W241_Final_Project_v3.Rmd

---
title: "W241 Class Project - Analysis"
output:
  html_notebook: default
---

# 1. Load libraries, data

Load up the data and do simple analysis. This version uses the complete dataset.

```{r,error=FALSE, error=FALSE, message=FALSE, warning=FALSE, results='hide'}

# Libraries
library(lmtest)
library(sandwich)
library(ggplot2)
library(data.table)
library(stargazer)
library(ri)
library(multiwayvcov)
library(AER)

rm(list=ls())

d <- read.csv('~/Documents/mids-w241-final/Analysis/Combined Log.csv')
#d <- read.csv("C:/Users/Chris/OneDrive/Documents/MIDS/WS241/final/mids-w241-final/Analysis/Combined Log.csv")
d <- data.table(d)
# d <- d[complete.cases(d),] drops any row that is too incomplete - too stringent since we have some cols which are not essential
d <- d[!is.na(no)] # Just drop row with missing values

# Base data
head(d)

# Convert, transform data for analysis

# Drop some cols
d[,c('title','full_URL', 'reply_email_TO_BE_FILLED_IN_standard','posting_ID','notes') :=NULL]

# Set gender = 1 for Jane
d[treatment_assignment=='Jane_Control' | treatment_assignment=='Jane_Treat_High' | treatment_assignment=='Jane_Treat_Low',gender:=1]
d[treatment_assignment=='John_Control' | treatment_assignment=='John_Treat_High' | treatment_assignment=='John_Treat_Low',gender:=0]

# Set treatment variable = 0 for control, 1 for low, 2 for high
d[treatment_assignment=='Jane_Control' | treatment_assignment=='John_Control', treatment:=0]
d[treatment_assignment=='Jane_Treat_Low' | treatment_assignment=='John_Treat_Low', treatment:=1]
d[treatment_assignment=='Jane_Treat_High' | treatment_assignment=='John_Treat_High', treatment:=2]

# Alternatively, treat treatment types as categorical variables instead of continuous
d[treatment_assignment=='Jane_Treat_Low' | treatment_assignment=='John_Treat_Low', low_treatment:=1]
d[treatment_assignment=='Jane_Treat_High' | treatment_assignment=='John_Treat_High', high_treatment:=1]
d$low_treatment[is.na(d$low_treatment)] <- 0
d$high_treatment[is.na(d$high_treatment)] <- 0

d[low_treatment==1 | high_treatment==0, assigned:=1]
d$assigned[is.na(d$assigned)] <- 0

# Capture compliers
d[sent!='', compliers:=1]
d$compliers[is.na(d$compliers)] <- 0

# Labeling data
d$gender <- factor(d$gender,labels = c("Male", "Female"))
d$outcome <- factor(d$outcome, labels = c("No Response", "Response"))
d$bedrooms <- factor(d$bedrooms, labels = c("1-bedroom", "2-bedroom"))

```


# 2. Check data, do simple tables to check for balance

For the most part it looks like we have a balanced dataset. 

```{r}

cat('Table of Outcomes:')
table(d$outcome)

cat('\nTable of Outcomes (By Gender):')
table(d$outcome, d$gender)

cat('\nTable of Outcomes (By Treatment):')
table(d$outcome, d$treatment)

cat('\nTable of Outcomes (By Treatment and Gender):')
table(d$outcome, factor(d$treatment_assignment))

cat('\nTable of Outcomes (By City):')
table(d$outcome,factor(d$city))

cat('\nTable of Outcomes (By Rooms):')
table(d$outcome,factor(d$bedrooms))

ggplot(d,aes(x=price))+geom_histogram()+facet_grid(~outcome)+labs(x="Price",y="Number") 

# Sqft info has missing values => we can drop all cases (see above) but for now leave this alone
# Similar but somewhat worse issue for professional, same.email info

```



# 3. Analysis

# Simple Analysis

Doing chi-squared test of independence. Can't reject. 

```{r}
tbl <- table(d$outcome,d$gender)
chisq.test(tbl)

tbl <- table(d$outcome,d$treatment)
chisq.test(tbl)

tbl <- table(d$outcome,factor(d$treatment_assignment))
tbl
chisq.test(tbl)

```


# Regression

*Blocking - by gender, by city, bedroom?
*Cluster - none
*Compliance - none
*Spillover - yes, with same email; not sure how to incorporate

Basic model
  
    Outcome variable = alpha + B_high + B_low + gender + covariates
  

```{r}

# Model 1 - Basic model
m1 <- lm(outcome~treatment,data=d)
stargazer(m1,type='text')
coeftest(m1, vcovHC(m1)) # Robust se 

# Model 2 - Treatment & gender
m2 <- lm(outcome~treatment*gender,data=d)
stargazer(m2,type='text')
coeftest(m2, vcovHC(m2)) # Robust se 

# Model 3 - Treatment & gender + covariates
m3 <- lm(outcome~treatment*gender+factor(city)+factor(bedrooms),data=d)
stargazer(m3,type='text')
coeftest(m3, vcovHC(m3)) # Robust se 

# Model 4 - Treatment & gemder + covariates
m4 <- lm(outcome~treatment*gender+factor(city)+factor(bedrooms)+price,data=d)
stargazer(m4,type='text')
coeftest(m4, vcovHC(m4)) # Robust se 


```
We cannot reject the null hypothesis of no effect. 

Alternative model with treatment variables coded as categorical factors

```{r}

# Model 1 - Basic model
m1 <- lm(outcome ~ low_treatment + high_treatment,data=d)                                                               
stargazer(m1,type='text')
coeftest(m1, vcovHC(m1)) # Robust se 

# Model 2 - Treatment & gender
m2 <- lm(outcome~low_treatment + high_treatment*gender,data=d)
stargazer(m2,type='text')
coeftest(m2, vcovHC(m2)) # Robust se 

# Model 3 - Treatment & gender + covariates
m3 <- lm(outcome~low_treatment + high_treatment + gender + factor(city) + factor(bedrooms) + price,data=d)
stargazer(m3,type='text')
coeftest(m3, vcovHC(m3)) # Robust se 


```


## Try with RI

```{r}
di <- d
di[treatment==2,treatment:=1]
di[,city:=as.numeric(factor(d$city))]

hist(di$treatment)
hist(di$city)

y <- d$outcome
Z <- d$treatment
cls <- d$gender
blk <- d$city
  
perms <- genperms(Z, clustvar = NULL, blockvar = blk)
probs <- genprobexact(Z, clustvar = NULL, blockvar = blk) # probability of treatment
ate <- estate(y,Z,prob=probs) # estimate the ATE


Ys <- genouts(y,Z,ate=0) # generate potential outcomes under sharp null of no effect
distout <- gendist(Ys,perms, prob=probs) # generate sampling dist. under sharp null
dispdist(distout, ate, quantiles = c(0.025, 0.975), display.plot = TRUE) # display characteristics of sampling dist. for inference

```

## CACE
```{r}
# Using Models # NEEDS WORK
itt_fit <- lm(outcome ~ treatment, data = d)
summary(itt_fit)
coeftest(itt_fit, vcovHC(itt_fit))

itt_d_fit <- lm(compliers ~ treatment, data = d)
coeftest(itt_d_fit)
coeftest(itt_d_fit,vcovHC(itt_d_fit))

itt_fit$coefficients[2] / itt_d_fit$coefficients[2]
```


```{r}
# Manually compute CACE
itt <- d[, mean(outcome[assigned == 1]) - mean(outcome[assigned == 0])]

prop_treated <- d[ , mean(compliers/assigned, na.rm = T)]
prop_treated <- d[assigned == 1, mean(compliers)]

sprintf("%.10f", itt / prop_treated)
```