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Copy path3.SFA_CSH.R
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3.SFA_CSH.R
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# 0. Imports --------------------------------------------------------------
library(frontier)
library(dplyr)
library(tidyr)
library(ggplot2)
library(xtable)
library(plm)
library(stargazer)
library(purrr)
library(stringr)
library(gridExtra)
# I. SFA Portugal Continent for Operational Costs -------------------------
## 1. Data --------------------------------------------------------------
load("0.DataBase/CSH.RData")
dir.create("3.SFA_outputs")
setwd("3.SFA_outputs")
dir.create("CSH")
setwd("CSH")
dir.create("1. Portugal Frontier (operational)")
setwd("1. Portugal Frontier (operational)")
### A. Select variables and test correlation --------------------------
# correlation testing
corr_table = CSH |>
select(operational_ACSS, in_days, RO, surg, app, urge,
patient_dis, wait_scheduled_surg) |>
cor()
# Discard volume variables that have high correlation
#(choosen the scale variable will capture the effects of the others)
CSH_0 = CSH |> select(hospital, year, in_days, RO, azo, region, operational_ACSS,
surg, wait_scheduled_surg) |>
filter(azo == 0) |>
drop_na()
### B. Panel data -----------------------------------------------------
CSH_panel = pdata.frame(CSH_0, c("hospital", "year"))
### C. Define functional forms ----------------------------------------
form = log(operational_ACSS) ~ log(in_days) + log(RO) # includes Dummy variable
formt = log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) + log(RO)
# Firm level inefficiencies models BC95
# mean inefficiency of u_it is "determined" by factors z_it
formz = log(operational_ACSS) ~ log(in_days) +log(surg) | wait_scheduled_surg
formtz = log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) | RO + wait_scheduled_surg
# FE model G05 (Greene)
# time invariant individual heterogeneity is not separate from individual innefficieny
form_r = log(operational_ACSS) ~ log(in_days) + log(RO) + factor(region)
formt_r = log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) + log(RO) + factor(region)
## 2. Operational Cost function : Continent -----------------------------
### 2.1 Estimation: time invariant inefficiencies ------------------------
#### A. Cobb-Douglas (form) -------------------------------------------
sfront = sfa( form,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfront, extraPar = TRUE)
#### B. Trans log (formt) ---------------------------------------------
sfrontt = sfa( formt,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfrontt)
#### C. Cobb-Douglas with z_it (formz) --------------------------------
sfrontz = sfa( formz,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfrontz)
#### D. Trans log with z_it (formtz) ----------------------------------
sfronttz = sfa( formtz,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfronttz)
#### E. Cobb-Douglas with FE by region (form_r) -----------------------
sfrontr = sfa( form_r,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfrontr)
#### F. Trans Log with FE by region (form_r) --------------------------
sfronttr = sfa( formt_r,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfronttr)
## 3. Tables ------------------------------------------------------------
#### A. BC92 ------------------------------------------------------------
# Creative approach to export SFA tables (since normal packages don't support format)
# save the coefficients and p-v as vectors:
c1 = as.vector(coef(sfront))
c2 = as.vector(coef(sfrontt))
pv1 = as.vector(coef(summary(sfront))[,4])
pv2 = as.vector(coef(summary(sfrontt))[,4])
# save gamma parameter, nº of time periods, log-likelihood and mean efficiency
g1 = round(as.vector(coef(summary(sfront, extraPar = TRUE))[nrow(coef(summary(sfront, extraPar = TRUE))),1]), 3)
g2 = round(as.vector(coef(summary(sfrontt, extraPar = TRUE))[nrow(coef(summary(sfront, extraPar = TRUE))),1]),3)
ll1 = round(as.numeric(logLik(sfront, which = "mle")),3)
ll2 = round(as.numeric(logLik(sfrontt, which = "mle")),3)
me1 = round(summary(sfrontz)$efficMean,3)
me2 = round(summary(sfronttz)$efficMean,3)
#run the same specifications using a linear model
# (remember to change the "|" before the z variables to a "+" in the linear model):
lm1 = lm(form, data = CSH_panel)
lm2 = lm(formt, data = CSH_panel)
#Finally, use stargazer on the linear models, and change the coefficients and the standard errors reported using the "coef" and "se" arguments:
stargazer(lm1, lm2,
coef = list(c1,c2),
se = list(c1,c2),
p = list(pv1,pv2),
t.auto = FALSE,
p.auto = FALSE,
intercept.bottom = FALSE,
digits = 3, float.env = "table",
dep.var.labels=c("$\\log$ Operational Costs"),
title = "Stochastic Frontier: Hospital Healthcare",
column.labels = c("Cobb-Douglas", "Translog"),
model.numbers = TRUE,
out = "SFAregression_table_CSH.tex",
omit.stat = c("rsq", "adj.rsq", "ser", "f"),
add.lines = list(c("Gamma", g1, g2),
c("Log-likelihood value", ll1,ll2),
c("Mean efficiency", me1, me2)),
covariate.labels = c("Constant","$\\log \\text{inpatient days}$",
"$(\\log \\text{inpatient days}) ^2$",
"$\\log$ Rate of Occupancy"))
#### B. BC95 ------------------------------------------------------------
# Creative approach to export SFA tables (since normal packages don't support format)
# save the coefficients and p-v as vectors:
c1 = as.vector(coef(sfrontz))
c2 = as.vector(coef(sfronttz))
pv1 = as.vector(coef(summary(sfrontz))[,4])
pv2 = as.vector(coef(summary(sfronttz))[,4])
# save gamma parameter, nº of time periods, log-likelihood and mean efficiency
g1 = round(as.vector(coef(summary(sfrontz, extraPar = TRUE))[9,1]), 3)
g2 = round(as.vector(coef(summary(sfronttz, extraPar = TRUE))[9,1]),3)
ll1 = round(as.numeric(logLik(sfrontz, which = "mle")),3)
ll2 = round(as.numeric(logLik(sfronttz, which = "mle")),3)
me1 = round(summary(sfrontz)$efficMean,3)
me2 = round(summary(sfronttz)$efficMean,3)
#run the same specifications using a linear model
# (remember to change the "|" before the z variables to a "+" in the linear model):
lm1 = lm(log(operational_ACSS) ~ log(in_days) + log(RO) + RO + wait_scheduled_surg, data = CSH_panel)
lm2 = lm(log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) + log(RO) + RO + wait_scheduled_surg, data = CSH_panel)
#Finally, use stargazer on the linear models, and change the coefficients and the standard errors reported using the "coef" and "se" arguments:
stargazer(lm1, lm2,
coef = list(c1,c2),
p = list(pv1,pv2),
se = list(pv1,pv2),
t.auto = FALSE,
p.auto = FALSE,
intercept.bottom = FALSE,
digits = 3, float.env = "table",
dep.var.labels=c("$\\log$ Operational Costs"),
title = "Stochastic Frontier: Hospital Healthcare",
column.labels = c("Cobb-Douglas", "Translog"),
model.numbers = TRUE,
out = "SFAregressionz_table_CSH.tex",
omit.stat = c("rsq", "adj.rsq", "ser", "f"),
add.lines = list(c("Gamma", g1, g2),
c("Log-likelihood value", ll1,ll2),
c("Mean efficiency", me1, me2)),
covariate.labels = c("Constant", "$\\log \\text{inpatient days}$",
"$(\\log \\text{inpatient days}) ^2$",
"Z Constant", "Rate of Occupancy", "Wait for Scheduled Surgeries"))
## 4. Azores Prediction: Continent Frontier -----------------------------
### 4.1 Prediction Portugal Continent -----------------------------------
CSH_predict = CSH_panel |> select(hospital, year, operational_ACSS)
# A. prediction tables
prediction_sfa = data.frame(predict = predict(sfront, newdata = CSH_panel),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfa" = "predict")
prediction_sfat = data.frame(predict = predict(sfrontt, newdata = CSH_panel),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfat" = "predict")
prediction_sfaz = data.frame(predict = predict(sfrontz, newdata = CSH_panel),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfaz" = "predict")
prediction_sfatz = data.frame(predict = predict(sfronttz, newdata = CSH_panel),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfatz" = "predict")
# B. Join all data frames
list_df = list(CSH_predict, prediction_sfa,
prediction_sfat, prediction_sfaz, prediction_sfatz)
CSH_predict = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital",
"year" = "year"),
.init = NULL))
### 4.2 Prediction Azores Island ----------------------------------------
CSH_panel_a = CSH |> select(hospital, year, operational_ACSS, in_days, RO, azo, region,
surg, app, urge, patient_dis, wait_scheduled_surg) |>
filter(azo ==1) |> drop_na() |> pdata.frame(c("hospital", "year"))
CSH_predict_a = CSH_panel_a |> select(hospital, year, operational_ACSS)
# A. prediction tables
prediction_sfa = data.frame(predict = exp(predict(sfront, newdata = CSH_panel_a)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel_a)))) |>
separate("hospital", c("hospital", "year"),sep = "-")
prediction_sfat = data.frame(predict = exp(predict(sfrontt, newdata = CSH_panel_a)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel_a)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predictt" = "predict")
prediction_sfaz = data.frame(predict = exp(predict(sfrontz, newdata = CSH_panel_a)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel_a)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predictz" = "predict")
prediction_sfatz = data.frame(predict = exp(predict(sfronttz, newdata = CSH_panel_a)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel_a)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predicttz" = "predict")
# B. Join all data frames
list_df = list(CSH_predict_a, prediction_sfa,
prediction_sfat, prediction_sfaz, prediction_sfatz)
CSH_predict_a = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital",
"year" = "year"),
.init = NULL))
# C. Differences
# These differences are too high
CSH_predict_a = CSH_predict_a |> mutate(difference = operational_ACSS - predict, differencet = operational_ACSS - predictt,
differencez = operational_ACSS - predictz, differencetz = operational_ACSS - predicttz)
### 4.3 Efficiency Portugal Continent -----------------------------------
# A. Efficiency tables
efficiencies_sfa = data.frame(hospital = rownames(efficiencies(sfront, newdata = CSH_panel)),
efficiency = efficiencies(sfront, newdata = CSH_panel)) |>
rename("efficiency_sfa" = "efficiency")
efficiencies_sfat = data.frame(efficiency = efficiencies(sfrontt, newdata = CSH_panel),
hospital = rownames(efficiencies(sfrontt, newdata = CSH_panel))) |>
rename("efficiency_sfat" = "efficiency")
efficiencies_sfaz = data.frame(efficiency = efficiencies(sfrontz, newdata = CSH_panel),
hospital = rownames(efficiencies(sfrontz, newdata = CSH_panel)))
efficiencies_sfatz = data.frame(efficiency = efficiencies(sfronttz, newdata = CSH_panel),
hospital = rownames(efficiencies(sfronttz, newdata = CSH_panel))) |>
rename("efficiencyt.2015" = "efficiency.2015", "efficiencyt.2016" = "efficiency.2016",
"efficiencyt.2017" = "efficiency.2017", "efficiencyt.2018" = "efficiency.2018",
"efficiencyt.2019" = "efficiency.2019", "efficiencyt.2020" = "efficiency.2020",
"efficiencyt.2021" = "efficiency.2021")
# B. Join all efficiency tables
list_df = list(efficiencies_sfa, efficiencies_sfat,
efficiencies_sfaz, efficiencies_sfatz)
CSH_effi = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital"),
.init = NULL))
# C. Descriptive
CSH_effi = CSH_effi |> mutate(mean_efficiencyz = rowMeans(CSH_effi[,4:10], na.rm = TRUE),
mean_efficiencytz = rowMeans(CSH_effi[,11:16], na.rm = TRUE))
### 4.4 Efficiency Azores Island ----------------------------------------
# A. Efficiency tables
efficiencies_sfa = data.frame(efficiency = efficiencies(sfront, newdata = CSH_panel_a),
hospital = rownames(efficiencies(sfront, newdata = CSH_panel_a))) |>
rename("efficiency_sfa" = "efficiency")
efficiencies_sfat = data.frame(efficiency = efficiencies(sfrontt, newdata = CSH_panel_a),
hospital = rownames(efficiencies(sfrontt, newdata = CSH_panel_a))) |>
rename("efficiency_sfat" = "efficiency")
efficiencies_sfaz = data.frame(efficiency = efficiencies(sfrontz, newdata = CSH_panel_a),
hospital = rownames(efficiencies(sfrontz, newdata = CSH_panel_a)))
efficiencies_sfatz = data.frame(efficiency = efficiencies(sfronttz, newdata = CSH_panel_a),
hospital = rownames(efficiencies(sfronttz, newdata = CSH_panel_a))) |>
rename("efficiencyt.2015" = "efficiency.2015", "efficiencyt.2016" = "efficiency.2016",
"efficiencyt.2017" = "efficiency.2017", "efficiencyt.2018" = "efficiency.2018",
"efficiencyt.2019" = "efficiency.2019", "efficiencyt.2020" = "efficiency.2020",
"efficiencyt.2021" = "efficiency.2021")
# B. Join all efficiency tables
list_df = list(efficiencies_sfa, efficiencies_sfat,
efficiencies_sfaz, efficiencies_sfatz)
CSH_effi_a = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital"),
.init = NULL))
# C. Descriptive
CSH_effi = CSH_effi |> mutate(mean_efficiencyz = rowMeans(CSH_effi[,4:10], na.rm = TRUE),
mean_efficiencytz = rowMeans(CSH_effi[,11:16], na.rm = TRUE))
### 4.5 Prediction Azores and Portugal ----------------------------------
CSH_panel = CSH |> select(azo, hospital, year, operational_ACSS, in_days, RO, azo, region,
surg, urge, wait_scheduled_surg) |>
drop_na() |> pdata.frame(c("hospital", "year"))
CSH_predict = CSH_panel |> select(hospital, year, operational_ACSS,azo)
# A. prediction tables
prediction_sfa = data.frame(predict = exp(predict(sfront, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfa" = "predict")
prediction_sfat = data.frame(predict = exp(predict(sfrontt, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfat" = "predict")
prediction_sfaz = data.frame(predict = exp(predict(sfrontz, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfaz" = "predict")
prediction_sfatz = data.frame(predict = exp(predict(sfronttz, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfatz" = "predict")
# B. Join all data frames
list_df = list(CSH_predict, prediction_sfa,
prediction_sfat, prediction_sfaz, prediction_sfatz)
CSH_predict = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital",
"year" = "year"),
.init = NULL))
# C. Differences
# These differences are too high
CSH_predict = CSH_predict |> mutate(difference = operational_ACSS - predict_sfa, differencet = operational_ACSS - predict_sfat,
differencez = operational_ACSS - predict_sfaz, differencetz = operational_ACSS - predict_sfatz,
difference_perc_sfa = (operational_ACSS - predict_sfa)/predict_sfa,
difference_perc_sfat = (operational_ACSS - predict_sfat)/predict_sfat,
difference_perc_sfaz = (operational_ACSS - predict_sfaz)/predict_sfaz,
difference_perc_sfatz = (operational_ACSS - predict_sfatz)/predict_sfatz)
write.csv(CSH_predict, "CSH_predict.csv", row.names = FALSE)
### 4.6 Efficiency Azores and Portugal ----------------------------------
# A. Efficiency tables
efficiencies_sfa = data.frame(efficiency = efficiencies(sfront, newdata = CSH_panel),
hospital = rownames(efficiencies(sfront, newdata = CSH_panel))) |>
rename("efficiency_sfa" = "efficiency")
efficiencies_sfat = data.frame(efficiency = efficiencies(sfrontt, newdata = CSH_panel),
hospital = rownames(efficiencies(sfrontt, newdata = CSH_panel))) |>
rename("efficiency_sfat" = "efficiency")
efficiencies_sfaz = data.frame(hospital = rownames(efficiencies(sfrontz, newdata = CSH_panel)),
efficiency = efficiencies(sfrontz, newdata = CSH_panel)) |>
pivot_longer(c("efficiency.2015","efficiency.2016", "efficiency.2017", "efficiency.2018",
"efficiency.2019", "efficiency.2020", "efficiency.2021"),
names_to = "year", values_to = "efficiency_sfa_z") |>
mutate( year = str_remove(year, ".*\\.")) # .(any character) *(zero or more occurences) \\. (".")
efficiencies_sfatz = data.frame(efficiency = efficiencies(sfronttz, newdata = CSH_panel),
hospital = rownames(efficiencies(sfronttz, newdata = CSH_panel))) |>
pivot_longer(c("efficiency.2015","efficiency.2016", "efficiency.2017", "efficiency.2018",
"efficiency.2019", "efficiency.2020", "efficiency.2021"),
names_to = "year", values_to = "efficiency_sfa_tz") |>
mutate( year = str_remove(year, ".*\\."))
# B. Join all efficiency tables
list_df = list(efficiencies_sfa, efficiencies_sfat,
efficiencies_sfaz, efficiencies_sfatz)
CSH_effi = full_join(efficiencies_sfaz, efficiencies_sfatz,
by = c("hospital" = "hospital", "year" = "year"))
CSH_effi = bind_rows(CSH_effi, full_join(efficiencies_sfa,efficiencies_sfat),
by = c("hospital" = "hospital"))
write.csv(CSH_effi, "CSH_effi.csv", row.names = FALSE)
# II. SFA Portugal & Islands for Operational Costs -----------------------
## 1. Data --------------------------------------------------------------
rm(list = setdiff(ls(), c("CSH", "sfrontz")))
setwd("..")
dir.create("2. Frontier w Azores Dummy (operational)")
setwd("2. Frontier w Azores Dummy (operational)")
#### A. Select variables and test correlation -------------------------
CSH_panel = CSH |> select(hospital, year, operational_ACSS, in_days, RO, azo, region,
surg, wait_scheduled_surg) |>
drop_na() |>
pdata.frame(c("hospital", "year"))
## 1.1 Define functional forms ----------------------------------------
form = log(operational_ACSS) ~ log(in_days) + log(RO) + azo
formt = log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) + log(RO) + azo
# Firm level inefficiencies models BC95
# mean inefficiency of u_it is "determined" by factors z_it
formz = log(operational_ACSS) ~ log(in_days) + log(surg) + azo| wait_scheduled_surg
formtz = log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) + azo| RO + wait_scheduled_surg
## 2. Operational Cost function: Azores Dummy ---------------------------
#(choosen the scale variable will capture the effects of the others)
CSH_0 = CSH |> select(hospital, year, operational_ACSS, in_days, RO, azo, region,
surg, urge, wait_scheduled_surg) |>
drop_na()
### 2.1 Estimation: time invariant inefficiencies --------------------
#### A. Cobb-Douglas (form) ----------------------------------------
sfrontd = sfa( form,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfrontd, extraPar = TRUE)
#### B. Trans log (formt) ------------------------------------------
sfronttd = sfa( formt,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfronttd)
#### C. Cobb-Douglas with z_it (formz) ------------------------------
sfrontzd = sfa( formz,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfrontzd)
summary(sfrontz)
#### D. Trans log with z_it (formtz) --------------------------------
sfronttzd = sfa( formtz,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfronttzd)
## 3. Tables ------------------------------------------------------------
### A. BC92 -----------------------------------------------------------
# Creative approach to export SFA tables (since normal packages don't support format)
# save the coefficients and p-v as vectors:
c1 = as.vector(coef(sfrontd))
c2 = as.vector(coef(sfronttd))
pv1 = as.vector(coef(summary(sfrontd))[,4])
pv2 = as.vector(coef(summary(sfronttd))[,4])
# save gamma parameter, nº of time periods, log-likelihood and mean efficiency
g1 = round(as.vector(coef(summary(sfrontd, extraPar = TRUE))[nrow(coef(summary(sfrontd, extraPar = TRUE))),1]), 3)
g2 = round(as.vector(coef(summary(sfronttd, extraPar = TRUE))[nrow(coef(summary(sfrontd, extraPar = TRUE))),1]),3)
ll1 = round(as.numeric(logLik(sfrontd, which = "mle")),3)
ll2 = round(as.numeric(logLik(sfronttd, which = "mle")),3)
me1 = round(summary(sfrontzd)$efficMean,3)
me2 = round(summary(sfronttzd)$efficMean,3)
#run the same specifications using a linear model
# (remember to change the "|" before the z variables to a "+" in the linear model):
lm1 = lm(form, data = CSH_panel)
lm2 = lm(formt, data = CSH_panel)
#Finally, use stargazer on the linear models, and change the coefficients and the standard errors reported using the "coef" and "se" arguments:
stargazer(lm1, lm2,
coef = list(c1,c2),
se = list(c1,c2),
p = list(pv1,pv2),
t.auto = FALSE,
p.auto = FALSE,
intercept.bottom = FALSE,
digits = 3, float.env = "table",
dep.var.labels=c("$\\log$ Operational Costs"),
title = "Stochastic Frontier: Hospital Healthcare",
column.labels = c("Cobb-Douglas", "Translog"),
model.numbers = TRUE,
out = "SFAregression_table_1_CSH.tex",
omit.stat = c("rsq", "adj.rsq", "ser", "f"),
add.lines = list(c("Gamma", g1, g2),
c("Log-likelihood value", ll1,ll2),
c("Mean efficiency", me1, me2)),
covariate.labels = c("Constant","$\\log \\text{inpatient days}$",
"$(\\log \\text{inpatient days}) ^2$",
"$\\log$ Rate of Occupancy", "Azores"))
### B. BC95 -----------------------------------------------------------
# Creative approach to export SFA tables (since normal packages don't support format)
# save the coefficients and p-v as vectors:
c1 = as.vector(coef(sfrontzd))
c2 = as.vector(coef(sfronttzd))
pv1 = as.vector(coef(summary(sfrontzd))[,4])
pv2 = as.vector(coef(summary(sfronttzd))[,4])
# save gamma parameter, nº of time periods, log-likelihood and mean efficiency
g1 = round(as.vector(coef(summary(sfrontzd, extraPar = TRUE))[9,1]), 3)
g2 = round(as.vector(coef(summary(sfronttzd, extraPar = TRUE))[9,1]),3)
ll1 = round(as.numeric(logLik(sfrontzd, which = "mle")),3)
ll2 = round(as.numeric(logLik(sfronttzd, which = "mle")),3)
me1 = round(summary(sfrontzd)$efficMean,3)
me2 = round(summary(sfronttzd)$efficMean,3)
#run the same specifications using a linear model
# (remember to change the "|" before the z variables to a "+" in the linear model):
lm1 = lm(log(operational_ACSS) ~ log(in_days) + azo + log(RO) + RO + wait_scheduled_surg, data = CSH_panel)
lm2 = lm(log(operational_ACSS) ~ log(in_days) + I((log(in_days)^2)/2) + azo + log(RO) + RO + wait_scheduled_surg, data = CSH_panel)
#Finally, use stargazer on the linear models, and change the coefficients and the standard errors reported using the "coef" and "se" arguments:
stargazer(lm1, lm2,
coef = list(c1,c2),
p = list(pv1,pv2),
se = list(pv1,pv2),
t.auto = FALSE,
p.auto = FALSE,
intercept.bottom = FALSE,
digits = 3, float.env = "table",
dep.var.labels=c("$\\log$ Operational Costs"),
title = "Stochastic Frontier: Hospital Healthcare",
column.labels = c("Cobb-Douglas", "Translog"),
model.numbers = TRUE,
out = "SFAregression_table_2_CSH.tex",
omit.stat = c("rsq", "adj.rsq", "ser", "f"),
add.lines = list(c("Gamma", g1, g2),
c("Log-likelihood value", ll1,ll2),
c("Mean efficiency", me1, me2)),
covariate.labels = c("Constant", "$\\log \\text{inpatient days}$",
"$(\\log \\text{inpatient days}) ^2$", "Azores",
"Z Constant", "Rate of Occupancy", "Wait for Scheduled Surgeries"))
### B. BC95: w/ and wthout/ dummy -------------------------------------
# Creative approach to export SFA tables (since normal packages don't support format)
# save the coefficients and p-v as vectors:
c1 = as.vector(coef(sfrontz))
c2 = as.vector(coef(sfrontzd))
pv1 = as.vector(coef(summary(sfrontz))[,4])
pv2 = as.vector(coef(summary(sfrontzd))[,4])
# save gamma parameter, nº of time periods, log-likelihood and mean efficiency
g1 = round(as.vector(coef(summary(sfrontz, extraPar = TRUE))[6,1]), 3)
g2 = round(as.vector(coef(summary(sfrontzd, extraPar = TRUE))[7,1]),3)
ll1 = round(as.numeric(logLik(sfrontz, which = "mle")),3)
ll2 = round(as.numeric(logLik(sfrontzd, which = "mle")),3)
me1 = round(summary(sfrontz)$efficMean,3)
me2 = round(summary(sfrontzd)$efficMean,3)
#run the same specifications using a linear model
# (remember to change the "|" before the z variables to a "+" in the linear model):
lm1 = lm(log(operational_ACSS) ~ log(in_days) + RO + wait_scheduled_surg, data = CSH_panel)
lm2 = lm(log(operational_ACSS) ~ log(in_days) + log(surg) + azo + RO + wait_scheduled_surg, data = CSH_panel)
#Finally, use stargazer on the linear models, and change the coefficients and the standard errors reported using the "coef" and "se" arguments:
stargazer(lm1, lm2,
coef = list(c1,c2),
p = list(pv1,pv2),
se = list(pv1,pv2),
t.auto = FALSE,
p.auto = FALSE,
intercept.bottom = FALSE,
digits = 3, float.env = "table",
dep.var.labels=c("$\\log$ Operational Costs"),
title = "Stochastic Frontier: Hospital Healthcare",
column.labels = c("Cobb-Douglas", "Translog"),
model.numbers = TRUE,
out = "SFAregression_dummy_table_3_CSH.tex",
omit.stat = c("rsq", "adj.rsq", "ser", "f"),
add.lines = list(c("Gamma", g1, g2),
c("Log-likelihood value", ll1,ll2),
c("Mean efficiency", me1, me2)),
covariate.labels = c("Constant", "$\\log \\text{inpatient days}$","$\\log \\text{surgeries}$",
"Azores",
"Z Constant", "Wait for Scheduled Surgeries"))
## 4. Azores Prediction: Dummy Frontier ---------------------------------
### 4.1 Prediction ----------------------------------------------------
CSH_predict = CSH_panel |> select(hospital, year, operational_ACSS, azo, in_days)
# A. prediction tables
# SFA
prediction_sfa = data.frame(predict = exp(predict(sfrontd, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfrontd, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfa" = "predict")
# SFA Trans
prediction_sfat = data.frame(predict = exp(predict(sfronttd, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfrontd, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfat" = "predict")
# SFA Z
prediction_sfaz = data.frame(predict = exp(predict(sfrontzd, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfronttzd, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfaz" = "predict")
# SFA Trans Z
prediction_sfatz = data.frame(predict = exp(predict(sfronttzd, newdata = CSH_panel)),
hospital = rownames(data.frame(predict(sfronttzd, newdata = CSH_panel)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfatz" = "predict")
# B. Join all data frames
list_df = list(CSH_predict, prediction_sfa,
prediction_sfat, prediction_sfaz, prediction_sfatz)
CSH_predict = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital",
"year" = "year"),
.init = NULL))
# C. Differences
# These differences are too high
CSH_predict = CSH_predict |> mutate(difference = operational_ACSS - predict_sfa, differencet = operational_ACSS - predict_sfat,
differencez = operational_ACSS - predict_sfaz, differencetz = operational_ACSS - predict_sfatz,
difference_perc_sfa = (operational_ACSS - predict_sfa)/predict_sfa,
difference_perc_sfat = (operational_ACSS - predict_sfat)/predict_sfat,
difference_perc_sfaz = (operational_ACSS - predict_sfaz)/predict_sfaz,
difference_perc_sfatz = (operational_ACSS - predict_sfatz)/predict_sfatz)
write.csv(CSH_predict, "CSH_predict.csv", row.names = FALSE)
CSH_predict_summary = CSH_predict |> group_by(hospital) |>
summarise(operational = mean(operational_ACSS), predict_sfa = mean(predict_sfa), difference = mean(difference),
differencez = mean(differencez), difference_perc_sfa = mean(difference_perc_sfa),
difference_perc_sfaz = mean(difference_perc_sfa))
write.csv(CSH_predict_summary, "CSH_predict_summary.csv", row.names = FALSE)
### 4.2 Efficiency ----------------------------------------------------
# A. Efficiency tables
# SFA
efficiencies_sfa = data.frame(efficiency = efficiencies(sfrontd, newdata = CSH_panel),
hospital = rownames(efficiencies(sfrontd, newdata = CSH_panel))) |>
rename("efficiency_sfa" = "efficiency")
# SFA Trans
efficiencies_sfat = data.frame(efficiency = efficiencies(sfronttd, newdata = CSH_panel),
hospital = rownames(efficiencies(sfronttd, newdata = CSH_panel))) |>
rename("efficiency_sfat" = "efficiency")
# SFA Z
efficiencies_sfaz = data.frame(hospital = rownames(efficiencies(sfrontzd, newdata = CSH_panel)),
efficiency = efficiencies(sfrontzd, newdata = CSH_panel)) |>
pivot_longer(c("efficiency.2015","efficiency.2016", "efficiency.2017", "efficiency.2018",
"efficiency.2019", "efficiency.2020", "efficiency.2021", "efficiency.2022"),
names_to = "year", values_to = "efficiency_sfa_z") |>
mutate( year = str_remove(year, ".*\\.")) # .(any character) *(zero or more occurences) \\. (".")
# SFA Trans
efficiencies_sfatz = data.frame(efficiency = efficiencies(sfronttzd, newdata = CSH_panel),
hospital = rownames(efficiencies(sfronttzd, newdata = CSH_panel))) |>
pivot_longer(c("efficiency.2015","efficiency.2016", "efficiency.2017", "efficiency.2018",
"efficiency.2019", "efficiency.2020", "efficiency.2021", "efficiency.2022"),
names_to = "year", values_to = "efficiency_sfa_tz") |>
mutate( year = str_remove(year, ".*\\."))
# B. Join all efficiency tables
list_df = list(efficiencies_sfa, efficiencies_sfat,
efficiencies_sfaz, efficiencies_sfatz)
CSH_effi = full_join(efficiencies_sfaz, efficiencies_sfatz,
by = c("hospital" = "hospital", "year" = "year"))
CSH_effi = bind_rows(CSH_effi, full_join(efficiencies_sfa,efficiencies_sfat),
by = c("hospital" = "hospital"))
write.csv(CSH_effi, "CSH_effi.csv", row.names = FALSE)
# III. SFA Portugal & Azores H. Center for Operational ACSS --------------
## 1. Data --------------------------------------------------------------
rm(list = setdiff(ls(), c("CSH")))
setwd("..")
dir.create("3. Frontier w Azores Hospital Centre (operational ACSS)")
setwd("3. Frontier w Azores Hospital Centre (operational ACSS)")
### A. Select variables and test correlation --------------------------
hosp_centre = CSH |> filter(azo == 1| mad == 1)
# Panel for SFA analysis
CSH_panel = CSH |>
filter(azo== 0) |>
select(hospital, year,operational_ACSS, in_days, azo,case_mix, patient_dis, app,
urge, surg, wait_scheduled_surg, n_polos, den, fem, aging) |>
drop_na()
CSH_panel = pdata.frame(CSH_panel, c("hospital", "year"))
# Correlation table
corr_table = CSH_panel |>
select(operational_ACSS, in_days, case_mix, patient_dis, app, urge,
surg, wait_scheduled_surg, n_polos, den, fem, aging) |>
cor()
write.csv(corr_table, "01.Correlation_table.csv", row.names = FALSE)
### B Define functional forms -----------------------------------------
form = log(operational_ACSS) ~ log(in_days) + log(surg) + log(case_mix)
form2 = log(operational_ACSS) ~ log(in_days)+ log(surg) + log(case_mix) + log(fem) # no issues. but if fem replaced with den or aging, then gamma close to boundary and errors are left skewed.
#form = log(operational_ACSS) ~ log(in_days) + log(urge)
#form = log(operational_ACSS) ~ log(in_days) + log(urge) + log(surg) + log(n_polos) + log(case_mix) + log(aging) + log(fem) + log(den)
#form = log(operational_ACSS) ~ log(in_days) + log(urge) + log(n_polos) + log(case_mix) + log(aging) + log(fem) + log(den)
#form = log(operational_ACSS) ~ log(in_days) + log(urge) + log(n_polos) + log(case_mix) + log(aging) + log(fem) + log(den)
#formz = log(operational_ACSS) ~ log(in_days)+ log(surg) + log(urge) + log(den) + log(case_mix) + log(n_polos)
#form2 = log(operational_ACSS) ~ log(in_days) + log(surg) + log(urge) + log(case_mix) # no issues. but if surg replaced with urge then gamma close to boundary
## 2. Operational Cost function -----------------------------------------
### 2.1 Estimation: time invariant inefficiencies ---------------------
#### A. Cobb-Douglas (form) ----------------------------------------
sfront = sfa( form,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfront, extraPar = TRUE)
#### B. Cobb-Douglas (form2) ----------------------------------------
sfront2 = sfa( form2,
data = CSH_panel,
ineffDecrease = F, # FALSE for cost function and TRUE for production
truncNorm = FALSE, # FALSE -> errors have half normal distribution TRUE -> truncated distribution (mu parameter is added)
timeEffect = FALSE, # time is allowed to have an effect on efficiency
printIter = 1 )
summary(sfront, extraPar = TRUE)
## 3. Table -------------------------------------------------------------
dir.create("0.Latex Tables")
setwd("0.Latex Tables")
# BC 92/95
# Creative approach to export SFA tables (since normal packages don't support format)
# save the coefficients and p-v as vectors:
c1 = as.vector(coef(sfront))
c2 = as.vector(coef(sfront2))
pv1 = as.vector(coef(summary(sfront))[,4])
pv2 = as.vector(coef(summary(sfront2))[,4])
se1 = as.vector(coef(summary(sfront))[,2])
se2 = as.vector(coef(summary(sfront2))[,2])
# save gamma parameter, nº of time periods, log-likelihood and mean efficiency
g1 = round(as.vector(coef(summary(sfront, extraPar = TRUE))[nrow(coef(summary(sfront))),1]), 3)
g2 = round(as.vector(coef(summary(sfront2, extraPar = TRUE))[nrow(coef(summary(sfront2))),1]),3)
ll1 = round(as.numeric(logLik(sfront, which = "mle")),3)
ll2 = round(as.numeric(logLik(sfront2, which = "mle")),3)
me1 = round(summary(sfront)$efficMean,3)
me2 = round(summary(sfront2)$efficMean,3)
#run the same specifications using a linear model
# (remember to change the "|" before the z variables to a "+" in the linear model):
lm1 = lm(form, data = CSH_panel)
lm2 = lm(form2, data = CSH_panel)
#form2 = log(operational_ACSS) ~ log(in_days)+ log(surg) + log(case_mix) + log(fem)
#Finally, use stargazer on the linear models, and change the coefficients and the standard errors reported using the "coef" and "se" arguments:
stargazer(lm1, lm2,
coef = list(c1,c2),
se = list(se1,se2),
p = list(pv1,pv2),
t.auto = FALSE,
p.auto = FALSE,
intercept.bottom = FALSE,
digits = 3, float.env = "table",
dep.var.labels=c("$\\log$ Operational Costs"),
title = "Stochastic Frontier: Hospital Healthcare",
column.labels = c("Cobb-Douglas", "Translog"),
model.numbers = TRUE,
out = "SFAregression_table_1_CSH.tex",
omit.stat = c("rsq", "adj.rsq", "ser", "f"),
add.lines = list(c("Gamma", g1, g2),
c("Log-likelihood value", ll1,ll2),
c("Mean efficiency", me1, me2)),
covariate.labels = c("Constant","$\\log \\text{inpatient days}$",
"$\\log \\text{surgeries}$", "$\\log \\text{Casemix Index}$",
"$\\log$ Female proportion"))
setwd("..")
## 4. Azores Prediction: Dummy Frontier ---------------------------------
### 4.1 Prediction HC -------------------------------------------------
CSH_predict = CSH |> pdata.frame(c("hospital", "year"))
hosp_centre = hosp_centre |> pdata.frame(c("hospital", "year"))
#### A. prediction tables Azores --------------------------------------
# SFA
prediction_sfa = data.frame(predict = exp(predict(sfront, newdata = hosp_centre)),
names = rownames(data.frame(predict(sfront, newdata = hosp_centre)))) |>
mutate(hospital = str_remove(names, "-.*"), year = str_remove(names, ".*-"),
year = as.factor(year)) |>
select(-names) |>
rename("predict_sfa" = "predict")
# SFA Z
prediction_sfa2 = data.frame(predict = exp(predict(sfront2, newdata = hosp_centre)),
names = rownames(data.frame(predict(sfront2, newdata = hosp_centre)))) |>
mutate(hospital = str_remove(names, "-.*"), year = str_remove(names, ".*-"),
year = as.factor(year)) |>
select(-names) |>
rename("predict_sfa2" = "predict")
#### B. Join all data frames Azores -----------------------------------
list_df = list(hosp_centre,prediction_sfa, prediction_sfa2)
CSH_predict_Azor = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital",
"year" = "year"),
.init = NULL))
#### C. Prediction tables whole sample --------------------------------
# SFA
prediction_sfa = data.frame(predict = exp(predict(sfront, newdata = CSH_predict)),
hospital = rownames(data.frame(predict(sfront, newdata = CSH_predict)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfa" = "predict")
# SFA Z
prediction_sfa2 = data.frame(predict = exp(predict(sfront2, newdata = CSH_predict)),
hospital = rownames(data.frame(predict(sfront2, newdata = CSH_predict)))) |>
separate("hospital", c("hospital", "year"),sep = "-") |>
rename("predict_sfa2" = "predict")
#### D. Join all data frames ------------------------------------------
list_df = list(CSH_predict,prediction_sfa, prediction_sfa2)
CSH_predict = list_df |>
reduce(function(x, y) full_join(x, y, by = c("hospital" = "hospital",
"year" = "year"),
.init = NULL))
#### E. Differences Azores --------------------------------------------
# These differences are too high
CSH_predict_Azor = CSH_predict_Azor |> mutate(difference = operational_ACSS - predict_sfa, difference2 = operational_ACSS - predict_sfa2,
difference_perc_sfa = (operational_ACSS - predict_sfa)/predict_sfa,
difference_perc_sfa2 = (operational_ACSS - predict_sfa2)/predict_sfa2)
write.csv(CSH_predict, "02.CSH_predict_Islands.csv", row.names = FALSE)
CSH_predict_summary = CSH_predict_Azor |> group_by(hospital) |>
summarise(operational_ACSS = mean(operational_ACSS),
predict_sfa = mean(predict_sfa),predict_sfa2 = mean(predict_sfa2),
difference = mean(difference), difference2 = mean(difference2),
difference_perc_sfa = mean(difference_perc_sfa), difference_perc_sfa2 = mean(difference_perc_sfa2))
write.csv(CSH_predict_summary, "03.CSH_predict_Islands_summary.csv", row.names = FALSE)
### 4.2 Efficiency HC -------------------------------------------------
#### A. Efficiency tables Azores ------------------------------------
# SFA
efficiencies_sfa = data.frame(efficiency = efficiencies(sfront, newdata = hosp_centre),
hospital = rownames(efficiencies(sfront, newdata = hosp_centre))) |>
rename("efficiency_sfa" = "efficiency")
# SFA Z
efficiencies_sfa2 = data.frame(hospital = rownames(efficiencies(sfront2, newdata = hosp_centre)),
efficiency = efficiencies(sfront2, newdata = hosp_centre)) |>
rename("efficiency_sfa2" = "efficiency")
#### B. Join all efficiency tables Azores ---------------------------
list_df = list(CSH_predict_Azor, efficiencies_sfa, efficiencies_sfa2)
CSH_predict_Azor = list_df |> reduce(function(x,y) full_join(x, y, by = c("hospital" = "hospital"),
.init = NULL))
write.csv(CSH_predict_Azor, "04.CSH_effi_pred_Islands.csv", row.names = FALSE)
#### C. Efficiency tables whole DB ------------------------------------
# SFA
efficiencies_sfa = data.frame(efficiency = efficiencies(sfront, newdata = CSH_predict),
hospital = rownames(efficiencies(sfront, newdata = CSH_predict))) |>
rename("efficiency_sfa" = "efficiency")
# SFA Z
efficiencies_sfa2 = data.frame(efficiency = efficiencies(sfront2, newdata = CSH_predict),
hospital = rownames(efficiencies(sfront2, newdata = CSH_predict))) |>
rename("efficiency_sfa2" = "efficiency")
#### D. Join all efficiency tables (whole sample) -------------------
CSH_predict = full_join(CSH_predict, efficiencies_sfa2, by = c("hospital" = "hospital"))
CSH_predict = full_join(CSH_predict, efficiencies_sfa, by = c("hospital" = "hospital"))
write.csv(CSH_predict_Azor, "04.CSH_effi_pred.csv", row.names = FALSE)
### 4.3 Over cost Estimation -----------------------------------------
# A. Mean efficiency Portugal and Azores
innef_P = 1-round(summary(sfront)$efficMean,3)
innef2_P = 1-round(summary(sfront2)$efficMean,3)
# B. Table with overcosts Islands
CSH_predict_Azor = CSH_predict_Azor |>
mutate(Inef_Cost_Cont = innef_P * predict_sfa,
Inef_Cost_Cont2 = innef2_P * predict_sfa2,
Innef_Cost_Isl = (1-efficiency_sfa)*predict_sfa,
Innef_Cost_Isl2 = (1-efficiency_sfa2)*predict_sfa2,
overcost = Innef_Cost_Isl- Inef_Cost_Cont,
overcost2 = Innef_Cost_Isl2 - Inef_Cost_Cont2,
mean_overcost = overcost/pop, mean_overcost2 = overcost2/pop,
op_pop = operational_ACSS/pop) |>
select(hospital, year, operational_ACSS, predict_sfa, predict_sfa2, efficiency_sfa,
efficiency_sfa2, Inef_Cost_Cont, Inef_Cost_Cont2, Innef_Cost_Isl,
Innef_Cost_Isl2, overcost, overcost2, mean_overcost, mean_overcost2, op_pop)
# C. Save PDF Azores to directory
write.csv(CSH_predict_Azor, "05.CSH_predict_overcost_Azores.csv", row.names = FALSE)
# Save the summary table as a PDF file
pdf(paste0("05.CSH_predict_overcost_azores.pdf"), width = 20, height = 8)
grid.table(CSH_predict_Azor, rows = NULL)
dev.off()
# D. Table with overcosts Continent and Islands
CSH_predict = CSH_predict |>
mutate(Inef_Cost_Cont = innef_P * predict_sfa,
Inef_Cost_Cont2 = innef2_P * predict_sfa2,
Innef_Cost_Isl = (1-efficiency_sfa)*predict_sfa,
Innef_Cost_Isl2 = (1-efficiency_sfa2)*predict_sfa2,
overcost = Innef_Cost_Isl- Inef_Cost_Cont,
overcost2 = Innef_Cost_Isl2 - Inef_Cost_Cont2)
## 5. Graphic Representation --------------------------------------------
### A. Database for graph
CSH_predict = CSH_predict |> mutate(pred_overcost = predict_sfa + overcost)
d = CSH_predict |> select(azo, predict_sfa, predict_sfa2, pred_overcost, overcost2, overcost)
### B. GRaph for Azores
ggplot(data = filter(CSH_predict, year == 2018), aes(x = in_days, y = operational_ACSS, color = azo)) +
geom_point(alpha = 0.7) +
geom_line(data = filter(CSH_predict, azo == 0 & mad == 0), aes(y = predict_sfa), linetype = "dashed", color = "lightgreen") +
geom_point(data = filter(CSH_predict, azo == 1, year == 2018), aes(x = in_days, y = pred_overcost), color = "red", shape = 4, size = 3) +
geom_segment(data = filter(CSH_predict, azo == 1, year == 2018), aes(x = in_days, y = predict_sfa, xend = in_days, yend = pred_overcost), color = "red", linetype = "dotted") +
geom_segment(data = filter(CSH_predict, azo == 1, year == 2018), aes(x = in_days, y = pred_overcost, xend = in_days, yend = operational_ACSS), color = "blue", linetype = "dotted") +
geom_point(data = filter(CSH_predict, azo == 1, year == 2018), aes(x = in_days, y = predict_sfa), color = "pink") +
labs(x = "Consultas", y = "Custos com Pessoal", title = "Fronteira Estocástica", caption = "Note: This graphic depict a Cobb Douglas cost function for the year 2018." ) +
scale_color_manual(values = c("1" = "lightblue", "0" = "lightgreen"),
labels = c("Açores", "Portugal Continental"),
name = "")
ggsave(filename = "CDgraph_eff_pred_azo.png", plot = last_plot(), width = 10, height = 8, dpi = 300)
### B. GRaph for Madeira
ggplot(data = filter(CSH_predict, year == 2018), aes(x = in_days, y = operational_ACSS, color = azo)) +
geom_point(alpha = 0.7) +
geom_line(data = filter(CSH_predict, azo == 0 & mad == 0), aes(y = predict_sfa), linetype = "dashed", color = "lightgreen") +
geom_point(data = filter(CSH_predict, mad == 1, year == 2018), aes(x = in_days, y = pred_overcost), color = "red", shape = 4, size = 3) +
geom_segment(data = filter(CSH_predict, mad == 1, year == 2018), aes(x = in_days, y = predict_sfa, xend = in_days, yend = pred_overcost), color = "red", linetype = "dotted") +
geom_segment(data = filter(CSH_predict, mad == 1, year == 2018), aes(x = in_days, y = pred_overcost, xend = in_days, yend = operational_ACSS), color = "blue", linetype = "dotted") +
geom_point(data = filter(CSH_predict, mad == 1, year == 2018), aes(x = in_days, y = predict_sfa), color = "pink") +
labs(x = "Consultas", y = "Custos com Pessoal", title = "Fronteira Estocástica", caption = "Note: This graphic depict a Cobb Douglas cost function for the year 2018." ) +
scale_color_manual(values = c("1" = "lightblue", "0" = "lightgreen"),
labels = c("Açores", "Portugal Continental"),
name = "")
ggsave(filename = "CDgraph_eff_pred_mad.png", plot = last_plot(), width = 10, height = 8, dpi = 300)
# IV. SFA Portugal Continent for Staff Costs ------------------------------
## 1. Data -----------------------------------------------------------------
rm(list = setdiff(ls(), "CSH"))
setwd("..")
dir.create("4. Portugal Frontier (staff)")
setwd("4. Portugal Frontier (staff)")
### B. Select variables and test correlation --------------------------
CSH_0 = CSH |> select(hospital, year, staff, in_days, RO, azo, region,
surg, app, urge, beds, patient_dis, wait_scheduled_surg) |>
drop_na()
# correlation testing RO
corr_table = CSH_0 |>
select(staff, in_days, RO,beds, surg, app, urge,
patient_dis, wait_scheduled_surg) |>
cor()