International Choice Modelling Conference, International Choice Modelling Conference 2017

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Choice modelling with time-varying attributes, with an application to train crowding
Andrew T Collins, David A Hensher

Last modified: 28 March 2017


When estimating discrete choice models, the attributes of the choice alternatives are a key component of most model specifications. Measures of time or duration are common types of attributes investigated by analysts. Examples include travel time in the field of transportation, life expectancy in health economics, and product life in marketing. Other attributes are linked to time, in that they are a measure of the quality of the alternative either at some point in time, or for some length of time. For example, travel time when driving is sometimes broken down into time in one of several driving conditions, such as freeflow, slowed down and stop-start (e.g., Hensher 2001). Essentially, the aggregate time attribute is decomposed, such that it represents the sum of time spent in various conditions. Other possible applications include time in various crowding conditions when travelling by train (the focus of this study), the quality of cycling infrastructure along a route, the deterioration of health over a life expectancy, and the degradation of performance of a phone over the length of its life. This paper is an investigation of these types of attributes, which we refer to as time-varying attributes (TVAs). A similar concept called common-metric attributes has been suggested in the literature (Layton and Hensher 2010), which refers to attributes that have the same metric and might be processed in certain ways, such as aggregation. However, TVAs are a specific case of common-metrics attributes, and relate explicitly to time under certain conditions. This paper will consider motivations for the use of TVAs, the additional insights that may be gained, the various challenges such as the representation of risk, the elicitation of values in a revealed preference context, and the presentation of TVAs in discrete choice experiments (DCEs). Empirical results from a study into train crowding will be presented.

The time-varying aspect of TVAs recognizes that the attribute performance or level may realistically change over a length of time. The attribute is likely to be continuous in nature (e.g., crowding levels), or have some degree of ambiguity about the levels (e.g., driving conditions). In practice, breaking the attribute down into specific categories or conditions is necessary, just as it is often necessary to restrict the number of attribute levels when designing DCEs. For example, whilst there has been a shift in recent years to the use of many crowding levels in the public transport crowding literature (e.g. Whelan and Crockett 2009; Hensher et al. 2011; Li and Hensher 2011, 2013), there will be some limit to the number of crowding levels that can be applied. Such restraint is particularly important for TVAs, as potentially all conditions might be experienced, with time attached to each level, and the extra respondent burden might outweigh any potential behavioural insights. In the present study into train crowding, we utilized five intuitive conditions: time sitting with adjacent space, time sitting next to a stranger, and time standing at three different levels of crowding. Each condition lasts for a certain length of time, which may be zero.

The use of TVAs allows a number of possibilities to be investigated whilst keeping the overall time/duration in a reasonable range. Sensitivities to certain conditions can be estimated without having to assign that condition to the entire time, where the latter may be very unrealistic (for example, standing in heavy crowding for a long trip). Non-linear responses to certain conditions can be more effectively tested, over the full domain of the time/duration. Finally, thresholds on certain conditions can be tested. For example, if a train user must ever stand, there may be a penalty beyond the value of standing travel time savings.

There has been an increasing interest in integrating risk into discrete choice models (e.g., Rasouli and Timmermans 2014; Hensher et al. 2011a). However, the attributes considered typically vary over one dimension only, including for time/duration attributes. For example, the overall travel time may be allowed to vary (e.g., Senna 1994). Risky outcomes are complicated for TVAs, as not only may the aggregate time measure vary, but the component time measures as well. Under risk, we can consider the TVAs to be multivariate random variables. In this paper, we investigate the risk attitudes towards TVAs, by using a mean-variance model (see Li et al. 2010) using an appropriate variance measure that considers all dimensions/conditions of the attribute. Additionally, we test for further threshold effects, which are present if a certain condition is ever experienced by a decision maker, across multiple outcomes.

When using revealed preference data, the collection of individual data on TVAs may be complicated by their multidimensional nature, as the individual needs to recall time spent under potentially arbitrary conditions chosen by the analyst. Obtaining information on TVAs when the outcomes vary complicates matters further, as the attribute varies both across the conditions, and across outcomes. In this paper, we draw upon the elicitation literature (see Garthwaite et al., 2005) for guidance on how this may be achieved. The inclusion of risky outcomes for TVAs in DCEs presents a challenging integration exercise for the respondent, and this paper will consider alternative ways that this can be achieved.

In addition to discussing various considerations around TVAs, this paper will present empirical evidence from a train crowding study conducted in Sydney in late 2016. In the study, commuters who travel to work by train must conduct an elicitation exercise, which provides information on the variability of crowding that they experience. Respondents also complete three types of DCE, each with a different type of presentation of crowding. In one format, a single crowding level is presented per choice alternative. In another format, each alternative includes the amount of time spent travelling in up to five crowding conditions. In the final format, three crowding experiences are presented per alternative, each with times for up to five crowding conditions, and an associated probability of occurrence. We leverage the TVA approach to provide insight into train crowding through the specification of non-linearities, thresholds, and the handling of risk. In doing so, we also address one of the criticisms made by Wardman and Whelan (2011) of the crowding literature: that use of a single crowding condition is unrealistic and implausible. The TVA approach makes the choice exercise more credible in this context, and could do so in other literatures that use DCEs as well, in particular health and marketing.


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