ApolloChoiceModelling forum

Hi

I have specified the following model;

V = list()
V[['alt1']] = Certain *(cost_B*(asc_B + torsk_B * KT1 + Cost1 + laks_B * VL1 + bunn_B * HB1 + land_B * KL1))+(1-Certain)*(cost_T*(asc_T + torsk_T * KT1 + Cost1 + laks_T * VL1 + bunn_T * HB1 + land_T * KL1))

V[['alt2']] = Certain * (cost_B*(torsk_B * KT2 + Cost2 + laks_B * VL2 + bunn_B * HB2 + land_B * KL2))+(1-Certain)* (cost_T*(torsk_T * KT2 + Cost2 + laks_T * VL2 + bunn_T * HB2 + land_T * KL2))

V[['alt3']] = Certain * (cost_B*(torsk_B * KT3 + Cost3 + laks_B * VL3 + bunn_B * HB3 + land_B * KL3))+
(1-Certain)* (cost_T*(torsk_T * KT3 + Cost3 + laks_T * VL3 + bunn_T * HB3 + land_T * KL3))

Certain and (1-Certain) denote two different sub-samples, each with their separate attribute coefficients (_B for baseline, _T for treatment). The attributes are KT, HB, KL, VL, Cost. In addition I have an ASC in alternative 1 for each sub-sample, indicating a preference for the SQ.

When I estimate this model, one set of attribute coefficients "explode", whereas the other behave more "normal". This is an example from one estimation:

Model run using Apollo for R, version 0.2.1 on Windows by maa033
www.ApolloChoiceModelling.com

Model name : MMNL_aqua_exp
Model description : MMNL model with fixed price
Model run at : 2022-01-03 13:53:21
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 293
Number of observations : 2599

Number of cores used : 3
Number of inter-individual draws : 200 (SobolOwenFaureTezuka)

LL(start) : -2855.293
LL(0) : -2855.293
LL(final) : -1935.703
Rho-square (0) : 0.3221
Adj.Rho-square (0) : 0.3151
AIC : 3911.41
BIC : 4028.66


Estimated parameters : 20
Time taken (hh:mm:ss) : 00:11:36.62
pre-estimation : 00:00:29.09
estimation : 00:05:39.16
post-estimation : 00:05:28.37
Iterations : 192
Min abs eigenvalue of Hessian : 0.028502
Some eigenvalues of Hessian are positive, indicating potential problems!

Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_B -1.988460 NA NA NA NA
asc_T -628.727387 NA NA NA NA
cost_B -0.647537 NA NA NA NA
torsk_B_mu -1.634535 NA NA NA NA
torsk_B_sig -1.628396 NA NA NA NA
laks_B_mu -1.651847 NA NA NA NA
laks_B_sig -1.570543 NA NA NA NA
bunn_B_mu 0.185837 NA NA NA NA
bunn_B_sig 1.000276 NA NA NA NA
land_B_mu -4.838971 NA NA NA NA
land_B_sig -1.911782 NA NA NA NA
cost_T 0.005645 NA NA NA NA
torsk_T_mu -146.111788 NA NA NA NA
torsk_T_sig -134.243391 NA NA NA NA
laks_T_mu -10.857449 NA NA NA NA
laks_T_sig -0.050540 NA NA NA NA
bunn_T_mu -11.771550 NA NA NA NA
bunn_T_sig -0.783184 NA NA NA NA
land_T_mu -4.654447 NA NA NA NA
land_T_sig -13.262613 NA NA NA NA


I have run the model and got non-NAs for std.errors etc.
However, if I specify the ASCs in preference space, while letting the attributes remain in WTP-space, the estimated coefficients turn out nicely and are comparable. Hence, I wonder why the model behave OK when ASCs are NOT included in WTP-space, whereas it collapse when they are included in WTP-space? I have tried various distributions of the attributes, have tried with log-normally distributed cost parameter, a common cost-parameter, etc. The result is always the same; I have to take the ASCs out of the WTP-formulation of the model and specify them in preference space.

So I wonder if there is a way to include the ASCs in the WTP-space part of the model and still get reasonable estimation results?

Thank you in advance for any response to this request.

Margrethe

Margrethe

first, you are using an ancient version of Apollo. Could you please first update it and try again as the newer versions will use analytical derivatives which will be more stable.

second, if you are using a non-random cost coefficient, there is no reason for working in WTP space

Stephane