I currently have the issue that i cannot be sure whether my estimation results from WTP Space are correct, or if I made a mistake in the Utility functions of my R Script. My difficulty comes from not being familiar with including a covariate (Age) for all parameters into the function. I want to estimate in WTP Space (instead of delta method), because I do so with all my models and can then easily compare and have the same method.
The WTP Estimates are not totally off, but I am just not sure if they are calculated correctly or if there is an error in my specification.
To give you details, i provide the relevant code from my R Script, and output.
Rscript:
Code: Select all
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "MNL_Model3_WTPSpace",
modelDescr = "MNL model 3 with sociodemographics Age in WTP Space",
indivID = "ResponseId",
outputDirectory = "output"
)
### Loading data from package
database = as.data.frame(final_data)
### Define settings for MNL model component before model estimation
choiceAnalysis_settings = list(
alternatives = c(oatdrink=1, soydrink =2, almonddrink=3, barleydrink=4, optout=5),
avail = list(oatdrink=1, soydrink =1, almonddrink=1, barleydrink=1, optout=1),
choiceVar = database$Choice,
explanators = database[,c("Age")]
)
### Run function to analyse choice data
apollo_choiceAnalysis(choiceAnalysis_settings, apollo_control, database)
### Coefficients
apollo_beta=c(wtp_asc_oatdrink = 0,
wtp_asc_oatdrink_age = 0,
wtp_asc_soydrink = 0,
wtp_asc_soydrink_age = 0,
wtp_asc_almonddrink = 0,
wtp_asc_almonddrink_age = 0,
wtp_asc_barleydrink = 0,
wtp_asc_barleydrink_age = 0,
asc_optout = 0,
wtp_organic = 0,
wtp_organic_age = 0,
wtp_regional_Country = 0, #two coefficients, because it is a dummy variable
wtp_regional_Country_age = 0,
wtp_regional_FedState = 0,
wtp_regional_FedState_age = 0,
wtp_protein = 0,
wtp_protein_age = 0,
b_price = 0,
b_price_age = 0
)
###one ASC needs to be fixed to 0 for the mnl to work
apollo_fixed = c("asc_optout")
apollo_inputs = apollo_validateInputs()
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
### Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))
### Create list of probabilities P
P = list()
### Create alternative-specific constants and coefficients using interactions with age for each attribute
asc_oatdrink_value = wtp_asc_oatdrink + wtp_asc_oatdrink_age * Age
asc_soydrink_value = wtp_asc_soydrink + wtp_asc_soydrink_age * Age
asc_almonddrink_value = wtp_asc_almonddrink + wtp_asc_almonddrink_age * Age
asc_barleydrink_value = wtp_asc_barleydrink + wtp_asc_barleydrink_age * Age
### Coefficients for attributes with interactions with age
b_organic_value = wtp_organic + wtp_organic_age* Age
b_regional_Country_value = wtp_regional_Country + wtp_regional_Country_age*Age
b_regional_FedState_value = wtp_regional_FedState + wtp_regional_FedState_age*Age
b_protein_value = wtp_protein + wtp_protein_age*Age
b_price_value = b_price + b_price_age*Age
### List of utilities:
V = list()
V[["oatdrink"]] = b_price_value * (asc_oatdrink_value + b_organic_value * oatdrink.organic + b_regional_Country_value * (oatdrink.regional == 1) + b_regional_FedState_value * (oatdrink.regional == 0) + b_protein_value * oatdrink.proteinlow + oatdrink.price)
V[["soydrink"]] = b_price_value * (asc_soydrink_value + b_organic_value * soydrink.organic + b_regional_Country_value * (soydrink.regional == 1) + b_regional_FedState_value * (soydrink.regional == 0) + b_protein_value * soydrink.proteinhigh + soydrink.price)
V[["almonddrink"]] = b_price_value * (asc_almonddrink_value + b_organic_value * almonddrink.organic + b_protein_value * almonddrink.proteinlow + almonddrink.price)
V[["barleydrink"]] = b_price_value * (asc_barleydrink_value + b_organic_value * barleydrink.organic + b_regional_Country_value * (barleydrink.regional == 1) + b_regional_FedState_value * (barleydrink.regional == 0) + b_protein_value * barleydrink.protein + barleydrink.price)
V[["optout"]] = asc_optout
### Define settings for MNL model component
mnl_settings = list(
alternatives = c(oatdrink=1, soydrink =2, almonddrink=3, barleydrink=4, optout=5),
avail = list(oatdrink=1, soydrink =1, almonddrink=1, barleydrink=1, optout=1),
choiceVar = Choice,
utilities = V
)
### Compute probabilities using MNL model
P[["model"]] = apollo_mnl(mnl_settings, functionality)
### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
model = apollo_estimate(apollo_beta,
apollo_fixed,
apollo_probabilities,
apollo_inputs)
###Default Output
apollo_modelOutput(model)
Code: Select all
Model name : MNL_Model3_WTPSpace
Model description : MNL model 3 with sociodemographics Age in WTP Space
Model run at : 2024-02-18 22:55:50.277622
Estimation method : bgw
Model diagnosis : Relative function convergence
Optimisation diagnosis : Maximum found
hessian properties : Negative definite
maximum eigenvalue : -2.570127
reciprocal of condition number : 4.49029e-07
Number of individuals : 275
Number of rows in database : 4125
Number of modelled outcomes : 4125
Number of cores used : 1
Model without mixing
LL(start) : -6638.93
LL at equal shares, LL(0) : -6638.93
LL at observed shares, LL(C) : -6092.08
LL(final) : -4657.3
Rho-squared vs equal shares : 0.2985
Adj.Rho-squared vs equal shares : 0.2958
Rho-squared vs observed shares : 0.2355
Adj.Rho-squared vs observed shares : 0.2332
AIC : 9350.6
BIC : 9464.45
Estimated parameters : 18
Time taken (hh:mm:ss) : 00:01:5.64
pre-estimation : 00:00:35.76
estimation : 00:00:6.3
initial estimation : 00:00:4.9
estimation after rescaling : 00:00:1.41
post-estimation : 00:00:23.58
Iterations : 11
initial estimation : 10
estimation after rescaling : 1
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
wtp_asc_oatdrink -4.631705 0.294722 -15.7155 0.523573 -8.8463
wtp_asc_oatdrink_age 0.080941 0.009335 8.6705 0.016929 4.7812
wtp_asc_soydrink -3.544120 0.375351 -9.4421 0.563221 -6.2926
wtp_asc_soydrink_age 0.077557 0.012028 6.4481 0.017948 4.3212
wtp_asc_almonddrink -2.760941 0.294614 -9.3714 0.617303 -4.4726
wtp_asc_almonddrink_age 0.051136 0.009146 5.5913 0.020992 2.4360
wtp_asc_barleydrink -2.772683 0.339844 -8.1587 0.538654 -5.1474
wtp_asc_barleydrink_age 0.063928 0.010823 5.9067 0.017879 3.5756
asc_optout 0.000000 NA NA NA NA
wtp_organic -0.386947 0.157769 -2.4526 0.276184 -1.4010
wtp_organic_age -0.014698 0.005132 -2.8638 0.009181 -1.6008
wtp_regional_Country -0.196627 0.198908 -0.9885 0.264015 -0.7448
wtp_regional_Country_age -0.017065 0.006559 -2.6018 0.008611 -1.9817
wtp_regional_FedState 0.242446 0.208383 1.1635 0.313081 0.7744
wtp_regional_FedState_age -0.033820 0.006884 -4.9128 0.010599 -3.1910
wtp_protein -0.051604 0.069761 -0.7397 0.070191 -0.7352
wtp_protein_age -0.002489 0.002226 -1.1182 0.002262 -1.1007
b_price -1.311163 0.074166 -17.6787 0.127061 -10.3192
b_price_age 0.009934 0.002033 4.8870 0.003558 2.7922Code: Select all
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "MNL_Model3",
modelDescr = "MNL model 3 with sociodemographics Age",
indivID = "ResponseId",
outputDirectory = "output"
)
### Loading data from package
database = as.data.frame(final_data)
### Define settings for MNL model component before model estimation
choiceAnalysis_settings = list(
alternatives = c(oatdrink=1, soydrink =2, almonddrink=3, barleydrink=4, optout=5),
avail = list(oatdrink=1, soydrink =1, almonddrink=1, barleydrink=1, optout=1),
choiceVar = database$Choice,
explanators = database[,c("Age")]
)
### Run function to analyse choice data
apollo_choiceAnalysis(choiceAnalysis_settings, apollo_control, database)
### Coefficients
apollo_beta=c(asc_oatdrink = 0,
asc_oatdrink_age = 0,
asc_soydrink = 0,
asc_soydrink_age = 0,
asc_almonddrink = 0,
asc_almonddrink_age = 0,
asc_barleydrink = 0,
asc_barleydrink_age = 0,
asc_optout = 0,
b_organic = 0,
b_organic_age = 0,
b_regional_Country = 0, #two coefficients, because it is a dummy variable
b_regional_Country_age = 0,
b_regional_FedState = 0,
b_regional_FedState_age = 0,
b_protein = 0,
b_protein_age = 0,
b_price = 0,
b_price_age = 0
)
###one ASC needs to be fixed to 0 for the mnl to work
apollo_fixed = c("asc_optout")
apollo_inputs = apollo_validateInputs()
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
### Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))
### Create list of probabilities P
P = list()
### Create alternative-specific constants and coefficients using interactions with age for each attribute
asc_oatdrink_value = asc_oatdrink + asc_oatdrink_age * Age
asc_soydrink_value = asc_soydrink + asc_soydrink_age * Age
asc_almonddrink_value = asc_almonddrink + asc_almonddrink_age * Age
asc_barleydrink_value = asc_barleydrink + asc_barleydrink_age * Age
### Coefficients for attributes with interactions with age
b_organic_value = b_organic + b_organic_age* Age
b_regional_Country_value = b_regional_Country + b_regional_Country_age*Age
b_regional_FedState_value = b_regional_FedState + b_regional_FedState_age*Age
b_protein_value = b_protein + b_protein_age*Age
b_price_value = b_price + b_price_age*Age
### List of utilities:
V = list()
V[["oatdrink"]] = asc_oatdrink_value + b_organic_value * oatdrink.organic + b_regional_Country_value * (oatdrink.regional == 1) + b_regional_FedState_value * (oatdrink.regional == 0) + b_protein_value * oatdrink.proteinlow + b_price_value * oatdrink.price
V[["soydrink"]] = asc_soydrink_value + b_organic_value * soydrink.organic + b_regional_Country_value * (soydrink.regional == 1) + b_regional_FedState_value * (soydrink.regional == 0) + b_protein_value * soydrink.proteinhigh + b_price_value * soydrink.price
V[["almonddrink"]] = asc_almonddrink_value + b_organic_value * almonddrink.organic + b_protein_value * almonddrink.proteinlow + b_price_value * almonddrink.price
V[["barleydrink"]] = asc_barleydrink_value + b_organic_value * barleydrink.organic + b_regional_Country_value * (barleydrink.regional == 1) + b_regional_FedState_value * (barleydrink.regional == 0) + b_protein_value * barleydrink.protein + b_price_value * barleydrink.price
V[["optout"]] = asc_optout
### Define settings for MNL model component
mnl_settings = list(
alternatives = c(oatdrink=1, soydrink =2, almonddrink=3, barleydrink=4, optout=5),
avail = list(oatdrink=1, soydrink =1, almonddrink=1, barleydrink=1, optout=1),
choiceVar = Choice,
utilities = V
)
### Compute probabilities using MNL model
P[["model"]] = apollo_mnl(mnl_settings, functionality)
### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
model = apollo_estimate(apollo_beta,
apollo_fixed,
apollo_probabilities,
apollo_inputs)
###Default Output
apollo_modelOutput(model)
Code: Select all
Model name : MNL_Model3
Model description : MNL model 3 with sociodemographics Age
Model run at : 2024-02-18 19:07:54.325985
Estimation method : bgw
Model diagnosis : Relative function convergence
Optimisation diagnosis : Maximum found
hessian properties : Negative definite
maximum eigenvalue : -2.973251
reciprocal of condition number : 4.06615e-07
Number of individuals : 275
Number of rows in database : 4125
Number of modelled outcomes : 4125
Number of cores used : 1
Model without mixing
LL(start) : -6638.93
LL at equal shares, LL(0) : -6638.93
LL at observed shares, LL(C) : -6092.08
LL(final) : -4660.81
Rho-squared vs equal shares : 0.298
Adj.Rho-squared vs equal shares : 0.2952
Rho-squared vs observed shares : 0.2349
Adj.Rho-squared vs observed shares : 0.2326
AIC : 9357.61
BIC : 9471.46
Estimated parameters : 18
Time taken (hh:mm:ss) : 00:00:44.33
pre-estimation : 00:00:21.89
estimation : 00:00:4.15
initial estimation : 00:00:3.39
estimation after rescaling : 00:00:0.75
post-estimation : 00:00:18.29
Iterations : 10
initial estimation : 9
estimation after rescaling : 1
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_oatdrink 4.820786 0.289155 16.6720 0.491465 9.8090
asc_oatdrink_age -0.084413 0.008205 -10.2883 0.014328 -5.8913
asc_soydrink 3.484251 0.345010 10.0990 0.509897 6.8332
asc_soydrink_age -0.073216 0.009915 -7.3843 0.014099 -5.1929
asc_almonddrink 2.802598 0.279704 10.0199 0.563693 4.9719
asc_almonddrink_age -0.050962 0.007761 -6.5663 0.017305 -2.9449
asc_barleydrink 2.745257 0.314256 8.7357 0.484154 5.6702
asc_barleydrink_age -0.061041 0.009002 -6.7810 0.014435 -4.2286
asc_optout 0.000000 NA NA NA NA
b_organic 0.713536 0.123677 5.7694 0.198213 3.5999
b_organic_age 0.003716 0.003686 1.0083 0.006095 0.6098
b_regional_Country 0.440345 0.173684 2.5353 0.220703 1.9952
b_regional_Country_age 0.008665 0.005294 1.6368 0.006394 1.3552
b_regional_FedState 0.121564 0.176510 0.6887 0.238249 0.5102
b_regional_FedState_age 0.021009 0.005338 3.9353 0.007085 2.9652
b_protein 0.102096 0.062089 1.6444 0.059519 1.7153
b_protein_age 8.0493e-04 0.001827 0.4405 0.001756 0.4585
b_price -1.274035 0.078668 -16.1950 0.145215 -8.7734
b_price_age 0.008827 0.002205 4.0030 0.004251 2.0761Best, Nico