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3.4. Further Improvements

The evidence described in the previous section indicates that the concept of relative utility is useful to represent some types of context dependencies. However, positive and negative outcomes of comparisons are treated indifferently in the analysis of Section 3.4. This shortcoming can be overcome by introducing the concept of prospect theory into relative utility.

3.4.1. Modelling Improvements

The author clarified the effectiveness of the model with both relative utility and prospect by comparing with two competing context dependence models: the random regret minimisation (RRM) model and the random advantage maximisation (RAM) model (Zhang, 2013). The model with both relative utility and prospect is called as MPRI model, where MP stands for multiple prospects and RI for relative interest. The author derived the MPRI model based on Eqs. (3.5) and (3.15)-(3.17).

The author formulated the RRM model as shown in Eqs. (3.24a)-(3.24c), following Chorus, Arentze, and Timmermans (2008) and Chorus (2013), and the RAM model in Eqs. (3.25a)-(3.25e), following Kivetz, Netzer, and Srinivasan (2004) and Leong and Hensher (2012), where Pni is the choice probability.

(3.24a)

(3.24c)

(3.25a)

(3.25b)

(3.25c)

(3.25d)

(3.25e)

In the RRM model, indicates random regret and is systematic regret. In the RAM model, refers tothe random relative advantage function, is systematic relative advantage, indicates individual ri s random relative advantage of alternative i to the competitor alternative j, and are the (3.24b) advantage and disadvantage of alternative i over alternative j with respect to attribute k, respectively. is a threshold to judge whether the difference between a pair of partial utilities is large enough to generate the advantage. Analogue toi,can also be calculated. In addition, constant terms and alternative-generic partial utilities are included into RRM and RAM models.

Note that as shown in Eqs. (3.1)-(3.3), theoretically, the concept of relative utility can include regret and relative advantage as a special case. In this sense, the concept included in relative utility can be applied to improve RRM and RAM models. For example, relative interest can be introduced into the RRM and RAM models as shown in Eqs. (3.26a) and (3.26b). The resulting models are called RRM_RI model and RAM_RI model, respectively.

(3.26a)

(3.26b)

 
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