546 Discrete Choice Modeling
Table 11.11 Estimated multinomial choice models (standard errors in parentheses)MNL MNPa NL (1)b NL (2)b NL (3)b HEVc RPLdαAIR 3.139
(.984)–2.769
(1.997)1.110
(.877)3.261
(.879)1.825
(.621)2.405
(2.692)6.930
(4.053)
αTRAIN 3.558
(.443)3.137
(1.0599)1.468
(.452)3.039
(.601)2.113
(.493)6.701
(2.852)17.994
(4.745)
αBUS 3.134
(.452)2.581
(.419).971
(.475)2.721
(.604)1.877
(.746)6.150
(2.483)16.556
(4.585)
αCAR .000
(0.000).000
(0.000).000
(0.000).000
(0.000).000
(0.000).000
(0.000).000
(0.000)
Term
time–.0963
(.0103)–.0548
(.0227)–.0655
(.0116)–.0742
(.00134)–.0415
(.0148)–.164
(.0799)–.385
(.0857)
Inv. time –.00379
(.00118)–.00447
(.00139)–.00422
(.000919)–.0167
(.00142)–.00767
(.00197)–.00744
(.00300)–.0241
(.00589)
Gen. cost –.00139
(.00623)–.0183
(.00827)–.000449
(.00467).00639
(.00679)–.00051
(.00340)–.0299
(.0185)–.0397
(.0238)
Income .0185
(.0108).0702
(.0398).0169
(.00691).0195
(.00878).00868
(.00389).0604
(.0456).156
(.0715)
Scale (1) 5.073
(2.172)3.097
(.627)1.278
(.289)3.400
(1.238).386
(.189).261
(.0794)
Scale (2) 1.221
(.911)1.989
(.423).197
(.0679)1.0839
(.109).745
(.376).0176
(.00564)
Scale (3) 1.000
(0.000)1.130
(.144).964
(.587).0369
(.0350)
Scale (4) 1.000
(0.000)1.000
(0.000)1.000
(0.000)
P. size –.208
(.0739)
ρ(air,
train).736
(.323)
ρ(air,
bus).649
(.475)
ρ
(train,
bus).655
(.292)lnL –193.4981 –191.8264 –178.7135 –166.3662 –190.9303 –186.1741 –168.1089aScale parameters are standard deviations.
bScale parameters are IV parameters.
cScale parameters areσj.
dScale parameters are standard deviations of random parameters.model with the variances allowed to differ across utility functions. In addition, we
introduced heteroskedasticity in the model, so that:
Var[εi,j]=σj^2 ×exp(θparty size).Finally, the last model, RPL (random parameters logit), is a random parameters
specification in which the parameters on TTME, INVT and GC are allowed to vary
randomly across individuals.