International Choice Modelling Conference, International Choice Modelling Conference 2015

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The next step in random regret modelling: New insights, new models, new empirical results
Sander Van Cranenburgh, Cristian Angelo Guevara, Caspar G. Chorus

Last modified: 11 May 2015

Abstract


Highlights

  • New insights: regret function in random regret models is not scale-invariant.
  • New models: µRRM model allows for estimation of the scale. Conventional RRM model and RUM model are special cases; P-RRM model generates strongest regret aversion.
  • New empirical results: re-analysis of datasets shows very substantial improvements in model fit when using the μRRM model as compared to the RUM and the conventional RRM model.

 

Abstract

Since its recent introduction, the Random Regret Minimization (RRM) model (Chorus 2010) has gained attention among a small but growing group of choice modellers. It has been used to explain and predict a wide variety of choices within and beyond the transportation-domain, such as departure time choices, route choices, mode-destination choices, activity choices, on-line dating choices, health-related choices and policy choices. In the core of the RRM model is the so-called attribute level regret function. This function maps attribute differences - between a considered alternative and a competing alternative - onto regret. As a result of the specific convex shape of this function the RRM model poses that the regret generated by a loss (relative to a competing alternative's attribute) looms larger than the ‘rejoice'  which is generated by an equivalent gain (relative to a competing alternative's attribute). As a consequence, - and unlike its linear additive RUM counterpart - the RRM model features a particular, reference-dependent type of semi-compensatory behaviour.

 

While earlier RRM studies mainly focussed on contrasting the empirical performance of the RRM model relative to the linear-additive RUM model, recent efforts are shifting towards exploring the behavioural and econometric properties of the model (e.g. Prato 2013; Hess et al. 2014; Guevara et al. in press). One theoretical property of the RRM model which has however not yet been addressed concerns the scale-invariance of the RRM model.

 

This paper starts by showing that the attribute level regret function is not scale-invariant, and that - as a result - the degree of regret minimization behaviour imposed by an RRM model depends crucially on the sizes of the estimated taste parameters in combination with the distribution of attribute-values in the data. Motivated by these insights, this paper makes two methodological contributions. Firstly, it introduces a formal measure of the degree of regret minimizing behaviour (or: profundity of regret) which is imposed by an RRM model. This ex post measure of the profundity of regret for attribute m, denoted αm, ranges from zero to one, is easy to compute after having estimated an RRM model, and allows for comparability within and across estimated models. Finding a value of αm which is close to one indicates a very strong profundity of regret with regard to the attribute. That is, for that attribute the regret generated by a loss looms considerably larger than the rejoice generated by an equivalent gain. Vice versa, finding a value of αm which is close to zero indicates a very mild profundity of regret, implying absence of non-linearity and reference-dependency in preferences. We show that insight into the profundity of regret is of crucial importance for the correct interpretation of estimation results of RRM models.

 

Secondly, and most importantly, by exploiting the fact that the RRM model is not scale-invariant this paper proposes two new family members of Random Regret Minimization models: the µRRM model and the Pure-RRM (henceforth abbreviated as P-RRM) model. The µRRM model is a generalization of the RRM model - having the scale parameter µ as an additional degree of freedom. Thereby it accommodates for different degrees of regret minimization behaviour. We show that the µRRM model has three special cases: 1) if µ is insignificantly different from one, then the conventional RRM model (Chorus 2010) is obtained; 2) if µ is arbitrarily large, then the resulting model does not impose random regret minimization behaviour (hence αm = 0 ∀ m). In this special limiting case the µRRM model exhibits linear-additive RUM behaviour; and 3) if µ is arbitrarily close to zero, then the resulting model imposes the strongest possible regret minimization behaviour within the random regret modelling paradigm (hence αm = 1 ∀ m). We call this model the P-RRM model.

 

As an additional empirical contribution to the literature we illustrate the new methodological insights developed in this paper by re-analysing 10 datasets which have been used to compare linear-additive RUM and RRM models in recently published papers. Based on our re-analyses, a series of observations is made. First, the profundity of regret that is imposed by the conventional RRM model is generally found to be very limited. This insight explains the small differences in model fit that have previously been reported in the literature between the conventional RRM model and the linear-additive RUM model (e.g. Chorus et al. 2014). Second, on 4 out of 10 datasets we find very substantial improvements in model fit when using the μRRM model as compared to the RUM and the conventional RRM model. Third, we find substantial differences in model fit between P-RRM and RUM models (both positive and negative). This indicates that the behaviour which is predicted by the conventional RRM model is typically much closer to random utility maximization behaviour than to pure random regret minimization behaviour.

 

 

References

Chorus, C., van Cranenburgh, S. & Dekker, T. (2014). Random regret minimization for consumer choice modeling: Assessment of empirical evidence. Journal of Business Research, 67(11), 2428 - 2436.

Chorus, C. G. (2010). A new model of random regret minimization. EJTIR, 10(2), 181-196.

Guevara, A., Chorus, C. G. & Ben-Akiva, M. (in press). Sampling of Alternatives in Random Regret Minimization Models. Transportation Science.

Hess, S., Beck, M. J. & Chorus, C. G. (2014). Contrasts between utility maximisation and regret minimisation in the presence of opt out alternatives. Transportation Research Part A: Policy and Practice, 66(0), 1-12.

Prato, C. G. (2013). Expanding the applicability of random regret minimization for route choice analysis. Transportation, 1-25.

 


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