1. Personalized Recommendations using Discrete Choice Models with Inter- and Intra-Consumer Heterogeneity
Moshe Ben-Akiva
With Felix Becker, Mazen Danaf, and Bilge Atasoy
Intelligent Transportation Systems Lab
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

2. Contents Objective Flexible Mobility on Demand (FMOD) The Model
Model Estimation
Online Application
Conclusion
Appendix
Making public transportation competitive
App based mobility service
Customer requests for trips (original, destination, time of travel)
App displays a menu of travel options
Customer makes a choice
Complements mass transit
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

3. Objective
Estimate consumer preferences for an app based recommendation system which predicts user responses to options:
- Stored user preferences, identified upon login.
- Online updates as more choices are made.
- Offline updates to account for population trends.
Apply method for a Flexible Mobility on Demand (FMOD) system.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

4. FMOD (1)
Flexible Mobility on Demand1 aims at making public transportation competitive by:
Personalization: tailoring options to individual preferences
Optimization: maximizing operator profit and user satisfaction
Flexibility: offering a variety of travel options
Making public transportation competitive
App based mobility service
Customer requests for trips (original, destination, time of travel)
App displays a menu of travel options
Customer makes a choice
Complements mass transit
1Atasoy, B., Ikeda, T., Song, X., and Ben-Akiva, M. (2015). The Concept and Impact Analysis of a Flexible Mobility on Demand System. Transportation Research Part C: Emerging Technologies, 56,
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

5. Para-transit with Flexible Route and Schedule
FMOD (2)
Para-transit with Flexible Route and Schedule
Taxi: door-to-door, private
Shared-taxi: door-to-door, shared
Mini-bus: fixed stops, shared
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

6. FMOD (3) An app-based personalized para-transit service whereby:
A customer requests a trip (origin, destination, time of travel)
The app displays a menu of options
The customer makes a choice
Making public transportation competitive
App based mobility service
Customer requests for trips (original, destination, time of travel)
App displays a menu of travel options
Customer makes a choice
Complements mass transit
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

7. Optimization and Preferences
FMOD (4)
User Experience
FMOD Server
Optimization and Preferences
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

8. FMOD (5) FMOD Algorithms Dynamic allocation of vehicles
taxi
shared
mini-bus
FMOD
server
choice
Fleet
offer
request
allocate
Customer
Maximizing
Profit / Welfare
Dynamic allocation of vehicles
Optimized assortment of modes
Based on individual level preferences
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

9. FMOD (6)
Individual level preferences are estimated and continuously updated through two interacting and repeated steps:
Online estimation: users’ preferences are updated in real-time as they make more choices.
Offline estimation: data are pooled periodically and used to update individual as well as population level parameters.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

10. The Model (1)
Discrete choice models that account for random taste variations on two levels:
Inter-consumer heterogeneity: random taste variations among individuals.
Intra-consumer heterogeneity: random taste variations among menus for a given individual.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

11. The Model (2)
McFadden’s hierarchical mixture model1 accounts for intra and inter-consumer heterogeneity by three levels of parameters:
Population-level parameters µ and Ωb: average tastes/preferences in the population and the inter-consumer variance-covariance matrix respectively.
Individual-level parameters ζn and Ωw: average tastes/preferences of a specific individual and the intra-consumer variance-covariance matrix respectively.
Menu-level parameters ηmn: to reflect menu-specific (choice specific) taste perturbations.
1Ben-Akiva, M., McFadden, D., and Train, K. (2015). Foundations of stated preference elicitation, consumer choice behavior and choice-based conjoint analysis.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

12. The Model (3)
Where:
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

13. The Model (4)
Where:
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

14. Model Estimation (1)
The model is estimated using Hierarchical Bayes (HB) and Monte Carlo Markov Chain (MCMC) with Gibbs sampling with an embedded Metropolis–Hastings (MH) algorithm 1,2.
1 Train, K. (2009), Discrete Choice Methods with Simulation, Cambridge University Press, Chapter 12.
2Ben-Akiva, M., McFadden, D., and Train, K. (2015). Foundations of stated preference elicitation, consumer choice behavior and choice-based conjoint analysis, pp. 57.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

15. Model Estimation (2) Unconditional posterior defined as: Where:
Draws from posterior distribution obtained by Gibbs sampling from five conditional posteriors.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

16. Model Estimation (3) Step I:
Normal Bayesian update of µ with a diffuse prior and ζn as the data.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

17. Model Estimation (4) Step II:
Normal Bayesian update of Ωb with a diffuse prior and ζn as the data.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

18. Model Estimation (5) Step III:
Normal Bayesian update of Ωw with a diffuse prior and ηmn as the data.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

19. Model Estimation (6) Step IV:
Normal Bayesian update of ζn with µ as a prior and ηmn as the data.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

20. Model Estimation (7) Step V: MH algorithm.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

21. Model Estimation (8) Model is tested using the Swissmetro data set1.
Nine stated choices of travel mode for each respondents offering as alternatives rail, Swissmetro, and car.
Estimation using choices 1-8 and testing on choice 9.
Random parameters used for travel cost, travel time, and headway
Money-metric utility specification.
1Bierlaire, M., Axhausen, K. and Abay, G. (2001). Acceptance of modal innovation: the case of the Swissmetro, Proceedings of the 1st Swiss Transportation Research Conference, Ascona, Switzerland.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

22. Model Estimation (9) Probability of Chosen Alternative in Menus 1-8
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

23. Model Estimation (10) Market Shares in Menus 1-8 Observed
Predicted (same dataset)
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

24. Model Estimation (11) Distribution of Random Parameters ζTime
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25. Model Estimation (12) Distribution of Random Parameters ζHeadway
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

26. Model Estimation (13) Distribution of Random Parameters
Scale parameter
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

27. Model Estimation (14)
Comparison of Single and Double Mixture Model: Probability of Chosen Alternative in Menus 1-8
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

28. Model Estimation (15) Probability of Chosen Alternative in Menu 9
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

29. Online Application (1) Continuously running MCMC:
Offline: periodically (e.g. Overnight or once every week), update all the parameters (µ, Ωb, ζn, Ωw , and ηmn) by iterating steps I through V.
Online: in real time, once a choice is made, update individual specific parameters (ζn and ηmn) using steps IV and V.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

30. Online Application (2) Compare three models:
Double mixture model estimation using menus 1-7 (representing periodical update)
Online procedure on menu 8 after double mixture model estimation on menus 1-7 (representing online update once a choice is made)
Double mixture model estimation using menus 1-8 (representing full offline procedure)
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

31. Online Application (3) Probability of Chosen Alternative in Menu 9
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

32. Conclusion
Demonstrated the application of a discrete choice model with both intra and inter-consumer heterogeneity.
Results showed significant improvements over the single mixture.
Preliminary results show the benefit from a process that combines online and offline updating.
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

33. Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015
THANK YOU!

34. APPENDIX A: Gibbs Sampling Procedure
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015
APPENDIX A: Gibbs Sampling Procedure

35. APPENDIX A (1)
Step I-a:
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

36. APPENDIX A (2)
Step I-b:
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37. APPENDIX A (3)
Step II:
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38. APPENDIX A (4)
Step III:
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39. APPENDIX A (5)
Step IV:
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40. APPENDIX A (6)
Step V:
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41. APPENDIX A (7)
Step V:
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42. APPENDIX B: Parameter Estimates in the Online Procedure
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015
APPENDIX B: Parameter Estimates in the Online Procedure

43. APPENDIX B (1) Distribution of Random Parameters
(Offline run on choices 1-7, online applied for 8th choice)
ζTime
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

44. APPENDIX B (2) Distribution of Random Parameters
(Offline run on choices 1-7, online applied for 8th choice)
ζHeadway
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015

45. APPENDIX B (3) Distribution of Random Parameters
(Offline run on choices 1-7, online applied for 8th choice)
Scale parameter
Workshop on Advances in Discrete Choice Models University of Cergy-Pontoise, December 18, 2015