[part 12] 1/38 discrete choice modeling stated preference discrete choice modeling william greene...

[Part 12] 1/38

Discrete Choice Modeling

Stated Preference


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

[Part 12] 2/38


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

[Part 12] 3/38


Stated Preference

Panel Data

Repeated Choice Situations Typically RP/SP constructions (experimental) Accommodating “panel data”

Multinomial Probit [marginal, impractical] Latent Class Mixed Logit

[Part 12] 4/38


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

[Part 12] 5/38


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)

[Part 12] 6/38


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

[Part 12] 7/38


Stated Preference

[Part 12] 8/38


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?

[Part 12] 9/38


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.

[Part 12] 10/38


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.

[Part 12] 11/38


Stated Preference

Stated Preference Data

Pure hypothetical – does the subject take it seriously?

No necessary anchor to real market situations

Vast heterogeneity across individuals

[Part 12] 12/38


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)

[Part 12] 13/38


Stated Preference

An Underlying Random Utility Model

[Part 12] 14/38


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.

[Part 12] 15/38


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

[Part 12] 16/38


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

[Part 12] 17/38


Stated Preference

Attribute Space: Conventional

[Part 12] 18/38


Stated Preference

Attribute Space: Electric

[Part 12] 19/38


Stated Preference

Attribute Space: Alternative

[Part 12] 20/38


Stated Preference

[Part 12] 21/38


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.

[Part 12] 22/38


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

[Part 12] 23/38


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

[Part 12] 24/38


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.

[Part 12] 25/38


Stated Preference

Stated Choice Experiment

Ancillary questions: Did you ignore any of these attributes?

[Part 12] 26/38


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

[Part 12] 27/38


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.

[Part 12] 28/38


Stated Preference


Individuals seem to be ignoring attributes. Uncertain to the analyst

[Part 12] 29/38


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

[Part 12] 30/38


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

[Part 12] 31/38


Stated Preference

Results for the 2K model

[Part 12] 32/38


Stated Preference

[Part 12] 33/38


Stated Preference

Choice Model with 6 Attributes

[Part 12] 34/38


Stated Preference


[Part 12] 35/38


Stated Preference

Latent Class Model – Prior Class Probabilities

[Part 12] 36/38


Stated Preference

Latent Class Model – Posterior Class Probabilities

[Part 12] 37/38


Stated Preference

6 attributes implies 64 classes. Strategy to reduce the computational burden on a small sample

[Part 12] 38/38


Stated Preference

Posterior probabilities of membership in the nonattendance class for 6 models

[Part 12] 39/38


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] 40/38


Stated Preference

Experimental Design

[Part 12] 41/38


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

[Part 12] 42/38


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


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?

[Part 12] 44/38


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

[Part 12] 45/38


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

[Part 12] 46/38


Stated Preference

Fuel Types Study

Conventional, Electric, Alternative 1,400 Sydney Households Automobile choice survey RP + 3 SP fuel classes

[Part 12] 47/38


Stated Preference

Attribute Space: Conventional

[Part 12] 48/38


Stated Preference

Attribute Space: Electric

[Part 12] 49/38


Stated Preference

Attribute Space: Alternative

[Part 12] 50/38


Stated Preference

[Part 12] 51/38


Stated Preference

Experimental Design

[Part 12] 52/38


Stated Preference

SP Study Using WTP Space

[Part 12] 53/38


Stated Preference

Rank Data and Best/Worst

[Part 12] 54/38


Stated Preference

[Part 12] 55/38


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.

[Part 12] 56/38


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

[Part 12] 57/38


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

[Part 12] 58/38


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)]

[Part 12] 59/38


Stated Preference

[Part 12] 60/38


Stated Preference

Choices

[Part 12] 61/38


Stated Preference

Best

[Part 12] 62/38


Stated Preference

Worst

[Part 12] 63/38


Stated Preference

[Part 12] 64/38


Stated Preference

Uses the result that if U(i,j) is the lowest utility, -U(i,j) is the highest.

[Part 12] 65/38


Stated Preference

Uses the result that if U(i,j) is the lowest utility, -U(i,j) is the highest.

[Part 12] 66/38


Stated Preference

Nested Logit Approach.

[Part 12] 67/38


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

[Part 12] 68/38


Stated Preference

[Part 12] 69/38


Stated Preference

[Part 12] 70/38


Stated Preference

[part 12] 1/38 discrete choice modeling stated preference discrete choice modeling william greene...

Documents

multinomial choice

ordered choice

binary choice

choice sets slide

hybrid choice slide

count data

enriched rpsp mixed

egress time slide