Abstract
There is a growing literature that promotes the presence of a mix of compensatory and semi-compensatory processing strategies in the way that individuals evaluate packages of attributes in real or hypothetical markets, and make choices. This paper proposes a specification for the utility form in a choice model to test if, given a pair of attributes with a common-metric (e.g., components of travel time or cost), the attribute with the dominating level defines the marginal (dis)utility that is assigned to both attributes. We refer to this processing strategy as a parameter transfer rule. We use a stated choice data set, in the context of car driving individuals choosing between tolled and non-tolled routes, to estimate a mixed logit model which incorporates the presence of the parameter transfer rule and the conventional fully compensatory rule, both existing up to a probability. We find that if this parameter transfer heuristic is part of the mix, the WTP is more than 30% higher, on average, than when only a fully compensatory rule is imposed. We also contrast the parameter transfer rule with other semi-compensatory heuristics which have been investigated in other papers, and show that the finding adds further support to the accumulating evidence that a semi-compensatory attribute processing rules tend to result in higher mean WTP estimates compared to the fully compensatory attribute processing rule.
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Notes
In contrast to SC experiments that generate attribute levels that may not bear any relationship to real experience.
Cognitive distance is a language used to refer to the perception and processing of the relationship between two attributes.
We also investigated a Weibull distribution. We computed the pdfs of the Weibull density and the probability that the each alternative would be added. We found that, in some sense, individuals appear to be fuzzy rational for marginal disutilities of time (or cost) that researchers might suggest were close, and hence individuals are inclined to add such attributes. This is in line with the evidence that a large percentage of the respondents stated, in supplementary questions (see Hensher 2008), that they added the components: 88.06 and 76.5%, respectively, for time and cost. We also considered the unit frechet which is the reciprocal of the exponential with distribution = exp(−λ/x). It provided essentially the same results.
The estimated model is of the mixed logit form (with error components), which ensures that the probabilities sum to 1.0 for each choice set.
That is, in the language of our model, when x 1 and x 2 are cognitively close, so that neither attribute is expected to dominate, and so the α sets are reversed.
We pivoted the choice experiment around a reference alternative in recognition of supporting theories in behavioural and cognitive psychology and economics such as prospect theory, case-based decision theory that argue in favour of anchoring the alternatives to be evaluated around a recent experience (Gilovich et al. 2002). In recent years pivot designs have been adopted in preference for non-pivot designs (see Rose et al. 2008) .
Sydney has a growing number of operating tollroads; hence drivers have had a lot of exposure to paying tolls. .
The SC experiment herein was designed for the multinomial logit model using priors from this model. We acknowledge that the design developed in 2004 is not as efficient as a design we might develop today in which we focus on the most complex model, namely the mixed logit (see Rose and Bliemer 2007). The priors were obtained from a simple linear MNL model form using the data reported in Hensher (2001). The prior parameters line up close to the estimates in Model 1 below.
VTTS refers to the amount of money an individual is willing to outlay to save a unit of time, holding income and other factors constant.
The survey designs are available from David.Hensher@sydney.edu.au.
This distinction does not imply that there is a specific minute of a trip that is free flow per se but it does tell respondents that there is a certain amount of the total time that is slowed down due to traffic etc. and hence a balance is not slowed down (i.e., is free flow like one observes typically at 3 am in the morning). .
We ran additional models with a SP1 constant, age and income, but these additional variables did not influence the parameter estimates associated with time and costs, the focus of this paper.
We also estimated a generalised mixed logit model to account for scale heterogeneity as per the suggestion of Fiebig et al. (2009), but did not find any statistically significant improvement in model fit of the model (indeed it was considerably inferior), as well as a statistically insignificant parameter for scale heterogeneity.
The spread is the standard deviation times \( \sqrt 6 \).
In an earlier version of the paper we undertook a grid-search to obtain estimates of the time and cost λ’s. Identification of a range in which each λ stabilises, took over 4 days of computation using Nlogit 5, with each model estimate running for approximately 20 min. There was a noticeable improvement in the log-likelihood for parameter-transfer model, in contrast to the fully compensatory equivalent model form (i.e., random parameter logit with error components) when λt and λc were evaluated over the range 0.00011–0.0004, with the lowest log-likelihood at the low end of the range. The log-likelihood varied from −2393.99 to −2406.72 in the λ range in the text. It did not improve for lambda’s approaching zero. However the WTP estimates were quite similar to those obtained from Model 2 reported in Table 3.
Unfortunately the supplementary questions were unable to establish whether addition also implied that a unit of free flow time and a unit of slowed down time were treated as one of the other etc.
Regardless of whether this was established through self-stated supplementary questions, or by the functional specification of the model (see Layton and Hensher 2009).
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Acknowledgements
Research funded under the Australian Research Council Discovery Program grant DP0770618 and the Behavioural Choice Group in the Faculty of Economics and Business at the University of Sydney. David Layton thanks ITLS for support during his academic year sabbatical leave at the University of Sydney. Discussions with John Rose, Stephane Hess and Bill Greene are appreciated, as is extensive advice from three referees and Martin Richards. The very helpful advice of the referees was way beyond what one normally receives.
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Hensher, D.A., Layton, D. Parameter transfer of common-metric attributes in choice analysis: implications for willingness to pay. Transportation 37, 473–490 (2010). https://doi.org/10.1007/s11116-010-9260-6
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DOI: https://doi.org/10.1007/s11116-010-9260-6