As seen above, the advantage/disadvantage of uni relative to unj, the relative importance parameter wnij in deriving the advantage/disadvantage of uni, and the relative importance parameter γni of each alternative are three key constructs to represent various context dependences. Especially, if the preference of alternative i is independent from some alternatives (i.e. weight wnij is zero), then the relative utility can be specified into two parts, namely the context-independent and context-dependent preferences. Thus, decomposing relative utility in different ways can derive choice models with more general context dependence structures. In this section, several empirical studies about relative utility models will be discussed and major findings for clarifying the models' strong points and limitations will be highlighted.

3.3.1. Choices of Destinations and Stop Patterns

The concept of relative utility was first applied to represent choices of destinations and stop patterns using data from a stated preference (SP) survey conducted in the Netherlands in 1997 (Zhang et al., 2004). The choice set in the SP survey contains five combinations of destinations and stop patterns, including a base alternative (i.e. none of combinations is preferred). For this analysis, 3013 valid SP responses from 335 respondents were used. Two types of relative utility models were built: an r_MNL model (Eq. (3.5)) and a nested logit model with relative utility (called r_NL model: Eqs. (3.18a)—(3.18c)).

(3.18a)

(3.18b)

(3.18c)

Here, d and m refer to either activity destination or stop, respectively, , and are non-stochastic terms of utility, and is the parameter of logsum variable

In this case study, relative utility parameters were directly estimated, that is Eq. (3.6) was not assumed. As a comparison, an MNL model and an NL model were also estimated. Tests ofstatistics suggest that both the r_MNL model (adjusted McFadden's rho-squared: 0.1150) and r_NL model (adjusted McFadden's rho-squared: 0.1231) are superior to their competitors. The degree of model accuracy improvement by the r-NL model is lower than that of the r-MNL. This may be because the NL structure itself has partly incorporated alternative similarity, which is one type of context dependency. Furthermore, both models estimated that trip makers do not deal with different alternatives in the choice set equally (three are larger than that of the base alternative in the r_MNL model and only one is smaller than that of the base alternative in the r_NL model). Familiarity with alternatives and/or expectations about alternatives were mentioned as potential reasons causing the unequal interests on one hand and the influence of both observed and unobserved heterogeneity should be clarified in future on the other. Furthermore, 22 out of total 29 parameters in the r-MNL model are smaller than the ones in the MNL model and 27 out of total 29 parameters in the r-NL model are larger than the ones in the NL model (note that relative parameter values were compared, rather than absolute values).

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