I recently read Article “Hess et al. (2018) - Analysis of mode choice for intercity travel: Application of a hybrid choice model to two distinct US corridors)” in which the Hybrid Choice Model was estimated using the Bayesian approach.Now I wanted to try estimating a HCM using HB and used Apollo example 25. However, I have found that the model results between Maximum Simulated Likelihood (MSL) and Bayes differ quite a lot.
MSL:
Code: Select all
Estimates:
Estimate Std.err. t.ratio(0) Rob.std.err. Rob.t.ratio(0)
b_brand_Artemis 0.0000 NA NA NA NA
b_brand_Novum -0.2767 0.0308 -8.98 0.0319 -8.66
b_brand_BestValue -0.5811 0.0661 -8.78 0.0643 -9.04
b_brand_Supermarket -0.2670 0.0673 -3.97 0.0662 -4.03
b_brand_PainAway -1.2493 0.0675 -18.51 0.0655 -19.08
b_country_CH 0.6704 0.0399 16.82 0.0388 17.28
b_country_DK 0.3376 0.0382 8.83 0.0375 8.99
b_country_USA 0.0000 NA NA NA NA
b_country_IND -0.2967 0.0573 -5.18 0.0581 -5.11
b_country_RUS -0.8937 0.0617 -14.48 0.0611 -14.62
b_country_BRA -0.6558 0.0602 -10.89 0.0617 -10.62
b_char_standard 0.0000 NA NA NA NA
b_char_fast 0.7699 0.0292 26.35 0.0289 26.65
b_char_double 1.2125 0.0378 32.10 0.0366 33.12
b_risk -0.0016 0.0001 -26.99 0.0001 -26.51
b_price -0.7243 0.0181 -39.97 0.0173 -41.90
lambda 0.6586 0.0325 20.26 0.0316 20.84
gamma_reg_user -0.7451 0.0798 -9.34 0.0794 -9.38
gamma_university -0.3797 0.0738 -5.14 0.0739 -5.14
gamma_age_50 0.6735 0.0763 8.82 0.0747 9.02
zeta_quality 0.5342 0.0393 13.59 0.0387 13.82
zeta_ingredient -0.5028 0.0402 -12.51 0.0396 -12.69
zeta_patent 0.6069 0.0410 14.81 0.0384 15.80
zeta_dominance -0.3960 0.0367 -10.80 0.0351 -11.30
sigma_qual 1.0616 0.0275 38.62 0.0270 39.37
sigma_ingr 1.1088 0.0279 39.79 0.0263 42.16
sigma_pate 1.0840 0.0291 37.21 0.0275 39.48
sigma_domi 1.0445 0.0253 41.26 0.0231 45.17
Summary statistics for dependent variable for model component "NormD":
Min. 1st Qu. Median Mean 3rd Qu. Max.
-1.741 -0.741 0.259 0.000 0.259 2.259
Summary statistics for dependent variable for model component "NormD":
Min. 1st Qu. Median Mean 3rd Qu. Max.
-2.232 -0.232 -0.232 0.000 0.768 1.768
Summary statistics for dependent variable for model component "NormD":
Min. 1st Qu. Median Mean 3rd Qu. Max.
-1.806 -0.806 0.194 0.000 1.194 2.194
Summary statistics for dependent variable for model component "NormD":
Min. 1st Qu. Median Mean 3rd Qu. Max.
-2.164 -0.164 -0.164 0.000 0.836 1.836
HB:
Code: Select all
Summary of parameter chains
Non-random coefficients
Mean SD
b_brand_Artemis 0.0000 NA
b_brand_Novum -0.1006 0.0093
b_brand_BestValue -0.1751 0.0065
b_brand_Supermarket -0.0318 0.0109
b_brand_PainAway -0.5641 0.0477
b_country_CH 0.4855 0.0210
b_country_DK 0.2851 0.0266
b_country_USA 0.0000 NA
b_country_IND -0.0796 0.0069
b_country_RUS -0.4323 0.0253
b_country_BRA -0.2872 0.0111
b_char_standard 0.0000 NA
b_char_fast 0.4366 0.0235
b_char_double 0.8598 0.0402
b_risk -0.0016 0.0001
b_price -0.4972 0.0161
lambda 0.4800 0.0404
gamma_reg_user 0.2984 0.0201
gamma_university 0.1369 0.0044
gamma_age_50 0.0414 0.0123
zeta_quality 0.0297 0.0393
zeta_ingredient -0.1351 0.0240
zeta_patent 0.0908 0.0267
zeta_dominance -0.1890 0.0075
sigma_qual 1.2087 0.0146
sigma_ingr 1.1820 0.0071
sigma_pate 1.2876 0.0134
sigma_domi 1.1064 0.0110
Upper level model results for mean parameters for underlying Normals
Mean SD
eta 0 0
Upper level model results for covariance matrix for underlying Normals (means across iterations)
eta
eta 1
Upper level model results for covariance matrix for underlying Normals (SD across iterations)
eta
eta 0
Summary of distributions of random coeffients (after distributional transforms)
Mean SD
[1,] 0.0049 0.9896
Results for posterior means for random coefficients
[,1] [,2]
eta 0.1335 0.7056
I would be happy if you could take a look at the R file and give me a hint. Thanks a lot in advance!
Best wishes
Nico