MIT1_201JF08_lec04

# MIT1_201JF08_lec04 - Discrete Choice Analysis II Moshe...

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Unformatted text preview: Discrete Choice Analysis II Moshe Ben-Akiva 1.201 / 11.545 / ESD.210 Transportation Systems Analysis: Demand & Economics Fall 2008 Review – Last Lecture ● Introduction to Discrete Choice Analysis ● A simple example – route choice ● The Random Utility Model – Systematic utility – Random components ● Derivation of the Probit and Logit models – Binary Probit – Binary Logit – Multinomial Logit 2 Outline – This Lecture ● Model specification and estimation ● Aggregation and forecasting ● Independence from Irrelevant Alternatives (IIA) property – Motivation for Nested Logit ● Nested Logit - specification and an example ● Appendix: – Nested Logit model specification – Advanced Choice Models 3 Specification of Systematic Components ● Types of Variables – Attributes of alternatives: Z in , e.g., travel time, travel cost – Characteristics of decision-makers: S n , e.g., age, gender, income, occupation – Therefore: X in = h(Z in , S n ) ● Examples: – X in1 = Z in1 = travel cost – X in2 = log(Z in2 ) = log (travel time) – X in3 = Z in1 /S n1 = travel cost / income ● Functional Form: Linear in the Parameters V in = β 1 X in1 + β 2 X in2 + ... + β k X inK V jn = β 1 X jn1 + β 2 X jn2 + ... + β k X jnK 4 Data Collection ● Data collection for each individual in the sample: – Choice set: available alternatives – Socio-economic characteristics – Attributes of available alternatives – Actual choice n Income Auto Time Transit Time Choice 1 35 15.4 58.2 Auto 2 45 14.2 31.0 Transit 3 37 19.6 43.6 Auto 4 42 50.8 59.9 Auto 5 32 55.5 33.8 Transit 6 15 N/A 48.4 Transit 5 Model Specification Example V auto = β + β 1 TT auto + β 2 ln(Income) V transit = β 1 TT transit β β 1 β 2 Auto 1 TT auto ln(Income) Transit 0 TT transit 0 6 Probabilities of Observed Choices ● Individual 1: V auto = β + β 1 15.4 + β 2 ln(35) V transit = β 1 58.2 e β 0 + 15.4 β 1 + ln(35) β 2 P(Auto) = e β 0 + 15.4 β 1 + ln(35) β 2 + e 58.2 β 1 ● Individual 2: V auto = β + β 1 14.2 + β 2 ln(45) V transit = β 1 31.0 e 31.0 β 1 P(Transit) = e β 0 + 14.2 β 1 + ln(45) β 2 + e 31.0 β 1 7 Maximum Likelihood Estimation ● Find the values of β that are most likely to result in the choices observed in the sample: – max L *( β ) = P 1 (Auto) P 2 (Transit)… P 6 (Transit) 0, if person 1, if person n chose alternative i ● If y in = n chose alternative j ● Then we maximize, over choices of { β 1 , β 2 …, β k }, the following expression: N L * ( β 1 , β 2 ,..., β k ) = ∏ P n ( i ) y in P n ( j ) y jn n = 1 ● β * = arg max β L* ( β 1 , β 2 ,…, β k ) = arg max β log L* ( β 1 , β 2 , …, β k ) 8 Sources of Data on User Behavior ● Revealed Preferences Data – Travel Diaries – Field Tests ● Stated Preferences Data – Surveys – Simulators 9 Stated Preferences / Conjoint Experiments ● Used for product design and pricing – For products with significantly different attributes...
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MIT1_201JF08_lec04 - Discrete Choice Analysis II Moshe...

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