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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
0 Introduction1 Methodology2 Binary Choice3 Panel Data4 Bivariate Probit5 Ordered Choice6 Count Data7 Multinomial Choice8 Nested Logit9 Heterogeneity10 Latent Class11 Mixed Logit12 Stated Preference13 Hybrid Choice
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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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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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Discrete Choice Modeling
Stated Preference
Application
Survey sample of 2,688 trips, 2 or 4 choices per situationSample consists of 672 individualsChoice 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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Discrete Choice Modeling
Stated Preference
Application: Shoe Brand Choice
Simulated 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
Heterogeneity: Sex (Male=1), Age (<25, 25-39, 40+)
Underlying data generated by a 3 class latent class process (100, 200, 100 in classes)
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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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Discrete Choice Modeling
Stated Preference
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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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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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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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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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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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Discrete Choice Modeling
Stated Preference
An Underlying Random Utility Model
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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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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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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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Discrete Choice Modeling
Stated Preference
Attribute Space: Conventional
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Discrete Choice Modeling
Stated Preference
Attribute Space: Electric
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Discrete Choice Modeling
Stated Preference
Attribute Space: Alternative
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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference
Choice StrategyHensher, 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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Discrete Choice Modeling
Stated Preference
Decision Strategy inMultinomial Choice
1 J
1 K
1 M
ij j i
Choice Situation: Alternatives A ,...,A
Attributes of the choices: x ,...,x
Characteristics of the individual: z ,...,z
Random utility functions: U(j| , ) = U( , ,x z x z
j
j m
)
Choice probability model: Prob(choice=j)=Prob(U U ) m j
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Discrete Choice Modeling
Stated Preference
Multinomial Logit Model
ij j i
J
ij j ij 1
exp[ ]Prob(choice j)
exp[ ]
Behavioral model assumes
(1) Utility maximization (and the underlying micro- theory)
(2) Individual pays attention to all attributes. That is the
z
z
βx
βx
implication of the nonzero .β
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Discrete Choice Modeling
Stated Preference
Individual Explicitly Ignores AttributesHensher, 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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Discrete Choice Modeling
Stated Preference
Stated Choice Experiment
Ancillary questions: Did you ignore any of these attributes?
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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 xij – xil, 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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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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Discrete Choice Modeling
Stated Preference
Stated Choice Experiment
Individuals seem to be ignoring attributes. Uncertain to the analyst
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Discrete Choice Modeling
Stated Preference
The 2K 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 2K candidate coefficient vectors
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Discrete Choice Modeling
Stated Preference
A Latent Class Model
4
5
61 2 3
4 5
4 6
5 6
4 5 6
Free Flow Slowed Start / Stop
0 0 0
0 0
0 0Uncertainty Toll Cost Running Cost
0 0
0
0
0
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Discrete Choice Modeling
Stated Preference
Results for the 2K model
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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference
Choice Model with 6 Attributes
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Discrete Choice Modeling
Stated Preference
Stated Choice Experiment
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Discrete Choice Modeling
Stated Preference
Latent Class Model – Prior Class Probabilities
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Discrete Choice Modeling
Stated Preference
Latent Class Model – Posterior Class Probabilities
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Discrete Choice Modeling
Stated Preference
6 attributes implies 64 classes. Strategy to reduce the computational burden on a small sample
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Discrete Choice Modeling
Stated Preference
Posterior probabilities of membership in the nonattendance class for 6 models
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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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Discrete Choice Modeling
Stated Preference
Experimental Design
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Discrete Choice Modeling
Stated Preference
Application
Survey sample of 2,688 trips, 2 or 4 choices per situationSample consists of 672 individualsChoice 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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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
[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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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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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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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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Discrete Choice Modeling
Stated Preference
Attribute Space: Conventional
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Discrete Choice Modeling
Stated Preference
Attribute Space: Electric
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Discrete Choice Modeling
Stated Preference
Attribute Space: Alternative
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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference
Experimental Design
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Discrete Choice Modeling
Stated Preference
SP Study Using WTP Space
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Discrete Choice Modeling
Stated Preference
Rank Data and Best/Worst
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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference
Rank Data and Exploded Logit
Alt 1 is the best overall
Alt 3 is the best amongremaining 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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Discrete Choice Modeling
Stated Preference
Exploded Logit
U[j] = jth favorite alternative among 5 alternatives
U[1] = the choice made if the individual indicates only the favorite
Prob{j = [1],[2],[3],[4],[5]} = Prob{[1]|choice set = [1]...[5]}
Prob{[2]|choice set = [2]...[5]}
Prob{[3]|choice set = [3]...[5]}
Prob{[4]|choice set = [4],[5]}
1
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Discrete Choice Modeling
Stated Preference
Exploded LogitU[j] = jth favorite alternative among 5 alternatives
U[1] = the choice made if the individual indicates only the favorite
Individual ranked the alternatives 1,3,5,2,4
Prob{This set of ranks}
31
1,2,3,4,5 2,3,4,5
5 2
2,4,5 2,4
exp( )exp( ) =
exp( ) exp( )
exp( ) exp( ) 1
exp( ) exp( )
j jj j
j jj j
xx
x x
x x
x x
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Discrete Choice Modeling
Stated Preference
Best Worst Individual simultaneously ranks best and worst
alternatives. Prob(alt j) = best = exp[U(j)] / mexp[U(m)]
Prob(alt k) = worst = exp[-U(k)] / mexp[-U(m)]
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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference
Choices
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Discrete Choice Modeling
Stated Preference
Best
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Discrete Choice Modeling
Stated Preference
Worst
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Discrete Choice Modeling
Stated Preference
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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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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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Discrete Choice Modeling
Stated Preference
Nested Logit Approach.
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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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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference
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Discrete Choice Modeling
Stated Preference