Non-linearities in Discrete Choice Attribute Valuations

Non-linearities in Discrete Choice Attribute Valuations


N Tapley, M Wardman and G Whelan, ITS, Leeds, UK


This paper evaluates the extent to which non-linearities occur in discrete choice attribute valuations. In particular, attributes relating to time and cost are examined as travel time valuations play a key role in project appraisal.



Travel time valuations play a crucial role in both the pre and post implementation appraisal of transport schemes. In fact, it has been estimated that time savings account for up to 80% of the monetised benefits of road investments. Conventional appraisal techniques assume that the valuation of time is linear in form and calculate monetised benefits accordingly. However, research in other areas of economics suggests that individuals? valuations of attributes can often be non-linear. The purpose of this research is to evaluate the extent to which these non-linearities occur, particularly in the valuation of time and cost attributes. If non-linearities do exist and are not accounted for, this may lead to inaccurate demand forecasts and miscalculated welfare benefits.

Previous Research

Two major value of time studies have been conducted in Britain. The first, conducted in the mid ?80?s and led by MVA paid little attention to non-linearities and analysed variations in attribute valuations according only to differing socio-economic and trip characteristics. The second study, conducted in the late ?90?s and led by the Hague Consulting Group (HCG) found some evidence of non-linear valuations; however it limited its analysis to in-vehicle time (IVT) in relation to car travel.

A recent meta-analysis by Wardman of 171 British studies containing 1167 attribute valuations was also conducted. The analysis showed that constant marginal valuations of time dominate transport planning literature and practice. Recent studies conducted for the Department for Transport have also recommended further research into the marginal valuations of time and cost.

Research Hypotheses

The following hypotheses are being tested as part of this research. An initial set of results has already been obtained, and will be detailed briefly in the next section.

·Sign of Change Effects

A sign effect denotes an asymmetry between the valuations of improvements and deteriorations. More specifically, diminishing marginal utility implies that losses will have a higher unit value than gains. The same prediction is made in the reference dependant preference theory formulated by Tversky and Kahneman. Many studies have identified sign effects in attribute valuations, however the few that have been transport-based have focused largely on IVT.

·Size of change effects

Both reference dependant preference theory and diminishing marginal utility suggest that the unit value of an attribute might vary with the size of its variation. Size effects may be particularly common in stated preference data since changes which are unrealistically large could be discounted and small variations ignored.

·Proportionate effects

Economic theory suggests that a saving of £1 has the same value, regardless of the source of the saving. However, it is likely that individuals would notice a £1 saving on a local bus fare much more than a £1 saving on a long-haul flight ticket price. This proportionate effect has been largely ignored by analysts and practitioners and will therefore be included in this analysis.

·Framing effects

Some SP exercises present the attributes as absolute amounts. Others, largely as a result of attempts to customise, offer them as a variation upon the current situation. There could be a ?framing? effect at work here whereupon size and sign effects are more likely to emerge as a result of the emphasis placed on changes. This fundamental issue of stimuli presentation has not been examined previously.

Initial results

An analysis of some of these hypotheses has already been made using data from the first British value of time study, led by MVA. This study asked motorists to choose between a tolled and non-tolled route in a series of stated preference tasks. The results show that non-linearities do exist, particularly in the valuation of free-flow IVT. As expected, losses were valued more highly than gains for this attribute, however the difference was relatively small (approximately 20%). A ?size effect? was also found as respondents showed a decreased sensitivity to free-flow IVT gains with increased variation in the attribute. The cost parameter did not show a significant sign effect, however recent research suggests that money may not be subject to loss aversion as it is a good held explicitly for the purposes of exchange. This matter will be investigated further with the additional data sets, mentioned in the next section. The congested IVT attribute did not show significant sign or size effects; however this may have been due to the relatively small variation of this attribute. Again this issue will be investigated further in the coming months.

Further Research

An analysis of other existing data sets is currently under way, and is expected to be complete by mid 2006. These data sets cover a wide range of choice situations, including both private car and public transport options. Included will be the HCG value of time study for the Department for Transport, the ITS rail fair regulation study for the Strategic Rail Authority (SRA) and the ITS interchange and integration study for the SRA. The choice attributes in these data sets include Out of Vehicle Time, Headway, Transfer Time, IVT and Cost, all of which will be analysed for non-linearities. Based on the results of these analyses a set of new choice data may be collected to address any remaining uncertainties and issues that arise. However, it is not expected that this phase will be completed by the end of the year.


Association for European Transport