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Explore Nested Logit models in transportation choice analysis, overcome errors in MNL models, and learn about nested choice structures and simultaneous estimation methods. Dive into Swissmetro examples and Biogeme implementations.
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GEV GEV models have the advantage that the choice probabilities usually take a closed form
The most widely used member of the GEV family is the Nested Logit
The Problem The common error components creates a covariance between the total error for bus and LRT This covariance violates the assumption underlying the MNL model
Nested logit model • Group similar alternatives in nests • Two-level choice: • Choice of nest • Choice of alternative within nest
Lower level model • Conditional probability • Choice between bus alternatives • Conditional on choice of the nest
Upper level model • Choice between car and bus • represents both bus alternatives • Nest systematic utility • Expected value of maximum utility • Define Vbusas the expected maximum utility of red bus and blue bus
Expected maximum utility • For i.i.d Gumbel errors • Inclusive value • Where µb is the scale parameter for the MNL associated with the choice between red bus and blue bus
Variance-covariance structure • MNL • NL
Simultaneous estimation Sequential estimation: Estimation of NL decomposed into two estimations of MNL Estimator is consistent but not efficient Simultaneous estimation: Log-likelihood function is generally non concave No guarantee of global maximum Estimator asymptotically efficient
Swissmetro example • MNL
Swissmetro example (2) • NL: model 1
Swissmetro example (3) • NL: model 2
NL in Biogeme • Specify nesting structure [NLNests] // Name paramvalue LowerBound UpperBound status list of alt Existing 1.0 1 10 0 1 3 Future 1.0 1 10 1 2 • Select model [Model] $NL • Nesting constraints [ConstraintNestCoef] // (CarNest = BusNest)
