Zhang, Sugie, Fujiwara, and Tamaki (2002)^{[1]} developed a dynamic combined SP/ RP model with relative utility and heterogeneous relative interest (dynamic r_SP/ RP model) using data on travel mode choice. Data were extracted from a four- wave SP panel survey implemented in Hiroshima, Japan, in 1987, 1990, 1993 and 1994. For this analysis, 904 valid SP responses were obtained with respect to choices of private car, bus, and a new transit system (NTS). In this case study, it is the first time to examine the influence of heterogeneity on relative interests (i.e. Eqs. (3.6) and (3.9a) were adopted). The dynamic r_SP/RP model can be expressed as follows:

(3.19)

(3.20a)

(3.20b)

(3.20c)

whereindicates the new alternative travel mode (i.e. NTS), refers to the constant term of existing alternative i, describes the SP bias, and is the constant term of NTS.

Four types of dynamic r_SP/RP models were estimated and the resulting model accuracy (adjusted McFadden's Rho-squared) ranged between 0.1570 and 0.1863. Tests of statistics suggest that dynamic r_SP/RP models perform better than their competitor (i.e. dynamic SP/RP models without relative utility).

In the RP submodel, it is observed that temporal change in the relative interest parameter of bus is very small. In the SP submodel, model estimation results show that relative interest parameters for all travel modes are not invariant across individuals. Influential factors affecting such heterogeneity include age, sex, occupation, household size and car use experience. Introducing NTS-specific attributes reduces variations of relative interest parameters over time; however, introducing car use experience (i.e. context dependence in the past) leads to a larger variation. The joint presence of NTS-specific attributes and car use experience in the model further increases temporal variations of relative interest parameters. In summary, introducing context dependency in the past affects not only model accuracy but also estimations of relative interest parameters, which further vary with what kinds of explanatory variables are used to explain the choice utility.

[1] In fact, this study was conducted after Zhang et al. (2004).

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