#### Apollo standard script #####

library(apollo) # Load apollo package 


database <- database_full %>% filter(!is.na(Treatment_A)) %>% 
  mutate(Dummy_Treated = case_when(Treatment_A == "Treated" ~ 1, TRUE ~ 0),
         Dummy_Vol_Treated = case_when(Treatment_A == "Vol_Treated" ~ 1, TRUE ~ 0))

  #initialize model 
  
  apollo_initialise()
  
  
  ### Set core controls
  apollo_control = list(
    modelName  = "MXL_wtp Case A",
    modelDescr = "MXL_wtp Case A",
    indivID    ="id",
    mixing     = TRUE,
    HB= FALSE,
    nCores     = n_cores, 
    outputDirectory = "Estimation_results/mxl"
  )
  
  ##### 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_nat_T = 0,
                mu_wd_T= 0,
                mu_asc_T = 0,
                mu_nat_VT = 0,
                mu_wd_VT= 0,
                mu_asc_VT = 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*(b_mu_natural * Naturalness_1 + b_mu_walking * WalkingDistance_1 +
                                mu_nat_T * Naturalness_1 * Dummy_Treated + mu_wd_T * WalkingDistance_1 * Dummy_Treated+
                                mu_nat_VT * Naturalness_1 * Dummy_Vol_Treated + mu_wd_VT * WalkingDistance_1 * Dummy_Vol_Treated
                              - Rent_1)
    
    V[['alt2']] = -b_mu_rent*(b_mu_natural * Naturalness_2 + b_mu_walking * WalkingDistance_2 +
                                mu_nat_T * Naturalness_2 * Dummy_Treated + mu_wd_T * WalkingDistance_2 * Dummy_Treated +
                              mu_nat_VT * Naturalness_2 * Dummy_Vol_Treated + mu_wd_VT * WalkingDistance_2 * Dummy_Vol_Treated
                              - Rent_2)
    
    V[['alt3']] = -b_mu_rent*(b_ASC_sq + b_mu_natural * Naturalness_3 + b_mu_walking * WalkingDistance_3 + mu_asc_T *  Dummy_Treated +
                                mu_asc_VT *  Dummy_Vol_Treated +mu_nat_T * Naturalness_3 * Dummy_Treated + mu_wd_T * WalkingDistance_3 * Dummy_Treated + 
                                mu_nat_VT * Naturalness_3 * Dummy_Vol_Treated + mu_wd_VT * WalkingDistance_3 * Dummy_Vol_Treated
                                - 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_a = 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_a)