R script.Rmd

## Start
```{r}
# clean database
rm(list=ls())

#scientific notation
options(scipen=999)

# for consistent results
set.seed(123)
```

## packages
```{r}
install.packages("haven")
install.packages("gplots")
install.packages("summarytools")
install.packages("corrplot")
install.packages("dplyr")
install.packages("coin")
install.packages("clinfun")
install.packages("gvlma")
install.packages("lmtest")
install.packages("tseries")
install.packages("AER")
install.packages("car")
install.packages("stargazer")
install.packages("ResourceSelection")
install.packages("MASS")
install.packages("pscl")
install.packages("kableExtra")
install.packages("MatchIt")
install.packages("ggplot2")
install.packages("Hmisc")
```

## Open data base
```{r}
library(haven)
instrumental3 <- read_sav("C:/Users/vieir/Desktop/Artigos (em progresso)/Artigo RAP/Submission/instrumental3.sav")
View(instrumental3)
```

################ Exploratory Analysis
```{r}
library(summarytools)
summarytools::descr(instrumental3)

#Shapiro-Wilk normality test
shapiro.test(instrumental3$corruption)

### The null hypothesis for this test is that the data are normally distributed. The Prob < W value listed in the output is the p-value. If the chosen alpha level is 0.05 and the p-value is less than 0.05, then the null hypothesis that the data are normally distributed is rejected. If the p-value is greater than 0.05, then the null hypothesis is not rejected.

#correlations
library(corrplot)
i_col <- sapply(instrumental3, class) %in% c("integer", "numeric");cor(instrumental3[which(i_col)])
corr_matrix <- cor(instrumental3)
corrplot(corr_matrix, type= "upper")
```


############################### Methodology
```{r}
library("gplots")
plotmeans(corruption ~ social_accountability, data = instrumental3, frame = FALSE,
          xlab = "Treatment", ylab = "Weight",
          main="Mean Plot with 95% CI") 

library(dplyr)
instrumental3 %>%
  group_by(region) %>%
  summarise(n_municip = n (),
            mean(corruption),
            std_error = sd (corruption) / sqrt(n_municip))

instrumental3 %>%
  group_by(size) %>%
  summarise(n_municip = n (),
            mean(corruption),
            std_error = sd (corruption) / sqrt(n_municip))

library(coin)
kruskal.test(corruption ~ region, data = instrumental3)
wilcox.test(corruption ~ size, data = instrumental3)


# 5 regiões para size==0
reg01_size00 <- instrumental3 %>% filter(region==1&size==0)
reg02_size00 <- instrumental3 %>% filter(region==2&size==0)
reg03_size00 <- instrumental3 %>% filter(region==3&size==0)
reg04_size00 <- instrumental3 %>% filter(region==4&size==0)
reg05_size00 <- instrumental3 %>% filter(region==5&size==0)

kruskal.test(corruption ~ social_accountability, data = reg01_size00)
kruskal.test(corruption ~ social_accountability, data = reg02_size00)
kruskal.test(corruption ~ social_accountability, data = reg03_size00)
kruskal.test(corruption ~ social_accountability, data = reg04_size00)
kruskal.test(corruption ~ social_accountability, data = reg05_size00)

# 5 regiões para size==1
reg01_size01 <- instrumental3 %>% filter(region==1&size==1)
reg02_size01 <- instrumental3 %>% filter(region==2&size==1)
reg03_size01 <- instrumental3 %>% filter(region==3&size==1)
reg04_size01 <- instrumental3 %>% filter(region==4&size==1)
reg05_size01 <- instrumental3 %>% filter(region==5&size==1)

kruskal.test(corruption ~ social_accountability, data = reg01_size01)
kruskal.test(corruption ~ social_accountability, data = reg02_size01)
kruskal.test(corruption ~ social_accountability, data = reg03_size01)
kruskal.test(corruption ~ social_accountability, data = reg04_size01)
kruskal.test(corruption ~ social_accountability, data = reg05_size01)
```


################################ Initial Results
```{r}
library(dplyr)
instrumental3 %>%
  group_by(social_accountability) %>%
  summarise(n_municip = n (),
            mean(corruption),
            std_error = sd (corruption) / sqrt(n_municip))
### I later transform in dichotomous variable (0+1+2 = 0 // 3+4 = 1)

library(coin)
wilcox.test(corruption ~ social_accountability_dic, data = instrumental3)
kruskal.test(corruption ~ social_accountability, data = instrumental3)
### The Kruskal–Wallis test by ranks, Kruskal–Wallis H test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate from the same distribution. It is used for comparing two or more independent samples of equal or different sample sizes. It extends the Mann–Whitney U test, which is used for comparing only two groups.

library(clinfun)
x <- c(instrumental3$corruption)
y <- c(instrumental3$social_accountability)
jonckheere.test(x, y)
### The Jonckheere-Terpstra test is a rank-based nonparametric test that can be used to determine if there is a statistically significant trend between an ordinal independent variable and a continuous or ordinal dependent variable. It is a test of distributional "locations", or stochastic prevalence.

```


#################################  NAIVE MODEL(OLS Regression)
```{r}
naive <- lm(corruption ~ social_accountability_dic + SO + south + southeast + midwest 
                 + north +  size, data = instrumental3)
naive1 <- lm(corruption ~ social_accountability + SO + south + southeast + midwest 
                 + north +  size, data = instrumental3)
#confidence interval
confint(naive,level=0.90)
confint(naive1,level=0.90)

library(gvlma)
gvlma::gvlma(naive)

#heteroscedasticity
library(lmtest)
bptest(naive, studentize=FALSE)
bptest(naive1, studentize=FALSE)

#normality
hist(naive$residuals,xlab="Residuals",main="")
hist(naive1$residuals,xlab="Residuals",main="")

qqnorm(naive$residuals)
qqline(naive$residuals, col="red")

qqnorm(naive1$residuals)
qqline(naive1$residuals, col="red")

#Jarque–Bera test
library(tseries)
jarque.bera.test(naive$residuals)
jarque.bera.test(naive1$residuals)
## we reject the null hypothesis and conclude that the residuals are not normally distributed. 
# functional form
plot(y=naive$residuals,x=naive$fitted.values, xlab="Fitted Values",ylab="Residuals")
plot(y=naive1$residuals,x=naive1$fitted.values, xlab="Fitted Values",ylab="Residuals")

# multicolineariety
library(AER)
vif(naive)
sqrt(vif(naive))
1/vif(naive)

vif(naive1)
sqrt(vif(naive1))
1/vif(naive1)

#outliers
library(car)
avPlots(naive)
avPlots(naive1)

#DFBetas (outliers test)
dfbetas(naive)
obj_anything <- dfbetas(naive)
View(obj_anything)

dfbetasPlots(naive)
dfbetaPlots(naive, id.method = "y", id.n = 1)
dfbetaPlots(naive, id.method = "identify")

dfbetas(naive1)
obj_anything1 <- dfbetas(naive1)
View(obj_anything1)

dfbetasPlots(naive1)
dfbetaPlots(naive1, id.method = "y", id.n = 1)
dfbetaPlots(naive1, id.method = "identify")

#Outliers, Leverage, and Influential Data Points
influenceIndexPlot(naive, vars=c("Cook","Studentized","hat"),id.n=5)

library(stargazer)
stargazer(naive1, naive, type= "text", out="1_naive.html")
```


############################## Generalized Linear Model
```{r}
## Exploring
xtabs(~corruption_dic + social_accountability_dic, data = instrumental3)

#Logit model (dummy)
mylogit3 <- glm(corruption_dic ~ social_accountability_dic + SO + south + southeast + midwest + north + size, data = instrumental3, family = binomial(link="logit"))
summary(mylogit3)
confint(mylogit3)
confint.default(mylogit3)

library(stargazer)
stargazer(mylogit3, type= "text", out="1_logistic.doc")

## odds-ratios (and confidence intervals column-wise)
exp(coef(mylogit3))
exp(cbind(OR = coef(mylogit3), confint(mylogit3)))

#regression model fit
library(ResourceSelection)
hoslem.test(instrumental3$corruption_dic, fitted(mylogit3))

#Poisson Regression
corruption.poisson<-glm(corruption ~ social_accountability_dic + SO + south + southeast + midwest 
                 + north + size, family=poisson(link=log),data=instrumental3)
summary(corruption.poisson)

# Negative Binomial Regression
library(MASS)
corruption.binominal<-glm.nb(corruption ~ social_accountability_dic + SO + south + southeast + midwest 
                 + north +  size, data=instrumental3)
summary(corruption.binominal)

#graphs
library(stats4)
forecast.nb<-predict(corruption.binominal, type="response")
forecast.poisson<-predict(corruption.poisson,type="response")

#Zero-inflated negative binomial regression 
library(pscl)
corruption.zero <- zeroinfl(corruption ~ social_accountability_dic + SO + south + southeast + midwest 
                 + north +  size, data = instrumental3, dist = "negbin")
summary(corruption.zero)

#Vuong test
vuong(corruption.poisson, corruption.zero)
## The Vuong test compares the zero-inflated model with an ordinary Poisson regression model. We can see that our test statistic is significant, indicating that the zero-inflated model is superior to the standard Poisson model.

library(stargazer)
stargazer(naive, mylogit3, corruption.poisson, corruption.binominal, corruption.zero, type= "text", out="1_glm.html")
```


####################################### MATCHING (EXACT)
```{r}
### Data Prep and EDA
library(dplyr)
instrumental3 %>%
  group_by(social_accountability_dic) %>%
  summarise(n_municip = n (),
            mean(corruption),
            std_error = sd (corruption) / sqrt(n_municip))
### NATE
t.test(instrumental3$corruption ~ instrumental3$social_accountability_dic)

### Balance Table
library(kableExtra)
instrumental3 %>%
  group_by(social_accountability_dic) %>%
  summarise_all(funs(mean(., na.rm = T))) %>% 
  t() %>% 
  as.data.frame() %>% 
  add_rownames("variable") %>% 
  rename(Less_CS = V1, More_CS = V2) %>% 
  mutate(difference = More_CS - Less_CS,
         differencePerc = difference / (More_CS + Less_CS)) %>% 
  mutate_if(is.numeric, round, 3) %>% 
  kable() %>%
  kable_styling() 

### Exploring MatchIt
library(MatchIt)
exact_match <- matchit(social_accountability_dic ~ SO + size + south + southeast + midwest 
                 + north + northeast, method = "exact",data = instrumental3, ratio = 1)
summary(exact_match)

# grab the matched data
exact_matchCSV = match.data(exact_match) 
write.csv(exact_matchCSV, "exact_match.csv")

data_exact_match <- match.data(exact_match)

## a dataframe containing only the matched observations
dta_m <- match.data(data_exact_match)
dim(dta_m)

# estimate t-test again
t.test(data_exact_match$corruption ~ data_exact_match$social_accountability_dic)

## the direction and magnitude of the covariate effects using a  linear model:
lm_exact <- lm(corruption ~ social_accountability_dic + SO + south + southeast + midwest 
                 + north + northeast + size, data = data_exact_match)
summary(lm_exact)

# estimate logit model
m_ps <- glm(social_accountability_dic ~ SO + south + southeast + midwest 
                 + north + northeast + size, family = binomial(), data = instrumental3)
summary(m_ps)

# extract predicted probabilities
# type = "response" option tells R to output probabilities of the form P(Y = 1|X)
library(ggplot2)
prs_df <- data.frame(pr_score = predict(m_ps, type = "response"),
                     social_accountability_dic = m_ps$model$social_accountability_dic) # the actual values
prs_df %>%
 ggplot(aes(x = pr_score, fill = factor(social_accountability_dic))) +
  geom_density(alpha = 0.1) +
  labs(x = "Propensity Score Distribution: Treatment and Control Groups",
       fill = "Social Accountability")
```

##################################  MATCHING (Nearest)
```{r}
one_match <- matchit(social_accountability_dic ~ SO + south + southeast + midwest 
                 + north + northeast + size, method = "optimal", ratio = 1, replace = FALSE, data = instrumental3)
summary(one_match)

# simple plot
plot(one_match, type="jitter")
plot(one_match, type = "hist")

# grab data set
data_prop_match <- match.data(one_match)

# check balance
data_prop_match %>%
  group_by(social_accountability_dic) %>%
  summarise_all(funs(mean)) %>%
  t() %>% 
  as.data.frame() %>% 
  add_rownames("variable") %>% 
  rename(no_CS = V1, CS = V2) %>% 
  mutate(difference = CS - no_CS,
         differencePerc = difference / (CS + no_CS)) %>% 
  mutate_if(is.numeric, round, 3) %>% 
  kable() %>% 
  kable_styling()

## estimate the treatment effect on the matched data set:
t.test(data_prop_match$corruption ~ data_prop_match$social_accountability_dic)

## the direction and magnitude of the covariate effects using a simple linear model:
lm_matched <- lm(corruption ~ social_accountability_dic + SO + south + southeast + midwest 
                 + north + northeast + size, data = data_prop_match)
summary(lm_matched)
```

############################### Matching comparative Analysis
```{r}
library(stargazer)
stargazer(lm_exact, lm_matched, type= "text", out="1_matching.html")
```


####################################### INTRUMENTAL VARIABLE
## Correlations
```{r}
library(Hmisc)
mydata.rcorr = rcorr(as.matrix(instrumental3))
mydata.rcorr

mydata.coeff = mydata.rcorr$r
mydata.p = mydata.rcorr$P

## correlation plot
library(corrplot)
corrplot(mydata.coeff)

### regression (corruption_dic ~ k_social)
ivp3 <- lm(corruption_dic ~ K_social + SO + size + south + southeast + midwest 
                 + north, data = instrumental3)
summary(ivp3)

### regression (social_accountability ~ k_social)
ivp4 <- lm(social_accountability_dic ~ K_social, data = instrumental3)
stargazer(ivp3, ivp4, type= "text", out="ivp.html")
summary(ivp4)
```

### Exploring our results (table)
```{r}
library(summarytools)
st_options(footnote = NA)
print(ctable(instrumental3$social_accountability_dic, instrumental3$K_social, prop = "n"), method = "pander") 

print(ctable(x = instrumental3$social_accountability_dic, y = instrumental3$K_social, prop = "r"), method = "pander")
```

### Exploring our results (graphs)
```{r}
library(ggplot2)
ggplot(instrumental3, aes(x = factor(K_social), y = factor(social_accountability_dic), 
                         color = factor(corruption_dic))) + geom_point() + 
  geom_jitter() + theme_minimal() + scale_x_discrete(labels = c("KS = 0", "KS = 1")) +
  scale_y_discrete(labels = c("CS = 0", "CS = 1")) +
  labs(x = "Encouragement", y = "Treatment", color = "")
```

#LATE model
```{r}
library(AER)
late_model <- ivreg(corruption ~ social_accountability_dic + SO + size + south + southeast + midwest 
                 + north | K_social + SO + size + south + southeast + midwest 
                 + north, data = instrumental3)
summary(late_model)
```

```{r}
library(dplyr)
instrumental3 %>% group_by(K_social) %>% summarise(mean(social_accountability_dic, na.rm=T))

```

```{r}
treat_en_model <- lm(social_accountability_dic ~ K_social, data= instrumental3)
summary(treat_en_model)
```

#IV summary
```{r}
library(stargazer)
stargazer(late_model, type= "text", out="1_IV.html")
```


```{r}
library(stargazer)
stargazer(naive, late_model, type= "text", out="2_All.html")
```