ApolloChoiceModelling forum

georkapo wrote: ↑29 Nov 2023, 12:32 Dear Stephane,

One additional question related to the previous one.
When I use a single random coefficient allowing for differences between men and women, there is a higher sd error for the attributes e.g.

> (mean(wtp_unit)); (sd(wtp_unit))
[1] 12.42137
[1] 587.157

while when I do not allow for differences between men and women, the sd is lower

> (mean(wtp_unit)); (sd(wtp_unit))
[1] 8.141867
[1] 360.8153

Thank you very much for your support.
Best regards,
Georgios

georkapo wrote: ↑01 Dec 2023, 14:39 Dear Stephane,

I have calculated two models, model A : ten random coefficients, model B : ten random coefficients and I have allowed for differences between genders in the cost coefficient

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randcoeff[["b_cost"]] = -exp( mu_log_b_cost + sigma_log_b_cost * draws_cost + (gender == 1) * ( mu_male_cost + sigma_male_cost * draws_male_cost))

Both models estimate quite similar values, however, when I calculate the wtp I get different values. Could you help with this?
here I put the results:
Model A:

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asc_A                                     2.151528     0.22276       9.658     0.26878         8.005
asc_B                                     2.211906     0.23028       9.605     0.27836         7.946
asc_C                                     0.000000          NA          NA          NA            NA
mu_b_Assistance_emergency_unit            0.030000          NA          NA          NA            NA
mu_b_Assistance_emergency_call            0.160136     0.09213       1.738     0.08260         1.939
mu_b_Assistance_smart_routes              0.577922     0.12109       4.773     0.12325         4.689
mu_b_Automatic_speed_safe_distance        0.100000          NA          NA          NA            NA
mu_b_Automatic_speed_speed_limit          0.560489     0.16221       3.455     0.17030         3.291
mu_b_Automatic_speed_risky_areas          0.345235     0.16378       2.108     0.16818         2.053
mu_b_Collision_avoidance_front_side       0.100000          NA          NA          NA            NA
mu_b_Collision_avoidance_rear_side        0.345127     0.09592       3.598     0.09306         3.709
mu_b_Collision_avoidance_blind_spot       0.346942     0.10482       3.310     0.10468         3.314
mu_log_b_cost                            -4.908550     0.07708     -63.678     0.08272       -59.337
sigma_b_Assistance_emergency_unit        -0.680916     0.18195      -3.742     0.18564        -3.668
sigma_b_Assistance_emergency_call        -0.444675     0.24878      -1.787     0.26330        -1.689
sigma_b_Assistance_smart_routes           1.300542     0.17620       7.381     0.19487         6.674
sigma_b_Automatic_speed_safe_distance     0.913538     0.18647       4.899     0.19675         4.643
sigma_b_Automatic_speed_speed_limit       0.540927     0.20983       2.578     0.20854         2.594
sigma_b_Automatic_speed_risky_areas      -0.689575     0.17069      -4.040     0.16743        -4.119
sigma_b_Collision_avoidance_front_side   -0.725422     0.17067      -4.251     0.16538        -4.386
sigma_b_Collision_avoidance_rear_side     0.465637     0.23245       2.003     0.22063         2.110
sigma_b_Collision_avoidance_blind_spot   -0.934059     0.16729      -5.584     0.17004        -5.493
sigma_log_b_cost                         -1.167197     0.07783     -14.996     0.08466       -13.787

Model B

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asc_A                                      2.12731     0.20462      10.396     0.25029         8.499
asc_B                                      2.19177     0.21065      10.405     0.25676         8.536
asc_C                                      0.00000          NA          NA          NA            NA
mu_b_Assistance_emergency_unit             0.03000          NA          NA          NA            NA
mu_b_Assistance_emergency_call             0.13904     0.08710       1.596     0.08286         1.678
mu_b_Assistance_smart_routes               0.53068     0.11150       4.760     0.11510         4.611
mu_b_Automatic_speed_safe_distance         0.10000          NA          NA          NA            NA
mu_b_Automatic_speed_speed_limit           0.54664     0.15187       3.599     0.15773         3.466
mu_b_Automatic_speed_risky_areas           0.31619     0.15504       2.039     0.15844         1.996
mu_b_Collision_avoidance_front_side        0.10000          NA          NA          NA            NA
mu_b_Collision_avoidance_rear_side         0.32022     0.08860       3.614     0.09112         3.514
mu_b_Collision_avoidance_blind_spot        0.29924     0.09811       3.050     0.09934         3.012
mu_log_b_cost                             -5.09219     0.07935     -64.176     0.09669       -52.668
mu_male_cost                              -0.26587     0.10362      -2.566     0.12654        -2.101
sigma_b_Assistance_emergency_unit         -0.46741     0.18346      -2.548     0.23588        -1.982
sigma_b_Assistance_emergency_call         -0.53741     0.14835      -3.623     0.15022        -3.578
sigma_b_Assistance_smart_routes           -1.30353     0.16783      -7.767     0.23157        -5.629
sigma_b_Automatic_speed_safe_distance      0.92836     0.17130       5.419     0.20661         4.493
sigma_b_Automatic_speed_speed_limit       -0.40859     0.15645      -2.612     0.15647        -2.611
sigma_b_Automatic_speed_risky_areas        0.62139     0.14442       4.303     0.15242         4.077
sigma_b_Collision_avoidance_front_side     0.60242     0.16110       3.739     0.17589         3.425
sigma_b_Collision_avoidance_rear_side     -0.35168     0.20753      -1.695     0.24409        -1.441
sigma_b_Collision_avoidance_blind_spot    -0.95595     0.14599      -6.548     0.17027        -5.614
sigma_log_b_cost                           1.34944     0.08403      16.058     0.09832        13.724
sigma_male_cost                            0.54037     0.08825       6.124     0.10083         5.359

Estimation of the WTP:
Model A :

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> (mean(wtp_routes)); (sd(wtp_routes))
[1] 154.4723
[1] 734.7984

Model B :

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> (mean(wtp_routes)); (sd(wtp_routes))
[1] 263.9358
[1] 2040.514

I calculate the wtp with the same approach by using apollo_unconditionals.
There is a big difference, while the coefficients are similar. Could you give any insights on this?

I really appreciate any hint. Thank you in advance.

Best regards,
Georgios

your second model allows for differences in cost sensitivity between men and women, so it's quite normal that you would get differences in the WTP. Does that not make sense to you?

wtp_routes  <- -(unconditionals[["Assistance_smart_routes"]]/unconditionals[["b_cost"]])

wtp_male_Assistance_smart_routes <- (unconditionals[["Assistance_smart_routes"]])/(unconditionals[["b_cost"]]) + (unconditionals[["Assistance_smart_routes"]])/(unconditionals[["b_cost"]]+model$estimate["mu_male_cost"]/model$estimate["sigma_male_cost"])