diff --git a/Scripts/logit/chr_vol_treat.R b/Scripts/logit/chr_vol_treat.R
index 399ec5456d29a9dbfbf3254420db5923e7ad3ccf..72c6b96f3dd1385d7683957ad19f972552f8d345 100644
--- a/Scripts/logit/chr_vol_treat.R
+++ b/Scripts/logit/chr_vol_treat.R
@@ -185,3 +185,7 @@ best_coords <- coords(roc_obj, "best", best.method="youden")
cut_off <- best_coords$threshold
+<<<<<<< HEAD
+
+=======
+>>>>>>> refs/remotes/origin/main
diff --git a/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching.R b/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching.R
new file mode 100644
index 0000000000000000000000000000000000000000..394659484c360abee856c957c7cb2cc9ca6cb0d9
--- /dev/null
+++ b/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching.R
@@ -0,0 +1,182 @@
+#### Apollo standard script #####
+
+library(apollo) # Load apollo package
+
+
+data_predictions <- readRDS("Data/predictions.RDS")
+
+database <- left_join(database_full, data_predictions, by="id")
+
+
+
+database <- database %>%
+ filter(!is.na(Treatment_new)) %>%
+ mutate(Dummy_Treated = case_when(Treatment_new == 1|Treatment_new == 2 ~ 1, TRUE ~ 0),
+ Dummy_Vol_Treated = case_when(Treatment_new == 5 |Treatment_new == 4 ~ 1, TRUE ~ 0),
+ Dummy_no_info = case_when(Treatment_new == 3 ~ 1, TRUE~0)) %>%
+ mutate(Dummy_Treated_Pred = case_when(Dummy_Treated == 1 & PredictedGroup == 1 ~1, TRUE~0),
+ Dummy_Treated_Not_Pred = case_when(Dummy_Treated == 1 & PredictedGroup == 0 ~1, TRUE~0))
+
+
+
+#initialize model
+
+apollo_initialise()
+
+
+### Set core controls
+apollo_control = list(
+ modelName = "MXL_wtp_Prediction matching",
+ modelDescr = "MXL wtp space Prediction matching",
+ indivID ="id",
+ mixing = TRUE,
+ HB= FALSE,
+ nCores = n_cores,
+ outputDirectory = "Estimation_results/mxl/prediction"
+)
+
+##### Define model parameters depending on your attributes and model specification! ####
+# set values to 0 for conditional logit model
+
+apollo_beta=c(mu_natural = 15,
+ mu_walking = -1,
+ mu_rent = -2,
+ ASC_sq = 0,
+ mu_ASC_sq_vol_treated = 0,
+ mu_ASC_sq_no_info = 0,
+ mu_ASC_sq_treat_pred = 0,
+ mu_ASC_sq_treat_not_pred = 0,
+ mu_nat_vol_treated = 0,
+ mu_nat_no_info = 0,
+ mu_nat_treat_pred = 0,
+ mu_nat_treat_not_pred = 0,
+ mu_walking_vol_treated = 0,
+ mu_walking_no_info = 0,
+ mu_walking_treat_pred = 0,
+ mu_walking_treat_not_pred = 0,
+ mu_rent_vol_treated = 0,
+ mu_rent_no_info = 0,
+ mu_rent_treat_pred = 0,
+ mu_rent_treat_not_pred = 0,
+ sig_natural = 15,
+ sig_walking = 2,
+ sig_rent = 2,
+ sig_ASC_sq = 2)
+
+### specify parameters that should be kept fixed, here = none
+apollo_fixed = c()
+
+### Set parameters for generating draws, use 2000 sobol draws
+apollo_draws = list(
+ interDrawsType = "sobol",
+ interNDraws = n_draws,
+ interUnifDraws = c(),
+ interNormDraws = c("draws_natural", "draws_walking", "draws_rent", "draws_asc"),
+ intraDrawsType = "halton",
+ intraNDraws = 0,
+ intraUnifDraws = c(),
+ intraNormDraws = c()
+)
+
+### Create random parameters, define distribution of the parameters
+apollo_randCoeff = function(apollo_beta, apollo_inputs){
+ randcoeff = list()
+
+ randcoeff[["b_mu_natural"]] = mu_natural + sig_natural * draws_natural
+ randcoeff[["b_mu_walking"]] = mu_walking + sig_walking * draws_walking
+ randcoeff[["b_mu_rent"]] = -exp(mu_rent + sig_rent * draws_rent)
+ randcoeff[["b_ASC_sq"]] = ASC_sq + sig_ASC_sq * draws_asc
+
+ return(randcoeff)
+}
+
+
+### validate
+apollo_inputs = apollo_validateInputs()
+apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
+
+ ### Function initialisation: do not change the following three commands
+ ### 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()
+
+ #### List of utilities (later integrated in mnl_settings below) ####
+ # Define utility functions here:
+
+ V = list()
+ V[['alt1']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred)*
+ (b_mu_natural*Naturalness_1 + b_mu_walking*WalkingDistance_1
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_1 + mu_nat_no_info * Dummy_no_info * Naturalness_1
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_1 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_1
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_1 + mu_walking_no_info* Dummy_no_info * WalkingDistance_1
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_1 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_1
+ - Rent_1)
+
+ V[['alt2']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred)*
+ (b_mu_natural*Naturalness_2 + b_mu_walking*WalkingDistance_2
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_2 + mu_nat_no_info * Dummy_no_info * Naturalness_2
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_2 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_2
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_2 + mu_walking_no_info* Dummy_no_info * WalkingDistance_2
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_2 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_2
+ - Rent_2)
+
+ V[['alt3']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred)*
+ (b_mu_natural*Naturalness_3 + b_mu_walking*WalkingDistance_3
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_3 + mu_nat_no_info * Dummy_no_info * Naturalness_3
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_3 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_3
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_3 + mu_walking_no_info* Dummy_no_info * WalkingDistance_3
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_3 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_3
+ + b_ASC_sq + mu_ASC_sq_vol_treated * Dummy_Vol_Treated + mu_ASC_sq_no_info * Dummy_no_info
+ + mu_ASC_sq_treat_pred * Dummy_Treated_Pred + mu_ASC_sq_treat_not_pred * Dummy_Treated_Not_Pred- Rent_3)
+
+
+ ### Define settings for MNL model component
+ mnl_settings = list(
+ alternatives = c(alt1=1, alt2=2, alt3=3),
+ avail = 1, # all alternatives are available in every choice
+ choiceVar = choice,
+ V = V#, # tell function to use list vector defined above
+
+ )
+
+ ### 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)
+
+ ### Average across inter-individual draws - nur bei Mixed Logit!
+ P = apollo_avgInterDraws(P, apollo_inputs, functionality)
+
+ ### Prepare and return outputs of function
+ P = apollo_prepareProb(P, apollo_inputs, functionality)
+ return(P)
+}
+
+
+
+# ################################################################# #
+#### MODEL ESTIMATION ##
+# ################################################################# #
+# estimate model with bfgs algorithm
+
+mxl_wtp_case_e = apollo_estimate(apollo_beta, apollo_fixed,
+ apollo_probabilities, apollo_inputs,
+ estimate_settings=list(maxIterations=400,
+ estimationRoutine="bfgs",
+ hessianRoutine="analytic"))
+
+
+
+# ################################################################# #
+#### MODEL OUTPUTS ##
+# ################################################################# #
+apollo_saveOutput(mxl_wtp_case_e)
+
+
diff --git a/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching_all.R b/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching_all.R
new file mode 100644
index 0000000000000000000000000000000000000000..526d9a6e417cb3f1fdcd940ecfb1f5d60d7bb039
--- /dev/null
+++ b/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching_all.R
@@ -0,0 +1,187 @@
+#### Apollo standard script #####
+
+library(apollo) # Load apollo package
+
+
+data_predictions <- readRDS("Data/predictions.RDS")
+
+database <- left_join(database_full, data_predictions, by="id")
+
+
+
+database <- database %>%
+ filter(!is.na(Treatment_new)) %>%
+ mutate(Dummy_Treated = case_when(Treatment_new == 1|Treatment_new == 2 ~ 1, TRUE ~ 0),
+ Dummy_Vol_Treated = case_when(Treatment_new == 5 |Treatment_new == 4 ~ 1, TRUE ~ 0),
+ Dummy_no_info = case_when(Treatment_new == 3 ~ 1, TRUE~0)) %>%
+ mutate(Dummy_Treated_Pred = case_when(Dummy_Treated == 1 & PredictedGroup == 1 ~1, TRUE~0),
+ Dummy_Treated_Not_Pred = case_when(Dummy_Treated == 1 & PredictedGroup == 0 ~1, TRUE~0)) %>%
+ mutate(Dummy_Control_Pred = case_when(Treatment_new == 6 & PredictedGroup == 1 ~1, TRUE~0))
+
+
+
+#initialize model
+
+apollo_initialise()
+
+
+### Set core controls
+apollo_control = list(
+ modelName = "MXL_wtp_Prediction matching all",
+ modelDescr = "MXL wtp space Prediction matching all",
+ indivID ="id",
+ mixing = TRUE,
+ HB= FALSE,
+ nCores = n_cores,
+ outputDirectory = "Estimation_results/mxl/prediction"
+)
+
+##### Define model parameters depending on your attributes and model specification! ####
+# set values to 0 for conditional logit model
+
+apollo_beta=c(mu_natural = 15,
+ mu_walking = -1,
+ mu_rent = -2,
+ ASC_sq = 0,
+ mu_ASC_sq_vol_treated = 0,
+ mu_ASC_sq_no_info = 0,
+ mu_ASC_sq_treat_pred = 0,
+ mu_ASC_sq_treat_not_pred = 0,
+ mu_ASC_sq_control_pred = 0,
+ mu_nat_vol_treated = 0,
+ mu_nat_no_info = 0,
+ mu_nat_treat_pred = 0,
+ mu_nat_treat_not_pred = 0,
+ mu_nat_control_pred = 0,
+ mu_walking_vol_treated = 0,
+ mu_walking_no_info = 0,
+ mu_walking_treat_pred = 0,
+ mu_walking_treat_not_pred = 0,
+ mu_walking_control_pred = 0,
+ mu_rent_vol_treated = 0,
+ mu_rent_no_info = 0,
+ mu_rent_treat_pred = 0,
+ mu_rent_treat_not_pred = 0,
+ mu_rent_control_pred = 0,
+ sig_natural = 15,
+ sig_walking = 2,
+ sig_rent = 2,
+ sig_ASC_sq = 2)
+
+### specify parameters that should be kept fixed, here = none
+apollo_fixed = c()
+
+### Set parameters for generating draws, use 2000 sobol draws
+apollo_draws = list(
+ interDrawsType = "sobol",
+ interNDraws = n_draws,
+ interUnifDraws = c(),
+ interNormDraws = c("draws_natural", "draws_walking", "draws_rent", "draws_asc"),
+ intraDrawsType = "halton",
+ intraNDraws = 0,
+ intraUnifDraws = c(),
+ intraNormDraws = c()
+)
+
+### Create random parameters, define distribution of the parameters
+apollo_randCoeff = function(apollo_beta, apollo_inputs){
+ randcoeff = list()
+
+ randcoeff[["b_mu_natural"]] = mu_natural + sig_natural * draws_natural
+ randcoeff[["b_mu_walking"]] = mu_walking + sig_walking * draws_walking
+ randcoeff[["b_mu_rent"]] = -exp(mu_rent + sig_rent * draws_rent)
+ randcoeff[["b_ASC_sq"]] = ASC_sq + sig_ASC_sq * draws_asc
+
+ return(randcoeff)
+}
+
+
+### validate
+apollo_inputs = apollo_validateInputs()
+apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
+
+ ### Function initialisation: do not change the following three commands
+ ### 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()
+
+ #### List of utilities (later integrated in mnl_settings below) ####
+ # Define utility functions here:
+
+ V = list()
+ V[['alt1']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred + mu_rent_control_pred * Dummy_Control_Pred)*
+ (b_mu_natural*Naturalness_1 + b_mu_walking*WalkingDistance_1
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_1 + mu_nat_no_info * Dummy_no_info * Naturalness_1
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_1 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_1 + mu_nat_control_pred * Dummy_Control_Pred * Naturalness_1
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_1 + mu_walking_no_info* Dummy_no_info * WalkingDistance_1
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_1 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_1 + mu_walking_control_pred * Dummy_Control_Pred * WalkingDistance_1
+ - Rent_1)
+
+ V[['alt2']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred + mu_rent_control_pred * Dummy_Control_Pred)*
+ (b_mu_natural*Naturalness_2 + b_mu_walking*WalkingDistance_2
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_2 + mu_nat_no_info * Dummy_no_info * Naturalness_2
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_2 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_2 + mu_nat_control_pred * Dummy_Control_Pred * Naturalness_2
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_2 + mu_walking_no_info* Dummy_no_info * WalkingDistance_2
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_2 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_2 + mu_walking_control_pred * Dummy_Control_Pred * WalkingDistance_2
+ - Rent_2)
+
+ V[['alt3']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred + mu_rent_control_pred * Dummy_Control_Pred)*
+ (b_mu_natural*Naturalness_3 + b_mu_walking*WalkingDistance_3
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_3 + mu_nat_no_info * Dummy_no_info * Naturalness_3
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_3 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_3 + mu_nat_control_pred * Dummy_Control_Pred * Naturalness_3
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_3 + mu_walking_no_info* Dummy_no_info * WalkingDistance_3
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_3 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_3 + mu_walking_control_pred * Dummy_Control_Pred * WalkingDistance_3
+ + b_ASC_sq + mu_ASC_sq_vol_treated * Dummy_Vol_Treated + mu_ASC_sq_no_info * Dummy_no_info
+ + mu_ASC_sq_treat_pred * Dummy_Treated_Pred + mu_ASC_sq_treat_not_pred * Dummy_Treated_Not_Pred + mu_ASC_sq_control_pred * Dummy_Control_Pred - Rent_3)
+
+
+ ### Define settings for MNL model component
+ mnl_settings = list(
+ alternatives = c(alt1=1, alt2=2, alt3=3),
+ avail = 1, # all alternatives are available in every choice
+ choiceVar = choice,
+ V = V#, # tell function to use list vector defined above
+
+ )
+
+ ### 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)
+
+ ### Average across inter-individual draws - nur bei Mixed Logit!
+ P = apollo_avgInterDraws(P, apollo_inputs, functionality)
+
+ ### Prepare and return outputs of function
+ P = apollo_prepareProb(P, apollo_inputs, functionality)
+ return(P)
+}
+
+
+
+# ################################################################# #
+#### MODEL ESTIMATION ##
+# ################################################################# #
+# estimate model with bfgs algorithm
+
+mxl_wtp_matching_all = apollo_estimate(apollo_beta, apollo_fixed,
+ apollo_probabilities, apollo_inputs,
+ estimate_settings=list(maxIterations=400,
+ estimationRoutine="bfgs",
+ hessianRoutine="analytic"))
+
+
+
+# ################################################################# #
+#### MODEL OUTPUTS ##
+# ################################################################# #
+apollo_saveOutput(mxl_wtp_matching_all)
+
+
diff --git a/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching_all_ref_control_pred.R b/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching_all_ref_control_pred.R
new file mode 100644
index 0000000000000000000000000000000000000000..066df114d8ce7ed0016caf930e88879389243f60
--- /dev/null
+++ b/Scripts/mxl/Prediction models/mxl_wtp_space_pred_matching_all_ref_control_pred.R
@@ -0,0 +1,187 @@
+#### Apollo standard script #####
+
+library(apollo) # Load apollo package
+
+
+data_predictions <- readRDS("Data/predictions.RDS")
+
+database <- left_join(database_full, data_predictions, by="id")
+
+
+
+database <- database %>%
+ filter(!is.na(Treatment_new)) %>%
+ mutate(Dummy_Treated = case_when(Treatment_new == 1|Treatment_new == 2 ~ 1, TRUE ~ 0),
+ Dummy_Vol_Treated = case_when(Treatment_new == 5 |Treatment_new == 4 ~ 1, TRUE ~ 0),
+ Dummy_no_info = case_when(Treatment_new == 3 ~ 1, TRUE~0)) %>%
+ mutate(Dummy_Treated_Pred = case_when(Dummy_Treated == 1 & PredictedGroup == 1 ~1, TRUE~0),
+ Dummy_Treated_Not_Pred = case_when(Dummy_Treated == 1 & PredictedGroup == 0 ~1, TRUE~0)) %>%
+ mutate(Dummy_Control_Not_Pred = case_when(Treatment_new == 6 & PredictedGroup == 0 ~1, TRUE~0))
+
+
+
+#initialize model
+
+apollo_initialise()
+
+
+### Set core controls
+apollo_control = list(
+ modelName = "MXL_wtp_Prediction matching all cp",
+ modelDescr = "MXL wtp space Prediction matching all cp",
+ indivID ="id",
+ mixing = TRUE,
+ HB= FALSE,
+ nCores = n_cores,
+ outputDirectory = "Estimation_results/mxl/prediction"
+)
+
+##### Define model parameters depending on your attributes and model specification! ####
+# set values to 0 for conditional logit model
+
+apollo_beta=c(mu_natural = 15,
+ mu_walking = -1,
+ mu_rent = -2,
+ ASC_sq = 0,
+ mu_ASC_sq_vol_treated = 0,
+ mu_ASC_sq_no_info = 0,
+ mu_ASC_sq_treat_pred = 0,
+ mu_ASC_sq_treat_not_pred = 0,
+ mu_ASC_sq_control_not_pred = 0,
+ mu_nat_vol_treated = 0,
+ mu_nat_no_info = 0,
+ mu_nat_treat_pred = 0,
+ mu_nat_treat_not_pred = 0,
+ mu_nat_control_not_pred = 0,
+ mu_walking_vol_treated = 0,
+ mu_walking_no_info = 0,
+ mu_walking_treat_pred = 0,
+ mu_walking_treat_not_pred = 0,
+ mu_walking_control_not_pred = 0,
+ mu_rent_vol_treated = 0,
+ mu_rent_no_info = 0,
+ mu_rent_treat_pred = 0,
+ mu_rent_treat_not_pred = 0,
+ mu_rent_control_not_pred = 0,
+ sig_natural = 15,
+ sig_walking = 2,
+ sig_rent = 2,
+ sig_ASC_sq = 2)
+
+### specify parameters that should be kept fixed, here = none
+apollo_fixed = c()
+
+### Set parameters for generating draws, use 2000 sobol draws
+apollo_draws = list(
+ interDrawsType = "sobol",
+ interNDraws = n_draws,
+ interUnifDraws = c(),
+ interNormDraws = c("draws_natural", "draws_walking", "draws_rent", "draws_asc"),
+ intraDrawsType = "halton",
+ intraNDraws = 0,
+ intraUnifDraws = c(),
+ intraNormDraws = c()
+)
+
+### Create random parameters, define distribution of the parameters
+apollo_randCoeff = function(apollo_beta, apollo_inputs){
+ randcoeff = list()
+
+ randcoeff[["b_mu_natural"]] = mu_natural + sig_natural * draws_natural
+ randcoeff[["b_mu_walking"]] = mu_walking + sig_walking * draws_walking
+ randcoeff[["b_mu_rent"]] = -exp(mu_rent + sig_rent * draws_rent)
+ randcoeff[["b_ASC_sq"]] = ASC_sq + sig_ASC_sq * draws_asc
+
+ return(randcoeff)
+}
+
+
+### validate
+apollo_inputs = apollo_validateInputs()
+apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
+
+ ### Function initialisation: do not change the following three commands
+ ### 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()
+
+ #### List of utilities (later integrated in mnl_settings below) ####
+ # Define utility functions here:
+
+ V = list()
+ V[['alt1']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred + mu_rent_control_not_pred * Dummy_Control_Not_Pred)*
+ (b_mu_natural*Naturalness_1 + b_mu_walking*WalkingDistance_1
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_1 + mu_nat_no_info * Dummy_no_info * Naturalness_1
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_1 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_1 + mu_nat_control_not_pred * Dummy_Control_Not_Pred * Naturalness_1
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_1 + mu_walking_no_info* Dummy_no_info * WalkingDistance_1
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_1 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_1 + mu_walking_control_not_pred * Dummy_Control_Not_Pred * WalkingDistance_1
+ - Rent_1)
+
+ V[['alt2']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred + mu_rent_control_not_pred * Dummy_Control_Not_Pred)*
+ (b_mu_natural*Naturalness_2 + b_mu_walking*WalkingDistance_2
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_2 + mu_nat_no_info * Dummy_no_info * Naturalness_2
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_2 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_2 + mu_nat_control_not_pred * Dummy_Control_Not_Pred * Naturalness_2
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_2 + mu_walking_no_info* Dummy_no_info * WalkingDistance_2
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_2 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_2 + mu_walking_control_not_pred * Dummy_Control_Not_Pred * WalkingDistance_2
+ - Rent_2)
+
+ V[['alt3']] = -(b_mu_rent + mu_rent_vol_treated * Dummy_Vol_Treated + mu_rent_no_info * Dummy_no_info + mu_rent_treat_pred * Dummy_Treated_Pred +
+ mu_rent_treat_not_pred * Dummy_Treated_Not_Pred + mu_rent_control_not_pred * Dummy_Control_Not_Pred)*
+ (b_mu_natural*Naturalness_3 + b_mu_walking*WalkingDistance_3
+ + mu_nat_vol_treated * Dummy_Vol_Treated * Naturalness_3 + mu_nat_no_info * Dummy_no_info * Naturalness_3
+ + mu_nat_treat_pred * Dummy_Treated_Pred * Naturalness_3 + mu_nat_treat_not_pred * Dummy_Treated_Not_Pred * Naturalness_3 + mu_nat_control_not_pred * Dummy_Control_Not_Pred * Naturalness_3
+ + mu_walking_vol_treated * Dummy_Vol_Treated * WalkingDistance_3 + mu_walking_no_info* Dummy_no_info * WalkingDistance_3
+ + mu_walking_treat_pred * Dummy_Treated_Pred * WalkingDistance_3 + mu_walking_treat_not_pred * Dummy_Treated_Not_Pred * WalkingDistance_3 + mu_walking_control_not_pred * Dummy_Control_Not_Pred * WalkingDistance_3
+ + b_ASC_sq + mu_ASC_sq_vol_treated * Dummy_Vol_Treated + mu_ASC_sq_no_info * Dummy_no_info
+ + mu_ASC_sq_treat_pred * Dummy_Treated_Pred + mu_ASC_sq_treat_not_pred * Dummy_Treated_Not_Pred + mu_ASC_sq_control_not_pred * Dummy_Control_Not_Pred - Rent_3)
+
+
+ ### Define settings for MNL model component
+ mnl_settings = list(
+ alternatives = c(alt1=1, alt2=2, alt3=3),
+ avail = 1, # all alternatives are available in every choice
+ choiceVar = choice,
+ V = V#, # tell function to use list vector defined above
+
+ )
+
+ ### 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)
+
+ ### Average across inter-individual draws - nur bei Mixed Logit!
+ P = apollo_avgInterDraws(P, apollo_inputs, functionality)
+
+ ### Prepare and return outputs of function
+ P = apollo_prepareProb(P, apollo_inputs, functionality)
+ return(P)
+}
+
+
+
+# ################################################################# #
+#### MODEL ESTIMATION ##
+# ################################################################# #
+# estimate model with bfgs algorithm
+
+mxl_wtp_matching_all_cp = apollo_estimate(apollo_beta, apollo_fixed,
+ apollo_probabilities, apollo_inputs,
+ estimate_settings=list(maxIterations=400,
+ estimationRoutine="bfgs",
+ hessianRoutine="analytic"))
+
+
+
+# ################################################################# #
+#### MODEL OUTPUTS ##
+# ################################################################# #
+apollo_saveOutput(mxl_wtp_matching_all_cp)
+
+