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[Part 12] 1/38 Discrete Choice Modeling Stated Preference Discrete Choice Modeling William Greene Stern School of Business New York University 0Introduction 1Methodology 2Binary Choice 3Panel Data 4Bivariate Probit 5Ordered Choice 6Count Data 7Multinomial Choice 8Nested Logit 9Heterogeneity 10Latent Class 11Mixed Logit 12Stated Preference 13Hybrid Choice

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[Part 12] 2/38 Discrete Choice Modeling Stated Preference Revealed and Stated Preference Data Pure RP Data Market (ex-post, e.g., supermarket scanner data) Individual observations Pure SP Data Contingent valuation (?) Validity Combined (Enriched) RP/SP Mixed data Expanded choice sets

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[Part 12] 3/38 Discrete Choice Modeling Stated Preference Panel Data Repeated Choice Situations Typically RP/SP constructions (experimental) Accommodating panel data Multinomial Probit [marginal, impractical] Latent Class Mixed Logit

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[Part 12] 4/38 Discrete Choice Modeling Stated Preference Application Survey sample of 2,688 trips, 2 or 4 choices per situation Sample consists of 672 individuals Choice based sample Revealed/Stated choice experiment: Revealed: Drive,ShortRail,Bus,Train Hypothetical: Drive,ShortRail,Bus,Train,LightRail,ExpressBus Attributes: Cost –Fuel or fare Transit time Parking cost Access and Egress time

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[Part 12] 5/38 Discrete Choice Modeling Stated Preference Application: Shoe Brand Choice S imulated Data: Stated Choice, 400 respondents, 8 choice situations, 3,200 observations 3 choice/attributes + NONE Fashion = High / Low Quality = High / Low Price = 25/50/75,100 coded 1,2,3,4 H eterogeneity: Sex (Male=1), Age (<25, 25-39, 40+) U nderlying data generated by a 3 class latent class process (100, 200, 100 in classes)

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[Part 12] 6/38 Discrete Choice Modeling Stated Preference Stated Choice Experiment: Unlabeled Alternatives, One Observation t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8

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[Part 12] 7/38 Discrete Choice Modeling Stated Preference

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[Part 12] 8/38 Discrete Choice Modeling Stated Preference Pooling RP and SP Data Sets - 1 Enrich the attribute set by replicating choices E.g.: RP: Bus,Car,Train (actual) SP: Bus(1),Car(1),Train(1) Bus(2),Car(2),Train(2),… How to combine?

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[Part 12] 9/38 Discrete Choice Modeling Stated Preference Each person makes four choices from a choice set that includes either two or four alternatives. The first choice is the RP between two of the RP alternatives The second-fourth are the SP among four of the six SP alternatives. There are ten alternatives in total.

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[Part 12] 10/38 Discrete Choice Modeling Stated Preference Revealed Preference Data Advantage: Actual observations on actual behavior Disadvantage: Limited range of choice sets and attributes – does not allow analysis of switching behavior.

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[Part 12] 11/38 Discrete Choice Modeling Stated Preference Stated Preference Data Pure hypothetical – does the subject take it seriously? No necessary anchor to real market situations Vast heterogeneity across individuals

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[Part 12] 12/38 Discrete Choice Modeling Stated Preference Customers Choice of Energy Supplier California, Stated Preference Survey 361 customers presented with 8-12 choice situations each Supplier attributes: Fixed price: cents per kWh Length of contract Local utility Well-known company Time-of-day rates (11¢ in day, 5¢ at night) Seasonal rates (10¢ in summer, 8¢ in winter, 6¢ in spring/fall)

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[Part 12] 13/38 Discrete Choice Modeling Stated Preference An Underlying Random Utility Model

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[Part 12] 14/38 Discrete Choice Modeling Stated Preference Nested Logit Approach Car Train Bus SPCar SPTrain SPBus RP Mode Use a two level nested model, and constrain three SP IV parameters to be equal.

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[Part 12] 15/38 Discrete Choice Modeling Stated Preference Enriched Data Set – Vehicle Choice Choosing between Conventional, Electric and LPG/CNG Vehicles in Single-Vehicle Households David A. Hensher William H. Greene Institute of Transport Studies Department of Economics School of Business Stern School of Business The University of Sydney New York University NSW 2006 Australia New York USA September 2000

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[Part 12] 16/38 Discrete Choice Modeling Stated Preference Fuel Types Study Conventional, Electric, Alternative 1,400 Sydney Households Automobile choice survey RP + 3 SP fuel classes Nested logit – 2 level approach – to handle the scaling issue

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[Part 12] 17/38 Discrete Choice Modeling Stated Preference Attribute Space: Conventional

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[Part 12] 18/38 Discrete Choice Modeling Stated Preference Attribute Space: Electric

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[Part 12] 19/38 Discrete Choice Modeling Stated Preference Attribute Space: Alternative

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[Part 12] 20/38 Discrete Choice Modeling Stated Preference

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[Part 12] 21/38 Discrete Choice Modeling Stated Preference Choice Strategy Hensher, D.A., Rose, J. and Greene, W. (2005) The Implications on Willingness to Pay of Respondents Ignoring Specific Attributes (DoD#6) Transportation, 32 (3), 203-222. Hensher, D.A. and Rose, J.M. (2009) Simplifying Choice through Attribute Preservation or Non-Attendance: Implications for Willingness to Pay, Transportation Research Part E, 45, 583- 590. Rose, J., Hensher, D., Greene, W. and Washington, S. Attribute Exclusion Strategies in Airline Choice: Accounting for Exogenous Information on Decision Maker Processing Strategies in Models of Discrete Choice, Transportmetrica, 2011 Hensher, D.A. and Greene, W.H. (2010) Non-attendance and dual processing of common-metric attributes in choice analysis: a latent class specification, Empirical Economics 39 (2), 413-426 Campbell, D., Hensher, D.A. and Scarpa, R. Non-attendance to Attributes in Environmental Choice Analysis: A Latent Class Specification, Journal of Environmental Planning and Management, proofs 14 May 2011. Hensher, D.A., Rose, J.M. and Greene, W.H. Inferring attribute non-attendance from stated choice data: implications for willingness to pay estimates and a warning for stated choice experiment design, 14 February 2011, Transportation, online 2 June 2001 DOI 10.1007/s11116- 011-9347-8.

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[Part 12] 22/38 Discrete Choice Modeling Stated Preference Decision Strategy in Multinomial Choice

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[Part 12] 23/38 Discrete Choice Modeling Stated Preference Multinomial Logit Model

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[Part 12] 24/38 Discrete Choice Modeling Stated Preference Individual Explicitly Ignores Attributes Hensher, D.A., Rose, J. and Greene, W. (2005) The Implications on Willingness to Pay of Respondents Ignoring Specific Attributes (DoD#6) Transportation, 32 (3), 203-222. Hensher, D.A. and Rose, J.M. (2009) Simplifying Choice through Attribute Preservation or Non-Attendance: Implications for Willingness to Pay, Transportation Research Part E, 45, 583-590. Rose, J., Hensher, D., Greene, W. and Washington, S. Attribute Exclusion Strategies in Airline Choice: Accounting for Exogenous Information on Decision Maker Processing Strategies in Models of Discrete Choice, Transportmetrica, 2011 Choice situations in which the individual explicitly states that they ignored certain attributes in their decisions.

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[Part 12] 25/38 Discrete Choice Modeling Stated Preference Stated Choice Experiment Ancillary questions: Did you ignore any of these attributes?

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[Part 12] 26/38 Discrete Choice Modeling Stated Preference Appropriate Modeling Strategy Fix ignored attributes at zero? Definitely not! Zero is an unrealistic value of the attribute (price) The probability is a function of x ij – x il, so the substitution distorts the probabilities Appropriate model: for that individual, the specific coefficient is zero – consistent with the utility assumption. A person specific, exogenously determined model Surprisingly simple to implement

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[Part 12] 27/38 Discrete Choice Modeling Stated Preference Individual Implicitly Ignores Attributes Hensher, D.A. and Greene, W.H. (2010) Non-attendance and dual processing of common-metric attributes in choice analysis: a latent class specification, Empirical Economics 39 (2), 413-426 Campbell, D., Hensher, D.A. and Scarpa, R. Non-attendance to Attributes in Environmental Choice Analysis: A Latent Class Specification, Journal of Environmental Planning and Management, proofs 14 May 2011. Hensher, D.A., Rose, J.M. and Greene, W.H. Inferring attribute non-attendance from stated choice data: implications for willingness to pay estimates and a warning for stated choice experiment design, 14 February 2011, Transportation, online 2 June 2001 DOI 10.1007/s11116-011-9347-8.

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[Part 12] 28/38 Discrete Choice Modeling Stated Preference Stated Choice Experiment Individuals seem to be ignoring attributes. Uncertain to the analyst

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[Part 12] 29/38 Discrete Choice Modeling Stated Preference The 2 K model The analyst believes some attributes are ignored. There is no indicator. Classes distinguished by which attributes are ignored Same model applies, now a latent class. For K attributes there are 2 K candidate coefficient vectors

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[Part 12] 30/38 Discrete Choice Modeling Stated Preference A Latent Class Model

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[Part 12] 31/38 Discrete Choice Modeling Stated Preference Results for the 2 K model

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[Part 12] 32/38 Discrete Choice Modeling Stated Preference

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[Part 12] 33/38 Discrete Choice Modeling Stated Preference Choice Model with 6 Attributes

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[Part 12] 34/38 Discrete Choice Modeling Stated Preference Stated Choice Experiment

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[Part 12] 35/38 Discrete Choice Modeling Stated Preference Latent Class Model – Prior Class Probabilities

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[Part 12] 36/38 Discrete Choice Modeling Stated Preference Latent Class Model – Posterior Class Probabilities

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[Part 12] 37/38 Discrete Choice Modeling Stated Preference 6 attributes implies 64 classes. Strategy to reduce the computational burden on a small sample

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[Part 12] 38/38 Discrete Choice Modeling Stated Preference Posterior probabilities of membership in the nonattendance class for 6 models

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[Part 12] 39/38 Discrete Choice Modeling Stated Preference Mixed Logit Approaches Pivot SP choices around an RP outcome. Scaling is handled directly in the model Continuity across choice situations is handled by random elements of the choice structure that are constant through time Preference weights – coefficients Scaling parameters Variances of random parameters Overall scaling of utility functions

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[Part 12] 40/38 Discrete Choice Modeling Stated Preference Experimental Design

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[Part 12] 41/38 Discrete Choice Modeling Stated Preference Application Survey sample of 2,688 trips, 2 or 4 choices per situation Sample consists of 672 individuals Choice based sample Revealed/Stated choice experiment: Revealed: Drive,ShortRail,Bus,Train Hypothetical: Drive,ShortRail,Bus,Train,LightRail,ExpressBus Attributes: Cost –Fuel or fare Transit time Parking cost Access and Egress time

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[Part 12] 42/38 Discrete Choice Modeling Stated Preference Mixed Logit Approaches Pivot SP choices around an RP outcome. Scaling is handled directly in the model Continuity across choice situations is handled by random elements of the choice structure that are constant through time Preference weights – coefficients Scaling parameters Variances of random parameters Overall scaling of utility functions

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[Part 12] 43/38 Discrete Choice Modeling Stated Preference Pooling RP and SP Data Sets Enrich the attribute set by replicating choices E.g.: RP: Bus,Car,Train (actual) SP: Bus(1),Car(1),Train(1) Bus(2),Car(2),Train(2),… How to combine?

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[Part 12] 44/38 Discrete Choice Modeling Stated Preference Each person makes four choices from a choice set that includes either 2 or 4 alternatives. The first choice is the RP between two of the 4 RP alternatives The second-fourth are the SP among four of the 6 SP alternatives. There are 10 alternatives in total. A Stated Choice Experiment with Variable Choice Sets

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[Part 12] 45/38 Discrete Choice Modeling Stated Preference Enriched Data Set – Vehicle Choice Choosing between Conventional, Electric and LPG/CNG Vehicles in Single-Vehicle Households David A. Hensher William H. Greene Institute of Transport Studies Department of Economics School of Business Stern School of Business The University of Sydney New York University NSW 2006 Australia New York USA September 2000

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[Part 12] 46/38 Discrete Choice Modeling Stated Preference Fuel Types Study Conventional, Electric, Alternative 1,400 Sydney Households Automobile choice survey RP + 3 SP fuel classes

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[Part 12] 47/38 Discrete Choice Modeling Stated Preference Attribute Space: Conventional

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[Part 12] 48/38 Discrete Choice Modeling Stated Preference Attribute Space: Electric

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[Part 12] 49/38 Discrete Choice Modeling Stated Preference Attribute Space: Alternative

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[Part 12] 50/38 Discrete Choice Modeling Stated Preference

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[Part 12] 51/38 Discrete Choice Modeling Stated Preference Experimental Design

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[Part 12] 52/38 Discrete Choice Modeling Stated Preference SP Study Using WTP Space

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[Part 12] 53/38 Discrete Choice Modeling Stated Preference Rank Data and Best/Worst

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[Part 12] 54/38 Discrete Choice Modeling Stated Preference

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[Part 12] 55/38 Discrete Choice Modeling Stated Preference Rank Data and Exploded Logit Alt 1 is the best overall Alt 3 is the best among remaining alts 2,3,4,5 Alt 5 is the best among remaining alts 2,4,5 Alt 2 is the best among remaining alts 2,4 Alt 4 is the worst.

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[Part 12] 56/38 Discrete Choice Modeling Stated Preference Exploded Logit

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[Part 12] 57/38 Discrete Choice Modeling Stated Preference Exploded Logit

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[Part 12] 58/38 Discrete Choice Modeling Stated Preference Best Worst Individual simultaneously ranks best and worst alternatives. Prob(alt j) = best = exp[U(j)] / m exp[U(m)] Prob(alt k) = worst = exp[-U(k)] / m exp[-U(m)]

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[Part 12] 59/38 Discrete Choice Modeling Stated Preference

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[Part 12] 60/38 Discrete Choice Modeling Stated Preference Choices

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[Part 12] 61/38 Discrete Choice Modeling Stated Preference Best

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[Part 12] 62/38 Discrete Choice Modeling Stated Preference Worst

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[Part 12] 63/38 Discrete Choice Modeling Stated Preference

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[Part 12] 64/38 Discrete Choice Modeling Stated Preference Uses the result that if U(i,j) is the lowest utility, -U(i,j) is the highest.

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[Part 12] 65/38 Discrete Choice Modeling Stated Preference Uses the result that if U(i,j) is the lowest utility, -U(i,j) is the highest.

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[Part 12] 66/38 Discrete Choice Modeling Stated Preference Nested Logit Approach.

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[Part 12] 67/38 Discrete Choice Modeling Stated Preference Nested Logit Approach – Different Scaling for Worst 8 choices are two blocks of 4. Best in one brance, worst in the second branch

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[Part 12] 68/38 Discrete Choice Modeling Stated Preference

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[Part 12] 69/38 Discrete Choice Modeling Stated Preference

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[Part 12] 70/38 Discrete Choice Modeling Stated Preference

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Discrete Choice Modeling William Greene Stern School of Business New York University.

Discrete Choice Modeling William Greene Stern School of Business New York University.

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