation with respect to parking choices and assumed that the choice set for destinations is given and visitors equally recognise all the seven destinations.

Introducing Eq. (3.7) into NL model lead to the following new type of NL model with endogenous generation of choice set (called r GenNL model).

(3.22a)

(3.22b)

(3.22c)

(3.22d)

Here,is the joint choice probability of individual n choosing alternative d from choice set D and alternative m from choice set M, is the choice probability of alternative m given alternative d, Pn(d) is the choice probability of alternative d, and μ is the parameter of logsum variable

Because individuals may have heterogeneous generation patterns of choice set, is further defined as,

(3.23a)

(3.23b)

where is a reference alternative,is the sth attribute of individual n, is the rth attribute of alternative i for individual n, and , are the parameters of. and , respectively.

McFadden's Rho-squared is 0.289 for the NL model and 0.483 for the r_GenNL model. The accuracy of r_GenNL model is 1.7 times higher than that of NL model. The parameter of logsum variable is 0.7987 being statistically significant. The parameter of walking distance to the nearest tram station that is not significant in the NL model becomes significant in the r_GenNL model. All these results suggest better performance of the r_GenNL model.

For the parameters about the probability Ψni of parking place i being included in the choice set, recognition of parking place and threshold of walking distance become statistically significant. A positive parameter for recognition of parking place means that if people know a particular parking place, then that parking place has a high possibility to become an alternative of parking choice set. A positive parameter for threshold of walking distance suggests that the longer the threshold walking distance, the higher the probability of a parking place being included as parking choice set. These results seem intuitive. In addition, recognition of parking place has the largest influence with the highest significance. This suggests the importance of using some marketing approaches to let people know about the parking places in case of promoting the use of particular parking places. However, parking information access behaviour and the existence of travel party seem not influential to the generation of parking choice set. Comparing the probability of a particular parking place being included in the choice set and the relative interest parameter for that parking place, it is found that they have quite similar trends. This might be due to they are derived from the same original interest parameter.

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