A joint model for stated choice and best-worst scaling data using latent attribute importance: application to rail-air intermodality

Abstract

This paper looks at modelling choices in the presence of a new mode of transport, where there is a need to understand the sensitivities to a number of new attributes. Stated choice (SC) data and two types of Best-worst scaling (BWS) data (i.e. case 1 and case 2) are collected from the same respondents. We mix survey methods rather than using a longer SC survey to better understand choice behaviour whilst reducing the boredom caused by one very long set of SC choices. Although BWS data has been increasingly collected alongside stated choice (SC) data, little is known about the relationships between BWS responses and SC responses at the level of individual respondents. Also, little effort has been made to jointly exploit the behavioural information from BWS data and SC data to improve the understanding of choices. This paper proposes a joint model which links the BWS and SC data through the notion of latent attribute importance. The modelling results show that people perceive attribute importance in a relatively consistent way across different survey methods, i.e. a person who perceives higher importance from an attribute is likely to show stronger sensitivity to that attribute in SC tasks, give more weight to the same attribute in BWS1 tasks and exhibit a wider gaps in terms of attractiveness between levels for the same attribute – in comparison with other individuals. This consistency shows that the additional behavioural information can be gained by using a joint model estimated on BWS1 and BWS2 data alongside more traditional SC data, helping us to improve the explanation of the choices and the role of the attributes. Our results however do not find a one-to-one relationship between different survey methods and analysts thus need to be mindful that there remain some differences in how attributes are evaluated between SC, BWS1 and BWS2 surveys.

Keywords:

• Stated choice
• best-worst scaling
• attribute importance
• MaxDiff model
• integrated choice and latent variable model

Acknowledgments

Fangqing Song acknowledges the support of the China Scholarship Council while Stephane Hess was supported by the European Research Council through the consolidator grant 615596-DECISIONS. We are grateful for the constructive comments received from the two anonymous reviewers who have helped us significantly improve this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In this presented paper, we use weight to describe the influence of an attribute in decision making in BWS Case 1 tasks and use attractiveness to describe the influence of an attribute level in decision making in BWS Case 2 tasks. Greater weight of an attribute or attractiveness of an attribute level means higher probability of this attribute or attribute level being chosen as the best and lower probability of it being chosen as the worst.

2 BWS approaches outweigh rating or ranking methods as BWS can take advantage of respondents' tendency of responding more consistently and accurately to extreme options on an underlying scale from a relatively small choice set (Marley and Louviere 2005). Thus conventional rating or ranking tasks are not used to help explain choices in our study.

3 BWS Case 1 and SC data is often collected at different moments of the survey design and data collection process. Outcomes of the former are for example regularly used to determine which attributes from a larger pool of attributes need to be included in the SC experiment.

4 Please refer to the definition of weight and attractiveness in footnote 1. It also needs to be noted that our definition of attribute importance is not equivalent to the importance defined by Marley, Flynn, and Joseph Louviere (2008), and we do not have the same identifiability problem as discussed in that paper as we are not trying to separate the impact of an attribute and a specific level on that attribute in BWS2 tasks.

5 The quoted term ‘utility’ is used for precision as utility by definition can only be derived from an alternative (McFadden 1973, 2001), rather than from a single attribute or attribute level.

6 In an ICLV model, it is common practice to use the latent variable solely to capture heterogeneity in the measurement component, and only a limited number of studies have also directly included additional randomness irrelevant from the latent variable in the measurement model. We have tried to estimate models with such direct random component in the measurement model for the BWS1 data. However, log-likelihood ratio test suggests accounting for such randomness cannot bring about significant improvement in fit or help better explain choices in our case. The interpretation of the estimation results are nevertheless quite similar to the old model, indicating that our findings about the correlation among different survey methods are relatively consistent across different model specifications. This also applies to the specification for BWS2 data in Equations (10(10) $B_{knm\mid 2}={\delta }_{k\mid 2}+{\gamma }_{k\mid 2}\cdot e^{{\zeta }_{k\mid 2}{\alpha }_{nk}}{x}_{knm\mid 2}.$(10) ) and (11(11) $B_{knm\mid 2}={\varphi }_{k_1\mid 2}(x_{knm\mid 2}==1)+\sum _{l=2}^{L_k}{\varphi }_{k_l\mid 2}\left(e^{{\zeta }_{k\mid 2}{\alpha }_{nk}}\right)(x_{knm\mid 2}==l).$(11) ).

7 A preliminary pilot survey conducted at Shanghai Hongqiao Airport where the HSR-air intermodal service was available suggested low chance of intercepting transfer passengers, low willingness of outbound passengers to participate in the survey, and little knowledge about HSR-air intermodality of the participants. This also explains why we instead collected data at Pudong International Airport for the formal survey as it was much easier to approach transfer passengers there.

8 Transfer time has three levels: it takes a value of 0min to indicate a seamless transfer in the same transport hub and takes the level of either 45min or 90min to suggest a transfer between two different hubs.

9 Simple best-minus-worst scores can be obtained by subtracting the total count of an item being chosen as the worst from the total count the same item being chosen as the best across all BWS choice tasks and across all respondents (Louviere, Flynn, and Marley 2015). Since each attribute appeared 4 times per person in our case, the simple B-W score averaged at the individual-level is between −4 and 4.

10 The levels were always shown in the order of connection time, delay protection, ticket integration and luggage integration to reduce cognitive burden. Comparisons between levels within a same attribute were not allowed.

11 Analytical B-W scores can be obtained by $\ln (\frac{1+\frac{N_b-N_w}{N_x}}{1-\frac{N_b-N_w}{N_x}})$, where $N_b-N_w$ is the simple B-W score and $N_x$ is the total times of the item being available, such that the score can rule out the impact of uneven occurrence of each attribute (Lipovetsky and Conklin 2014; Marley, Islam, and Hawkins 2016).

12 For the sake of consistency, in Section 4, parameters on attributes are notated with subscripts of the capital initials of the attributes as shown in Table 1, and parameters on attribute levels are represented with subscripts of the abbreviation of the attribute levels in lower case as listed in Table 3.

13 USD/CNY≈ 6.9 during the period of data collection.

Additional information

Funding

Fangqing Song acknowledges the support of the China Scholarship Council (201506260171) while Stephane Hess was supported by the European Research Council through the consolidator grant 615596-DECISIONS.