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WTW space with random coefficients

Ask questions about model specifications. Ideally include a mathematical explanation of your proposed model.
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Anna_Edenbrandt
Posts: 6
Joined: 27 Apr 2020, 20:01

WTW space with random coefficients

Post by Anna_Edenbrandt »

Hello
I want to estimate an RPL model in wtp space, where all wtp-parameters should be specified to take normal distributions, and the cost-parameter to take a lognormal distribution. First, I am estimating MNL models to figure out the wtp-space specification.
This works nicely with the specification below. However, this gives the SQ-parameter is preference space, not a wtp estimate. I have seen in the examples that you provide (example 16) that this is how you specify the ASCs.
V = list()
V[['alt_A']] = b_price * ( w_alt_A + w_org*org1 + price1 )
V[['alt_B']] = b_price * ( w_alt_B + w_org*org2 + price2 )
V[['alt_C']] = b_price * ( w_alt_C + w_org*org3 + price3 )
V[['alt_sq']] = b_sq
(w_alt_A=fixed to 0)
However, I want to estimate the SQ-parameter ("Don't buy") in wtp-space. This is what I obtain with the “mixlogitwtp”-command in STATA. My attempts to do so in Apollo have failed, and I therefore ask for your kind advice on what I do wrong. In the specifications below, I get “Inf” for all standard errors.
V = list()
V[['alt_A']] = b_price * ( w_alt_A + w_org*org1 + price1 )
V[['alt_B']] = b_price * ( w_alt_B + w_org*org2 + price2 )
V[['alt_C']] = b_price * ( w_alt_C + w_org*org3 + price3 )
V[['alt_sq']] = b_price * ( w_sq )

V = list()
V[['alt_A']] = b_price * ( w_alt_A + w_org*org1 + price1 )
V[['alt_B']] = b_price * ( w_alt_B + w_org*org2 + price2 )
V[['alt_C']] = b_price * ( w_alt_C + w_org*org3 + price3 )
V[['alt_sq']] = b_price * ( w_sq + price4 )
(price4=0 for all tasks.)

Thank you very much in advance!
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stephanehess
Site Admin
Posts: 1049
Joined: 24 Apr 2020, 16:29

Re: wtp space

Post by stephanehess »

Hi Anna

your specification looks correct, but if price4==0 for all, then you can just write:

V = list()
V[['alt_A']] = b_price * ( w_alt_A + w_org*org1 + price1 )
V[['alt_B']] = b_price * ( w_alt_B + w_org*org2 + price2 )
V[['alt_C']] = b_price * ( w_alt_C + w_org*org3 + price3 )
V[['alt_sq']] = b_price * w_sq

Can you show us the output for both models, please?

Also, I assume you mean negative Lognormal for price?

Best wishes

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk
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Anna_Edenbrandt
Posts: 6
Joined: 27 Apr 2020, 20:01

Re: wtp space

Post by Anna_Edenbrandt »

Dear Stephane

Thank you very much for the quick response!
Yes, true, I meant negative lognormal distribution for the cost parameter.

The following model specification and results are with the sq-parameter in wtp-space:
V = list()
V[['beef']] = b_price * ( w_beef + w_org*org1 + price1 )
V[['bp73']] = b_price * ( w_bp73 + w_org*org2 + price2 )
V[['bp55']] = b_price * ( w_bp55 + w_org*org3 + price3 )
V[['bbean']] = b_price * ( w_bbean + w_org*org4 + price4 )
V[['chick']] = b_price * ( w_chick + w_org*org5 + price5 )
V[['veg']] = b_price * ( w_veg + w_org*org6 + price6 )
V[['sq']] = b_price * w_sq

Number of individuals : 514
Number of observations : 3084
LL(start) : -6001.187
LL(0) : -6001.187
LL(final) : -5447.274
Estimate Std.err. t.ratio(0) Rob.std.err. Rob.t.ratio(0)
w_beef 0.0000 NA NA NA NA
w_bp73 -346.4327 Inf 0 NaN NaN
w_bp55 -228.6830 Inf 0 NaN NaN
w_bbean -449.2010 Inf 0 NaN NaN
w_chick -689.3991 Inf 0 NaN NaN
w_veg -512.5137 Inf 0 NaN NaN
w_sq -326.9425 Inf 0 NaN NaN
w_org 110.4470 Inf 0 NaN NaN
b_price 0.0027 Inf 0 NaN NaN


While the model where SQ is in preference space works fine:
V = list()
V[['beef']] = b_price * ( w_beef + w_org*org1 + price1 )
V[['bp73']] = b_price * ( w_bp73 + w_org*org2 + price2 )
V[['bp55']] = b_price * ( w_bp55 + w_org*org3 + price3 )
V[['bbean']] = b_price * ( w_bbean + w_org*org4 + price4 )
V[['chick']] = b_price * ( w_chick + w_org*org5 + price5 )
V[['veg']] = b_price * ( w_veg + w_org*org6 + price6 )
V[['sq']] = b_sq

Number of individuals : 514
Number of observations : 3084
LL(start) : -6001.187
LL(0) : -6001.187
LL(final) : -5346.365
Estimate Std.err. t.ratio(0) Rob.std.err. Rob.t.ratio(0)
w_beef 0.0000 NA NA NA NA
w_bp73 74.1530 6.5573 11.31 8.7673 8.46
w_bp55 53.6450 5.0357 10.65 7.6257 7.03
w_bbean 91.1401 7.9925 11.40 10.2998 8.85
w_chick 136.9745 11.8950 11.52 14.7182 9.31
w_veg 103.7445 8.9795 11.55 11.4234 9.08
b_sq -1.8650 0.0952 -19.60 0.1506 -12.38
w_org -25.6525 3.1062 -8.26 3.7028 -6.93
b_price -0.0153 0.0013 -12.00 0.0014

The MNL model in preference space gives:
Number of individuals : 514
Number of observations : 3084
LL(start) : -6001.187
LL(0) : -6001.187
LL(final) : -5346.362

Estimates:
Estimate Std.err. t.ratio(0) Rob.std.err. Rob.t.ratio(0)
b_beef 0.0000 NA NA NA NA
b_bp73 -1.1359 0.0605 -18.76 0.0863 -13.17
b_bp55 -0.8220 0.0545 -15.08 0.0940 -8.75
b_bbean -1.3977 0.0662 -21.11 0.0872 -16.03
b_chick -2.0971 0.0871 -24.08 0.1537 -13.64
b_veg -1.5890 0.0713 -22.28 0.1264 -12.57
b_sq -1.8711 0.0950 -19.70 0.1505 -12.44
b_org 0.3929 0.0394 9.97 0.0409 9.60
b_price -0.0154 0.0013 -12.13 0.0014 -11.05

kind regards,
Anna
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stephanehess
Site Admin
Posts: 1049
Joined: 24 Apr 2020, 16:29

Re: wtp space

Post by stephanehess »

Hi Anna

for MNL, the models in preference and WTP space will give exactly the same results, and this is confirmed by your final two models. However, the model where you use

Code: Select all

V[['sq']] = b_price * w_sq
has clearly run into trouble. The fit is worse and the b_price coefficient is positive. This is most likely a starting values issue. Did you start both b_price and w_sq at or near zero?

Best wishes

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk
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Anna_Edenbrandt
Posts: 6
Joined: 27 Apr 2020, 20:01

Re: wtp space

Post by Anna_Edenbrandt »

Hello

Thanks for the suggestion. After some testing with different starting values I found tha using good starting values, close to the ratio obtained in the MNL-model, solves the problem. Now I know that there is nothing wrong with the model specification, and can move forward with RPL-specifications.

Thanks for you advice!
Anna
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