R File Marriage Ages.R

## ---- warning=F----------------------------------------------------
library(MASS)
library(ggplot2)
library(kableExtra)


## ------------------------------------------------------------------
agehw <- read.table("C:\\Users\\roryq\\Downloads\\agehw.dat", header = T)
nrow(agehw)



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# Table Descriptive stat
`Mean Age of Wives`<-c(mean(agehw$agew))
`Mean Age of Husbands`<-c(mean(agehw$ageh))
table<-rbind(`Mean Age of Wives`,`Mean Age of Husbands`)
t(table) %>%
  kbl() %>%
  kable_styling()


## ------------------------------------------------------------------
`Standard Deviation for Age of Wives`<-c(sd(agehw$agew))
`Standard Deviation for Age of Husbands`<-c(sd(agehw$ageh))
table<-rbind(`Standard Deviation for Age of Wives`,`Standard Deviation for Age of Husbands`)
t(table) %>%
  kbl() %>%
  kable_styling()


## ------------------------------------------------------------------
# Table covariance
cov(agehw) %>%
  kbl() %>%
  kable_styling()


## ------------------------------------------------------------------
# Visualization of relationship between husbands and wives

plot(x=agehw$ageh, y= agehw$agew, pch=21, xlab="Age of Husband", ylab="Age of Wife", main="Relationship Between Age of Husbands and Wives (years)", col="black",bg="lightblue")


## ------------------------------------------------------------------
# Generate predictive data set (size 100) from average ages (theta) and cov matrix (sigma)


n = 100
s = 10
# Mean of ages
mu0 <- c(42,42)
L0 <- matrix(c(441, 330.75, 330.75, 441), nrow = 2, ncol = 2)
# Mean ages follow multivariate norm
theta <- mvrnorm(s, mu0, L0)

# sample sigmas following inverse wishart distribution
sigmas <- list()
for(i in 1:s){
 sigma <- solve(rWishart(1, 4, solve(L0))[,,1])
 sigmas[[i]] <- sigma
}

# Sample age from multivariate normal distribution
data <- data.frame(h_age= c(), w_age = c(), dataset= c())
for(i in 1:s){
 y <- mvrnorm(100, mu0, L0)
 new <- data.frame(h_age = y[,1], w_age = y[,2], dataset =i)
 data <- rbind(data, new)
 
}



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# Plot the 10 predictive datasets on scatter plot to see if it matches the trend of the original and confirm our selection of prior (inverse whishart for sigma and multivariate normal for theta)
ggplot(data = data, aes(x = h_age, y = w_age)) + geom_point(color='darkblue') + facet_wrap(~dataset)+ labs(x=" Age of Husband", y="Age of Wife", title="Age of Husband vs Wife for Predictive Data")


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# MCMC Approximations

#prior
mu0 <- c(42,42)
nu0 <- 4
L0 <- S0 <- matrix(c(150, 112.5, 112.5, 150), nrow = 2, ncol = 2)
ybar <- apply(agehw, 2, mean)
Sigma <- cov(agehw)
n <- dim(agehw)[1]
THETA<-SIGMA <- NULL
set.seed(10000)
for(s in 1:10000){
 
#Update theta
 Ln <- solve(solve(L0) + n * solve(Sigma))
 mun <- Ln %*% (solve(L0) %*% mu0 + n * solve(Sigma) %*% ybar)
 theta <- mvrnorm(1, mun, Ln)
 
#Update Simga
 Sn <- S0 + (t(agehw) - c(theta)) %*% t( t(agehw) - c(theta))
 Sigma <- solve( rWishart(1, nu0 + n, solve(Sn))[,,1])
 
# save results
 
 THETA <- rbind(THETA, theta) ; SIGMA <- rbind(SIGMA, c(Sigma))
}



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# Make MCMC correlations into dataframe and plot
cov <- SIGMA[,2]
var_h <- SIGMA[,1]
var_w <- SIGMA[,4]
corr <- cov/sqrt(var_h*var_w)
corr <- data.frame(corr)

# Plot Sampled Correlation
ggplot(data = corr, aes(x = corr)) + geom_density()+labs(title="Distribution of Correlation Samples")




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# Print Confidence intervals for descriptive statistics

`Average Age for Husband CI`<- c(quantile(THETA[,1],.05),quantile(THETA[,1],.95))
`Average Age of Wives CI`<- c(quantile(THETA[,2],.05),quantile(THETA[,2],.95))
`Correlation Coefficient CI`<-c(quantile(corr[,1], c(.05, .95)))

bt<- as.data.frame(rbind(`Average Age of Wives CI`,`Average Age for Husband CI`,`Correlation Coefficient CI`))

t(bt) %>%
  kbl() %>%
  kable_styling()


## ------------------------------------------------------------------
result <- t.test(agehw$agew)
# Extract the confidence interval
`Avg Age of Wives CI` <- result$conf.int

result1 <- t.test(agehw$ageh)
# Extract the confidence interval
`Avg Age of Husbands CI` <- result1$conf.int

# Correlations
`fcor` <- cor.test(~ ageh + agew, data = agehw)
`correlation Coefficient CI`<-`fcor`$conf.int


ft<-as.data.frame(rbind(`Avg Age of Wives CI`, `Avg Age of Husbands CI`,`correlation Coefficient CI`))

t(ft) %>% 
  kbl() %>%
  kable_styling()


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# Improvement with bayesian analysis

Improve<-as.data.frame(cbind(t(bt),t(ft)))

Improve$Improvement_Correlation<-abs(Improve$`Correlation Coefficient CI`-Improve$`correlation Coefficient CI`)

Improve$Wife_Improvement<- abs(Improve$`Average Age of Wives CI`-Improve$`Avg Age of Wives CI`)

Improve$Husband_Improvement<- abs(Improve$`Average Age for Husband CI`-Improve$`Avg Age of Husbands CI`)

Improve[,7:9] %>% 
  kbl() %>% 
  kable_styling()