Utility maximisation and regret minimisation - a mixture of a generalisation
Download as PPTX, PDF1 like609 views
The document discusses a latent class approach to modeling decision rule heterogeneity in route choice behavior among commuters, integrating random utility maximization (RUM) and random regret minimization (RRM). It proposes a generalized random regret minimization (G-RRM) model that reveals optimal specifications from data, demonstrating significant taste and decision rule heterogeneity. Initial findings indicate promising results with varied combinations of decision rules across respondents and attributes.
Utility maximisation and regret minimisation - a mixture of a generalisation
- 1. Utility maximisation and regret minimisation: A mixture of a generalisation Stephane Hess – Caspar Chorus Summary • Growing interest in decision rule heterogeneity across individual respondents but also across attributes • This paper brings these two issues together • Latent class approach which not only allows for different decision rules across classes, but also differences in the decision rules used across attributes within a given class • Focus on the specific case of random utility maximisation (RUM) and random regret minimisation (RRM) • Put forward the use of a generalised random regret minimisation (G-RRM) model within individual classes Data • SC route choice behaviour among commuters who travel from home to work by car, 9 tasks per person • 550 people sampled from an internet panel maintained in April 2011 Model structure • A general specification of a model allowing for different decision rules within a latent class framework is given by: 𝐿𝐶 𝑛 = 𝑠=1 𝑆 𝜋 𝑛,𝑠 𝐿𝐶 𝑛,𝑠, where LCn is the contribution to the likelihood function of the observed choices for respondent n • Individual classes use G-RRM models, allowing not just for mixtures between RUM and RRM, but also mixed RUM-RRM classes and classes with intermediate specifications • Base structure is a G-RRM model, with random regret given by: 𝑅𝑅𝑖 = 𝑗≠𝑖 𝑚 ln 𝛾 𝑚 + exp 𝛽 𝑚 ∙ 𝑥𝑗𝑚 − 𝑥𝑖𝑚 + 𝜐𝑖 where 𝜐𝑖 is IID EV1, and 𝛾 𝑚 is the regret-weight for attribute xm • Role of regret-weight: top panel shows the effect on the attribute regret function of a step-wise variation in γ, and the bottom panel shows the effect of a continuous change in γ ln( ϒ + exp(βm·(xjm-xim))) xjm-xim ϒ = 0ϒ = 0 ϒ = 0.01 ϒ = 0.1 ϒ = 0.5 ϒ =1 xjm-xim ϒ ϒ = 0.25 ln( ϒ + exp(βm·(xjm-xim))) ln( ϒ + exp(βm·(xjm-xim))) xjm-xim ϒ = 0ϒ = 0 ϒ = 0.01 ϒ = 0.1 ϒ = 0.5 ϒ =1 xjm-xim ϒ ϒ = 0.25 ln( ϒ + exp(βm·(xjm-xim))) 1 Route A Route B Route C Average travel time (minutes) 45 60 75 Percentage of travel time in congestion (%) 10% 25% 40% Travel time variability (minutes) ±5 ±15 ±25 Travel costs (Euros) €12,5 €9 €5,5 YOUR CHOICE □ □ □ Findings and conclusions • Allowing for different decision rules across classes and differences in decision rules across attributes would lead to very large number of different possible combinations • Put forward GRRM mixture as an alternative • Allows optimal specification in terms of split between RUM and RRM within a given class to be revealed by the data during estimation, rather than needing to be imposed by the analyst • Initial findings are promising and show a rich pattern of taste heterogeneity and decision rule heterogeneity across respondents and attributes Model A: 2x RUM Model B: 2x RRM Model C: 1x RUM, 1xRRM Model D: 2x G-RRM Log-likelihood -2,431.59 -2,416.78 -2,412.92 -2,412.83 parameters 9 9 9 10 adj ρ2 0.3671 0.3709 0.3719 0.3717 BIC 4,920.11 4,890.49 4,882.77 4,888.91 est. rob. t-rat. est. rob. t-rat. est. rob. t-rat. est. rob. t-rat. β1(trav. time) -0.0559 -10.15 -0.1582 -5.44 -0.0559 -9.71 -0.0558 -9.77 β1(% cong.) -0.0025 -1.44 -0.0052 -1.35 -0.0030 -1.65 -0.0034 -1.91 β1(tt var) -0.0261 -6.33 -0.0510 -4.54 -0.0260 -6.20 -0.0259 -6.22 β1(cost ) -0.0437 -4.63 -0.0864 -4.36 -0.0404 -4.16 -0.0808 -4.16 β2(trav. time) -0.0146 -12.81 -0.0314 -11.23 -0.0310 -12.23 -0.0309 -12.19 β2(% cong.) -0.0131 -13.38 -0.0266 -12.37 -0.0275 -12.74 -0.0276 -12.71 β2(tt var) -0.0088 -7.92 -0.0182 -8.27 -0.0180 -7.88 -0.0180 -7.87 β2(cost ) -0.0725 -15.72 -0.1451 -14.05 -0.1495 -13.75 -0.1496 -13.76 δ1(trav. time) - inf (fixed a priori) + inf (fixed a priori) - inf (fixed a priori) -0.6918 -4.10 δ1(% cong.) - inf (fixed a priori) + inf (fixed a priori) - inf (fixed a priori) - inf (fixed) δ1(tt var) - inf (fixed a priori) + inf (fixed a priori) - inf (fixed a priori) - inf (fixed) δ1(cost ) - inf (fixed a priori) + inf (fixed a priori) - inf (fixed a priori) + inf (fixed) γ1(trav. time) 0 1 0 0.33 γ1(% cong.) 0 1 0 0.00 γ1(tt var) 0 1 0 0.00 γ1(cost ) 0 1 0 1.00 δ2(trav. time) - inf (fixed a priori) + inf (fixed a priori) + inf (fixed a priori) + inf (fixed) δ2(% cong.) - inf (fixed a priori) + inf (fixed a priori) + inf (fixed a priori) + inf (fixed) δ2(tt var) - inf (fixed a priori) + inf (fixed a priori) + inf (fixed a priori) + inf (fixed) δ2(cost ) - inf (fixed a priori) + inf (fixed a priori) + inf (fixed a priori) + inf (fixed) γ2(trav. time) 0 1 1 1.00 γ2(% cong.) 0 1 1 1.00 γ2(tt var) 0 1 1 1.00 γ2(cost ) 0 1 1 1.00 π1 33.36% 31.54% 33.28% 33.36% π2 66.64% 68.46% 66.72% 66.64%