17/replication_package/code/analysis/structural/.Rhistory

install.packages("optimx")
library("optimx")
library("stats")
library("tidyverse")
square_function <- function(x){
y = x^2
return(y)
}
square_function(x=3)
square_function(x=0)
intial_values <- c(-2,1,2)
minimise_function <- optimr(intial_values, square_function)
intial_values <- c(-2)
minimise_function <- optimr(intial_values, square_function)
minimise_function <- optimr(intial_values, square_function, method = "Brent")
minimise_function <- optimr(intial_values, square_function)
minimise_function <- optimr(par = intial_values, fn=square_function, method = "Brent")
install.packages("Brent")
minimise_function <- optimize(f=square_function, lower = -10, upper=10)
minimise_function$par
minimise_function
minimise_function <- optimize(f=square_function, lower = -10000000, upper=100000000)
minimise_function
cube_function <- function(x){
y = x^3
return(y)
}
minimise_function        <- optimize(f=cube_function, lower = -10000000, upper=100000000)
minimise_function
sinus_function <- function(x){
y = sin(x)
return(y)
}
minimise_function        <- optimize(f=sinus_function, lower = -10000000, upper=100000000)
minimise_function
bivariate_function <- function(x,y){
z <- 2*x*(y**2)+2*(x**2)*y+x*y
return(z)
}
# 1. First try a few values of x, y and see how it affect z
x<- seq(-0.5,0.5, len=200)
y<- seq(-0.5,0.5, len=200)
z <- outer(x,y,bivariate_function)
persp(x,y,z, theta=-30,phi=15,ticktype="detailed")
image(x,y,z)
bivariate_function_vector <- function(vec){
x <- vec[1]
y <- vec[2]
z <- 2*x*(y**2)+2*(x**2)*y+x*y
return(z)
}
minimise_function_bivariate <- optimr(par = c(0.5,0.5),  bivariate_function_vector, control=list(fnscale=-1))
minimise_function_bivariate$par
minimise_function_bivariate <- optimr(par = c(0.5,0.5),  bivariate_function_vector)
minimise_function_bivariate$par
minimise_function_bivariate$par
minimise_function_bivariate <- optimr(par = c(0.5,0.5),  bivariate_function)
minimise_function_bivariate <- optimr(par = c(0.5,0.5),  bivariate_function_vector)
minimise_function_bivariate$par
bivariate_function_vector <- function(vec){
x <- vec[1]
y <- vec[2]
z <-  (1-x)^2 + 100*(y-x^2)
return(z)
}
minimise_function_bivariate <- optimr(par = c(0,0),  bivariate_function_vector)
minimise_function_bivariate$par
bivariate_function_vector <- function(vec){
x <- vec[1]
y <- vec[2]
z <-  (1-x)^2 + 100*(y-x^2)^2
return(z)
}
minimise_function_bivariate <- optimr(par = c(0,0),  bivariate_function_vector)
minimise_function_bivariate$par
remvove(list=ls())
remove(list=ls())
getwd()
setwd("/Users/houdanaitelbarj/Desktop/PhoneAddiction/analysis/structural")
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Setup
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Import plotting functions and constants from lib file
source('input/lib/r/ModelFunctions.R')
# Import data
df <- import_data()
param %<>%
list.merge(
#get_opt(df),
get_taus(df, winsorize=winsorize, full=full),
get_mispredict(df),
get_ideal(df),
get_predict(df),
get_wtp(df),
get_avg_use(df),
get_fb(df),
get_limit_last_week(df)
)
param <- param_initial
param %<>%
list.merge(
#get_opt(df),
get_taus(df, winsorize=winsorize, full=full),
get_mispredict(df),
get_ideal(df),
get_predict(df),
get_wtp(df),
get_avg_use(df),
get_fb(df),
get_limit_last_week(df)
)
winsorize=F
full=F
param %<>%
list.merge(
#get_opt(df),
get_taus(df, winsorize=winsorize, full=full),
get_mispredict(df),
get_ideal(df),
get_predict(df),
get_wtp(df),
get_avg_use(df),
get_fb(df),
get_limit_last_week(df)
)
View(param)
param %<>%
solve_sys_eq_1 %>%
as.list %>%
list.merge(param)
# Solve system of equations #2
param %<>%
solve_sys_eq_2(display_warning=display_warning) %>%
as.list %>%
list.merge(param)
display_warning=FALSE
# Solve system of equation #1
param %<>%
solve_sys_eq_1 %>%
as.list %>%
list.merge(param)
# Solve system of equations #2
param %<>%
solve_sys_eq_2(display_warning=display_warning) %>%
as.list %>%
list.merge(param)
param %<>%
solve_sys_eq_3 %>%
as.list %>%
list.merge(param)
# Solve for individual effects
tau_L_2_spec   <- find_tau_L2_spec(df)
tau_tilde_spec <- find_tau_L3_spec(df)
x_ss_i_data    <- calculate_x_ss_i_spec(df)
param %<>%
solve_effects_individual(x_ss_i_data= x_ss_i_data, tau_tilde_L=tau_tilde_spec, tau_L_2=tau_L_2_spec, w=df$w)%>%
as.list %>%
list.merge(param)
rho                               <- param[['rho']]
lambda                            <- param[['lambda']]
rho_res                               <- param[['rho_res']]
lambda_res                            <- param[['lambda_res']]
delta                             <- param[['delta']]
alpha                             <- param[['alpha']]
omega                             <- param[['omega']]
omega_est                          <- param[['omega_est']]
mispredict                        <- param[['mispredict']]
d_L                               <- param[['d_L']]
d_CL                              <- param[['d_CL']]
eta                               <- param[['eta']]
zeta                              <- param[['zeta']]
naivete                           <- param[['naivete']]
gamma_L_effect                    <- param[['gamma_L_effect']]
gamma_tilde_L_effect              <- param[['gamma_tilde_L_effect']]
gamma_tilde_L_effect_omega        <- param[['gamma_tilde_L_effect_omega']]
gamma_L_effect_omega              <- param[['gamma_L_effect_omega']]
gamma_L_effect_multiple           <- param[['gamma_L_effect_multiple']]
gamma_tilde_L_effect_multiple     <- param[['gamma_tilde_L_effect_multiple']]
gamma_L                           <- param[['gamma_L']]
gamma_tilde_L                     <- param[['gamma_tilde_L']]
gamma_tilde_L_omega               <- param[['gamma_tilde_L_omega']]
gamma_L_omega                     <- param[['gamma_L_omega']]
gamma_tilde_L_multiple            <- param[['gamma_tilde_L_multiple']]
gamma_L_multiple                  <- param[['gamma_L_multiple']]
gamma_B                           <- param[['gamma_B']]
gamma_tilde_B                     <- param[['gamma_tilde_B']]
gamma_tilde_B_multiple            <- param[['gamma_tilde_B_multiple']]
gamma_B_multiple                  <- param[['gamma_B_multiple']]
eta_res                               <- param[['eta_res']]
zeta_res                              <- param[['zeta_res']]
naivete_res                           <- param[['naivete_res']]
gamma_L_effect_res                    <- param[['gamma_L_effect_res']]
gamma_tilde_L_effect_res              <- param[['gamma_tilde_L_effect_res']]
gamma_tilde_L_effect_omega_res        <- param[['gamma_tilde_L_effect_omega_res']]
gamma_L_effect_omega_res              <- param[['gamma_L_effect_omega_res']]
gamma_tilde_L_effect_multiple_res     <- param[['gamma_tilde_L_effect_multiple_res']]
gamma_L_res                           <- param[['gamma_L_res']]
gamma_L_omega_res                     <- param[['gamma_L_omega_res']]
gamma_L_multiple_res                   <- param[['gamma_L_multiple_res']]
gamma_B_res                            <- param[['gamma_B_res']]
gamma_B_multiple_res                   <- param[['gamma_B_multiple_res']]
tau_L_2_signed                    <- param[['tau_L_2']]*-1
# Gamma-spec
term1                <- (1-alpha)*delta*rho
term2                <- term1*(1+lambda)
term3                <- (eta*lambda + zeta*(1 - lambda))*(rho*tau_L_2/omega)
num                  <- eta*tau_L_2/omega - term1*term3 - term2*naivete
denom                <- 1 - term2
num_omega            <- eta*tau_L_2/omega_est - term1*term3 - term2*naivete
gamma_spec                <- num/denom
gamma_spec_omega          <- num_omega/denom
gamma_tilde_spec          <- gamma_spec - naivete
gamma_tilde_spec_omega    <- gamma_spec_omega - naivete
tau_L_2 <- param[['tau_L_2']]
# Gamma-spec
term1                <- (1-alpha)*delta*rho
term2                <- term1*(1+lambda)
term3                <- (eta*lambda + zeta*(1 - lambda))*(rho*tau_L_2/omega)
num                  <- eta*tau_L_2/omega - term1*term3 - term2*naivete
denom                <- 1 - term2
num_omega            <- eta*tau_L_2/omega_est - term1*term3 - term2*naivete
gamma_spec                <- num/denom
gamma_spec_omega          <- num_omega/denom
gamma_tilde_spec          <- gamma_spec - naivete
gamma_tilde_spec_omega    <- gamma_spec_omega - naivete
intercept_spec                <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec,           gamma_spec,      alpha, rho, lambda, mispredict, eta, zeta)
intercept_het_L_effect        <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho, lambda, mispredict, eta, zeta)
intercept_het_B               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_B,              gamma_B,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L,              gamma_L,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_spec_omega          <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec_omega,     gamma_spec_omega,      alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_omega  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect_omega, gamma_L_effect_omega,  alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_omega         <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_omega,        gamma_L_omega,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_multiple  <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_multiple, gamma_L_effect_multiple,  alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_B_multiple         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B_multiple,        gamma_B_multiple,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_multiple         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_multiple,        gamma_L_multiple,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_eta_high  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho,  lambda, mispredict,  eta, zeta, eta_scale=1.1)
intercept_het_L_effect_eta_low  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho,  lambda, mispredict,   eta, zeta, eta_scale=0.9)
x_ss_spec                        <- calculate_steady_state(param,                gamma_tilde_spec, gamma_spec,  alpha, rho,  lambda, mispredict, eta, zeta, intercept_spec)
x_ss_zero_un                     <- calculate_steady_state(param,                     0,              0,        alpha, rho,  lambda,  0,          eta, zeta, intercept_spec)
x_ss_zero                        <- ifelse(x_ss_zero_un<0, 0, x_ss_zero_un)
delta_x                          <- x_ss_spec - x_ss_zero
x_ss_spec_w                   <- weighted.mean(x_ss_spec, w, na.rm=T)
w=df$w
x_ss_spec_w                   <- weighted.mean(x_ss_spec, w, na.rm=T)
rho                               <- param[['rho']]
lambda                            <- param[['lambda']]
rho_res                               <- param[['rho_res']]
lambda_res                            <- param[['lambda_res']]
delta                             <- param[['delta']]
alpha                             <- param[['alpha']]
omega                             <- param[['omega']]
omega_est                          <- param[['omega_est']]
mispredict                        <- param[['mispredict']]
d_L                               <- param[['d_L']]
d_CL                              <- param[['d_CL']]
eta                               <- param[['eta']]
zeta                              <- param[['zeta']]
naivete                           <- param[['naivete']]
gamma_L_effect                    <- param[['gamma_L_effect']]
gamma_tilde_L_effect              <- param[['gamma_tilde_L_effect']]
gamma_tilde_L_effect_omega        <- param[['gamma_tilde_L_effect_omega']]
gamma_L_effect_omega              <- param[['gamma_L_effect_omega']]
gamma_L_effect_multiple           <- param[['gamma_L_effect_multiple']]
gamma_tilde_L_effect_multiple     <- param[['gamma_tilde_L_effect_multiple']]
gamma_L                           <- param[['gamma_L']]
gamma_tilde_L                     <- param[['gamma_tilde_L']]
gamma_tilde_L_omega               <- param[['gamma_tilde_L_omega']]
gamma_L_omega                     <- param[['gamma_L_omega']]
gamma_tilde_L_multiple            <- param[['gamma_tilde_L_multiple']]
gamma_L_multiple                  <- param[['gamma_L_multiple']]
gamma_B                           <- param[['gamma_B']]
gamma_tilde_B                     <- param[['gamma_tilde_B']]
gamma_tilde_B_multiple            <- param[['gamma_tilde_B_multiple']]
gamma_B_multiple                  <- param[['gamma_B_multiple']]
eta_res                               <- param[['eta_res']]
zeta_res                              <- param[['zeta_res']]
naivete_res                           <- param[['naivete_res']]
gamma_L_effect_res                    <- param[['gamma_L_effect_res']]
gamma_tilde_L_effect_res              <- param[['gamma_tilde_L_effect_res']]
gamma_tilde_L_effect_omega_res        <- param[['gamma_tilde_L_effect_omega_res']]
gamma_L_effect_omega_res              <- param[['gamma_L_effect_omega_res']]
gamma_tilde_L_effect_multiple_res     <- param[['gamma_tilde_L_effect_multiple_res']]
gamma_L_res                           <- param[['gamma_L_res']]
gamma_L_omega_res                     <- param[['gamma_L_omega_res']]
gamma_L_multiple_res                   <- param[['gamma_L_multiple_res']]
gamma_B_res                            <- param[['gamma_B_res']]
gamma_B_multiple_res                   <- param[['gamma_B_multiple_res']]
tau_L_2 <- param[['tau_L_2']]
tau_L_2_signed                    <- param[['tau_L_2']]*-1
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Calculate individual intercepts and steady states under different strategies - Unrestricted alpha
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Gamma-spec
term1                <- (1-alpha)*delta*rho
term2                <- term1*(1+lambda)
term3                <- (eta*lambda + zeta*(1 - lambda))*(rho*tau_L_2/omega)
num                  <- eta*tau_L_2/omega - term1*term3 - term2*naivete
denom                <- 1 - term2
num_omega            <- eta*tau_L_2/omega_est - term1*term3 - term2*naivete
gamma_spec                <- num/denom
gamma_spec_omega          <- num_omega/denom
gamma_tilde_spec          <- gamma_spec - naivete
gamma_tilde_spec_omega    <- gamma_spec_omega - naivete
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Calculate individual intercepts and steady states under different strategies
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
intercept_spec                <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec,           gamma_spec,      alpha, rho, lambda, mispredict, eta, zeta)
intercept_het_L_effect        <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho, lambda, mispredict, eta, zeta)
intercept_het_B               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_B,              gamma_B,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L,              gamma_L,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_spec_omega          <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec_omega,     gamma_spec_omega,      alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_omega  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect_omega, gamma_L_effect_omega,  alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_omega         <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_omega,        gamma_L_omega,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_multiple  <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_multiple, gamma_L_effect_multiple,  alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_B_multiple         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B_multiple,        gamma_B_multiple,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_multiple         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_multiple,        gamma_L_multiple,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_eta_high  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho,  lambda, mispredict,  eta, zeta, eta_scale=1.1)
intercept_het_L_effect_eta_low  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho,  lambda, mispredict,   eta, zeta, eta_scale=0.9)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Calculate individual counterfactuals
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x_ss_spec                        <- calculate_steady_state(param,                gamma_tilde_spec, gamma_spec,  alpha, rho,  lambda, mispredict, eta, zeta, intercept_spec)
x_ss_zero_un                     <- calculate_steady_state(param,                     0,              0,        alpha, rho,  lambda,  0,          eta, zeta, intercept_spec)
x_ss_zero                        <- ifelse(x_ss_zero_un<0, 0, x_ss_zero_un)
delta_x                          <- x_ss_spec - x_ss_zero
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Calculate individual intercepts and steady states under different strategies - Restricted alpha
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Gamma-spec
alpha_res <- 1
term1_res                <- (1-alpha_res)*delta*rho_res
term2_res                <- term1_res*(1+lambda_res)
term3_res                <- (eta_res*lambda_res + zeta_res*(1 - lambda_res))*(rho_res*tau_L_2/omega)
num_res                  <- eta_res*tau_L_2/omega - term1_res*term3_res - term2_res*naivete_res
denom_res                <- 1 - term2_res
num_omega_res            <- eta_res*tau_L_2/omega_est - term1_res*term3_res - term2_res*naivete_res
gamma_spec_res                <- num_res/denom_res
gamma_spec_omega_res          <- num_omega_res/denom_res
gamma_tilde_spec_res          <- gamma_spec_res - naivete_res
gamma_tilde_spec_omega_res    <- gamma_spec_omega_res - naivete_res
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Calculate individual intercepts and steady states under different strategies
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
intercept_spec_res                <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec_res,           gamma_spec_res,      alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_effect_res        <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect_res,       gamma_L_effect_res,  alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_B_res               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_B,              gamma_B_res,         alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_res               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L,              gamma_L_res,         alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_spec_omega_res          <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec_omega_res,     gamma_spec_omega_res,      alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_effect_omega_res  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect_omega_res, gamma_L_effect_omega_res,  alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_omega_res         <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_omega,        gamma_L_omega_res,         alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_effect_multiple_res  <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_multiple, gamma_L_effect_multiple,  alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_B_multiple_res         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B_multiple,        gamma_B_multiple,         alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_multiple_res         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_multiple,        gamma_L_multiple,         alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res, zeta = zeta_res)
intercept_het_L_effect_eta_high_res  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res,  zeta =  zeta_res, eta_scale=1.1)
intercept_het_L_effect_eta_low_res  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha = 1, rho_res, lambda_res, mispredict,   eta = eta_res,  zeta =  zeta_res, eta_scale=0.9)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Calculate individual counterfactuals
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x_ss_spec_res                        <- calculate_steady_state(param,                gamma_tilde_spec_res, gamma_spec_res,  alpha = 1, rho_res, lambda_res, mispredict, eta = eta_res,  zeta =  zeta_res, intercept_spec_res)
x_ss_zero_un_res                     <- calculate_steady_state(param,                     0,              0,        alpha = 1, rho_res, lambda_res, 0,          eta = eta_res,  zeta =  zeta_res, intercept_spec_res)
x_ss_zero_res                        <- ifelse(x_ss_zero_un_res<0, 0, x_ss_zero_un_res)
delta_x_res                          <- x_ss_spec_res - x_ss_zero_res
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Compute population averages
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x_ss_spec_w                   <- weighted.mean(x_ss_spec, w, na.rm=T)
gamma_tilde_spec_w            <- weighted.mean(gamma_tilde_spec, w, na.rm=T)
gamma_spec_w                  <- weighted.mean(gamma_spec, w, na.rm=T)
gamma_spec_omega_w            <- weighted.mean(gamma_spec_omega, w, na.rm=T)
delta_x_spec                  <- weighted.mean(delta_x, w, na.rm=T)
x_ss_i_data                   <- weighted.mean(x_ss_i_data, w, na.rm=T)
remove(list=ls())
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Setup
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Import plotting functions and constants from lib file
source('input/lib/r/ModelFunctions.R')
# Import data
df <- import_data()
param <- param_initial
winsorize=F, full=F, display_warning=FALS
winsorize=F
full=F
display_warning=FALSE
param %<>%
list.merge(
#get_opt(df),
get_taus(df, winsorize=winsorize, full=full),
get_mispredict(df),
get_ideal(df),
get_predict(df),
get_wtp(df),
get_avg_use(df),
get_fb(df),
get_limit_last_week(df)
)
# Solve system of equation #1
param %<>%
solve_sys_eq_1 %>%
as.list %>%
list.merge(param)
# Solve system of equations #2
param %<>%
solve_sys_eq_2(display_warning=display_warning) %>%
as.list %>%
list.merge(param)
# Solve system of equations #3
param %<>%
solve_sys_eq_3 %>%
as.list %>%
list.merge(param)
# Solve for individual effects
tau_L_2_spec   <- find_tau_L2_spec(df)
tau_tilde_spec <- find_tau_L3_spec(df)
x_ss_i_data    <- calculate_x_ss_i_spec(df)
param %<>%
solve_effects_individual(x_ss_i_data= x_ss_i_data, tau_tilde_L=tau_tilde_spec, tau_L_2=tau_L_2_spec, w=df$w)%>%
as.list %>%
list.merge(param)
tau_tilde_L=tau_tilde_spec
tau_L_2=tau_L_2_spec
w=df$w
rho                               <- param[['rho']]
lambda                            <- param[['lambda']]
rho_res                               <- param[['rho_res']]
lambda_res                            <- param[['lambda_res']]
delta                             <- param[['delta']]
alpha                             <- param[['alpha']]
omega                             <- param[['omega']]
omega_est                          <- param[['omega_est']]
mispredict                        <- param[['mispredict']]
d_L                               <- param[['d_L']]
d_CL                              <- param[['d_CL']]
eta                               <- param[['eta']]
zeta                              <- param[['zeta']]
naivete                           <- param[['naivete']]
gamma_L_effect                    <- param[['gamma_L_effect']]
gamma_tilde_L_effect              <- param[['gamma_tilde_L_effect']]
gamma_tilde_L_effect_omega        <- param[['gamma_tilde_L_effect_omega']]
gamma_L_effect_omega              <- param[['gamma_L_effect_omega']]
gamma_L_effect_multiple           <- param[['gamma_L_effect_multiple']]
gamma_tilde_L_effect_multiple     <- param[['gamma_tilde_L_effect_multiple']]
gamma_L                           <- param[['gamma_L']]
gamma_tilde_L                     <- param[['gamma_tilde_L']]
gamma_tilde_L_omega               <- param[['gamma_tilde_L_omega']]
gamma_L_omega                     <- param[['gamma_L_omega']]
gamma_tilde_L_multiple            <- param[['gamma_tilde_L_multiple']]
gamma_L_multiple                  <- param[['gamma_L_multiple']]
gamma_B                           <- param[['gamma_B']]
gamma_tilde_B                     <- param[['gamma_tilde_B']]
gamma_tilde_B_multiple            <- param[['gamma_tilde_B_multiple']]
gamma_B_multiple                  <- param[['gamma_B_multiple']]
eta_res                               <- param[['eta_res']]
zeta_res                              <- param[['zeta_res']]
naivete_res                           <- param[['naivete_res']]
gamma_L_effect_res                    <- param[['gamma_L_effect_res']]
gamma_tilde_L_effect_res              <- param[['gamma_tilde_L_effect_res']]
gamma_tilde_L_effect_omega_res        <- param[['gamma_tilde_L_effect_omega_res']]
gamma_L_effect_omega_res              <- param[['gamma_L_effect_omega_res']]
gamma_tilde_L_effect_multiple_res     <- param[['gamma_tilde_L_effect_multiple_res']]
gamma_L_res                           <- param[['gamma_L_res']]
gamma_L_omega_res                     <- param[['gamma_L_omega_res']]
gamma_L_multiple_res                   <- param[['gamma_L_multiple_res']]
gamma_B_res                            <- param[['gamma_B_res']]
gamma_B_multiple_res                   <- param[['gamma_B_multiple_res']]
tau_L_2_signed                    <- param[['tau_L_2']]*-1
# Gamma-spec
num                  <- eta*tau_L_2/omega - (1-alpha)*delta*rho*(((eta-zeta)*tau_tilde_L/omega+zeta*rho*tau_L_2/omega) + (1+lambda)*mispredict*(-eta+(1-alpha)*delta*rho^2*((eta-zeta)*lambda+zeta)))
denom                <- 1 - (1-alpha)*delta*rho*(1+lambda)
num_omega            <- eta*tau_L_2/omega_est - (1-alpha)*delta*rho*(((eta-zeta)*tau_tilde_L/omega_est+zeta*rho*tau_L_2/omega) + (1+lambda)*mispredict*(-eta+(1-alpha)*delta*rho^2*((eta-zeta)*lambda+zeta)))
gamma_spec                <- num/denom
gamma_spec_omega          <- num_omega/denom
gamma_tilde_spec          <- gamma_spec - naivete
gamma_tilde_spec_omega    <- gamma_spec_omega - naivete
intercept_spec                <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec,           gamma_spec,      alpha, rho, lambda, mispredict, eta, zeta)
intercept_het_L_effect        <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho, lambda, mispredict, eta, zeta)
intercept_het_B               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_B,              gamma_B,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L               <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L,              gamma_L,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_spec_omega          <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_spec_omega,     gamma_spec_omega,      alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_omega  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect_omega, gamma_L_effect_omega,  alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_omega         <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_omega,        gamma_L_omega,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_multiple  <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_effect_multiple, gamma_L_effect_multiple,  alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_B_multiple         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_B_multiple,        gamma_B_multiple,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_multiple         <-  calculate_intercept_spec(x_ss_i_data, param, gamma_tilde_L_multiple,        gamma_L_multiple,         alpha, rho,  lambda, mispredict, eta, zeta)
intercept_het_L_effect_eta_high  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho,  lambda, mispredict,  eta, zeta, eta_scale=1.1)
intercept_het_L_effect_eta_low  <-  calculate_intercept_spec(x_ss_i_data, param,    gamma_tilde_L_effect,       gamma_L_effect,  alpha, rho,  lambda, mispredict,   eta, zeta, eta_scale=0.9)
x_ss_spec                        <- calculate_steady_state(param,                gamma_tilde_spec, gamma_spec,  alpha, rho,  lambda, mispredict, eta, zeta, intercept_spec)
x_ss_spec                        <- calculate_steady_state(param,                gamma_tilde_spec, gamma_spec,  alpha, rho,  lambda, mispredict, eta, zeta, intercept_spec)
calculate_steady_state <- function(param, gamma_tilde, gamma, alpha, rho, lambda, mispredict, eta, zeta, intercept=NA, eta_scale=1){
# Define
eta           <- eta * eta_scale
delta         <- param[['delta']]
p_B           <- param[['p_B']]
# Calculate
p <- 0
term_pre <- (1 - (1-alpha)*delta*rho)
term1 <- intercept - p*term_pre
term2 <- (1-alpha)*delta*rho
term3 <- (eta - zeta) * mispredict + gamma_tilde*(1+lambda)
num <- term1 - term2*term3 + gamma
terma <- term_pre*(-eta - zeta * (rho / (1 - rho)))
termb <- (1-alpha)*delta*rho*zeta
denom <- terma + termb
print(paste0("denom: ", denom))
x_ss_calc <- num /denom
return(x_ss_calc)
}
x_ss_spec                        <- calculate_steady_state(param,                gamma_tilde_spec, gamma_spec,  alpha, rho,  lambda, mispredict, eta, zeta, intercept_spec)
x_ss_zero_un                     <- calculate_steady_state(param,                     0,              0,        alpha, rho,  lambda,  0,          eta, zeta, intercept_spec)
x_ss_zero                        <- ifelse(x_ss_zero_un<0, 0, x_ss_zero_un)
delta_x                          <- x_ss_spec - x_ss_zero
x_ss_spec_w                   <- weighted.mean(x_ss_spec, w, na.rm=T)