# Edpsy 590BAY
# Fall 2019
# c.j.anderson
#
# Inference for a proportion:  GSS 2006, 2016 and 2018
#  Whould you favor or oppose a law which would require
#   and person to obtain a police permit before he or she 
#   could buy a gun?
#
# Some data from a few difference years
# 2006
favor.06 <- 1568
oppose.06 <- 395
(n.06 <- favor.06 + oppose.06)
(p.06 <- favor.06/(n.06))

# 2016 
favor.16 <- 1330
oppose.16 <- 528
(n.16 <- favor.16 + oppose.16)
(p.16 <- favor.16/(n.16))

# 2018: 
favor.18 <- 1102
oppose.18 <- 439
(n.18 <- favor.18 + oppose.18)
(p.18 <- favor.18/(n.18))


####################################
# Estimate proporton based just on #
#  data from 2006                  #
####################################
# Uniform priors
a06 <- favor.06 + 1
b06 <- oppose.06+1
(mean06 <- a06/(a06+b06))
(mode06 <- (a06-1)/(a06 + b06 - 2))

layout(matrix(c(1,1,0,0,1,1,3,3,2,2,3,3,2,2,0,0),4,4,byrow=FALSE))
pi <- seq(0,1,length.out=1000)

# no impact of uniform prior

prior <- dbeta(pi,1,1)
plot(pi,prior,type='l',main="Prior is beta(1,1)=uniform" )

likelihood <- dbeta(pi,a06,b06)
plot(pi,likelihood,type='l',main='Likelihood is beta(1569,396)')

posterior <- prior*likelihood/sum(prior*likelihood)
plot(pi,posterior,type='l', main='Posterior')