MA_712_HW3

by: Randy Cruz

library(maxLik)
library(Zelig)

data("turnout")
turnout

library(ggplot2)
library(dplyr)
eduinc <- turnout%>%
  group_by(educate)%>%
  summarize(avincome=mean(income), n = n(), totalinc = sum(income))%>%
  mutate(percent = n/sum(n))

Income In Relation to Education

Higher levels of education led to higher average of household Income.

ggplot(eduinc)+
  geom_col(aes(x = educate, y = avincome), color= "Aqua Marine1", fill= "Orange")

Income X Age Relationship

Ages 25 and 50 had higher reports of income. However, those who were 50+ displayed lower levels of income.

ggplot(turnout)+
  geom_point(aes(x = age, y = income), color= "Orange") + geom_smooth(aes(x = age, y = income), color= "Aqua Marine1")

Maximum Likelihood Estimation - Education X Age X Income

Overall, the analysis displays that age and education have a positive relationship with income. The MaxLik function adds to the analysis as it portrays for every 1 unit of education income goes up by (theta2).133. In addition, for every 1 unit of age, income increased by (theta3).017.

ols.lf2 <- function(param) {
  mu <- param[1]
  theta <- param[-1]
  y <- as.vector(turnout$income)
  x <- cbind(1, turnout$educate, turnout$age)
  sigma <- x%*%theta
  sum(dnorm(y, mu, sigma, log = TRUE))
}    
print(ols.lf2)

function(param) {
  mu <- param[1]
  theta <- param[-1]
  y <- as.vector(turnout$income)
  x <- cbind(1, turnout$educate, turnout$age)
  sigma <- x%*%theta
  sum(dnorm(y, mu, sigma, log = TRUE))
}

mle_ols2 <- maxLik(logLik = ols.lf2, start = c(mu = 1, theta1 = 1, theta2 = 1, theta3 = 1), method= "bfgs")
summary(mle_ols2)

--------------------------------------------
Maximum Likelihood estimation
BFGS maximization, 150 iterations
Return code 0: successful convergence 
Log-Likelihood: -4843.15 
4  free parameters
Estimates:
       Estimate Std. error t value  Pr(> t)    
mu     3.555011   0.069193  51.378  < 2e-16 ***
theta1 0.362114   0.204550   1.770   0.0767 .  
theta2 0.133349   0.010756  12.398  < 2e-16 ***
theta3 0.017507   0.002852   6.139 8.32e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
--------------------------------------------