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posterior-calcs.R
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############################################################################################
# Posterior Calculations - Undecided voters and polling bias in US presidential elections
# Author: Joshua J Bon
# Notes:
# - To appear in JRSS-A article by Bon, Ballard & Baffour
#
# - arXiv: https://arxiv.org/abs/1703.09430
#
# - Models:
# - Original SRGG model for 2004, 2008, 2012, 2016 US presidential elections
# - Extended SRGG with bias away from proportional allocation of undecided voters
# - Extended SRGG with bias away from even allocation of undecided voters
#
# - SRGG: Shirani-Mehr, H., Rothschild, D., Goel, S., & Gelman, A. (2018).
# Disentangling bias and variance in election polls.
# Journal of the American Statistical Association, 1-23
#
############################################################################################
#### Directory ####
setwd("~/Dropbox/Research/Code/undecided-voters-us-pres-elections/")
####
#### Libraries ####
library(rstan)
library(stringr)
library(plyr)
library(dplyr)
# devtools::install_version("rv", version="2.3.2", repos="http://cran.r-project.org")
library(rv)
library(gtools)
####
#### Load Models ####
# list of models (as environments)
models <- list()
models$prop <- readRDS("fitted_models/extended-SRGG-prop-fit.rds")
models$even <- readRDS("fitted_models/extended-SRGG-even-fit.rds")
models$SRGG <- readRDS("fitted_models/SRGG-fit.rds")
# set number of simulations for RV package
setnsims(length(rstan::extract(models$SRGG$stan_fit, "lp__")[[1]]))
getnsims()
if(any(diff(sapply(models, function(l){length(rstan::extract(l$stan_fit, "lp__")[[1]])})) != 0)){
warning("Simulations from stan objects loaded are not equal in length")
}
####
#### Extra rv functins ####
ilogit.rv <- function(x) rvmapply(FUN = inv.logit, x)
logit.rv <- function(x) rvmapply(FUN = logit, x)
####
#### Original model - Bias summaries ####
models$SRGG <- within(models$SRGG,{
postrv <- as.rv(stan_fit)
syid <- stan_data$state_year_id
p_i <- ilogit.rv(
logit(stan_data$vote[syid]) + postrv$alpha[syid] + postrv$beta[syid] * stan_data$t
)
p_i_e <- ilogit.rv(
logit(stan_data$vote[syid]) + postrv$alpha[syid]
)
sig_i <- sqrt(
(p_i * (1 - p_i) / stan_data$sample_size) + postrv$tau_sq[syid]
)
SRS_i <- sqrt(
(p_i * (1 - p_i) / stan_data$sample_size)
)
N_races <- stan_data$S
Y <- stan_data$Y
b_r <- rv(N_races)
b_r_e <- rv(N_races)
sd_r <- rv(N_races)
SRS_r <- rv(N_races)
for(i in 1:N_races){
b_r[i] <- mean(p_i[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_e[i] <- mean(p_i_e[i == stan_data$state_year_id]) - stan_data$vote[i]
sd_r[i] <- mean(sig_i[i == stan_data$state_year_id])
SRS_r[i] <- mean(SRS_i[i == stan_data$state_year_id])
}
# overall summaries (mean abs)
mabs_b_r <- mean(abs(b_r))
mabs_b_r_e <- mean(abs(b_r_e))
m_sd_r <- mean(sd_r)
m_SRS_r <- mean(SRS_r)
yearly_mabs_b_r <- rv(Y)
yearly_mabs_b_r_e <-rv(Y)
yearly_m_sd_r <-rv(Y)
yearly_m_SRS_r <-rv(Y)
# summaries by year
for(i in 1:4){
yearly_mabs_b_r[i] <- mean(abs(b_r[i == vote_data$year_id]))
yearly_mabs_b_r_e[i] <- mean(abs(b_r_e[i == vote_data$year_id]))
yearly_m_sd_r[i] <- mean(sd_r[i == vote_data$year_id])
yearly_m_SRS_r[i] <- mean(SRS_r[i == vote_data$year_id])
}
})
# remove unwanted rvs calculations
# and save summary rvs
remove_items <- c("postrv","stan_fit","i","stan_data","SRS_i","sig_i","p_i","p_i_e")
models$SRGG[remove_items] <- NULL
saveRDS(models$SRGG, file = "fitted_models/SRGG-summary-rvs.rds")
####
#### Extended model - Proportional (or even) Und Alloc - Bias summaries ####
# See Appendix B for more details
for(mdn in c("prop","even")){
models[[mdn]] <- within(models[[mdn]],{
postrv <- as.rv(stan_fit)
syid <- stan_data$state_year_id
# update gamm (if gamm * 10 is in stan model)
postrv$gamm <- postrv$gamm * 10
# Include undecided bias (if applicable)
p_i <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] +
postrv$beta[syid] * stan_data$t +
postrv$kappa[stan_data$house_id] -
postrv$gamm[stan_data$rmargin_year_id] * postrv$alpha_und[syid]
)
p_i_e <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] +
postrv$kappa[stan_data$house_id] -
postrv$gamm[stan_data$rmargin_year_id] * postrv$alpha_und[syid]
)
p_i_u <- ilogit.rv(
logit(stan_data$vote[syid]) -
postrv$gamm[stan_data$rmargin_year_id] * postrv$alpha_und[syid]
)
p_i_h <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$kappa[stan_data$house_id]
)
# Exclude undecideds
p_i_0u <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] +
postrv$beta[syid] * stan_data$t +
postrv$kappa[stan_data$house_id]
)
p_i_e_0u <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] +
postrv$kappa[stan_data$house_id]
)
# Exclude house effects
p_i_0h <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] +
postrv$beta[syid] * stan_data$t -
postrv$gamm[stan_data$rmargin_year_id] * postrv$alpha_und[syid]
)
p_i_e_0h <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] -
postrv$gamm[stan_data$rmargin_year_id] * postrv$alpha_und[syid]
)
# Exclude undecided bias and house effects
p_i_0uh <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid] +
postrv$beta[syid] * stan_data$t
)
p_i_e_0uh <- ilogit.rv(
logit(stan_data$vote[syid]) +
postrv$alpha[syid]
)
# Variance calcs
sig_i <- sqrt(
(p_i * (1 - p_i) / stan_data$sample_size) + postrv$tau_sq[syid]
)
SRS_i <- sqrt(
(p_i * (1 - p_i) / stan_data$sample_size)
)
# constants
N_races <- stan_data$S
Y <- stan_data$Y
# Setup bias
b_r <- rv(N_races)
b_r_e <- rv(N_races)
b_r_u <- rv(N_races)
b_r_h <- rv(N_races)
b_r_0u <- rv(N_races)
b_r_e_0u <- rv(N_races)
b_r_0h <- rv(N_races)
b_r_e_0h <- rv(N_races)
b_r_0uh <- rv(N_races)
b_r_e_0uh <- rv(N_races)
sd_r <- rv(N_races)
SRS_r <- rv(N_races)
for(i in 1:N_races){
b_r[i] <- mean(p_i[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_e[i] <- mean(p_i_e[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_u[i] <- mean(p_i_u[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_h[i] <- mean(p_i_h[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_0u[i] <- mean(p_i_0u[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_e_0u[i] <- mean(p_i_e_0u[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_0h[i] <- mean(p_i_0h[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_e_0h[i] <- mean(p_i_e_0h[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_0uh[i] <- mean(p_i_e_0uh[i == stan_data$state_year_id]) - stan_data$vote[i]
b_r_e_0uh[i] <- mean(p_i_e_0uh[i == stan_data$state_year_id]) - stan_data$vote[i]
sd_r[i] <- mean(sig_i[i == stan_data$state_year_id])
SRS_r[i] <- mean(SRS_i[i == stan_data$state_year_id])
}
# overall summaries (mean abs)
mabs_b_r <- mean(abs(b_r))
mabs_b_r_e <- mean(abs(b_r_e))
mabs_b_r_u <- mean(abs(b_r_u))
mabs_b_r_h <- mean(abs(b_r_h))
mabs_b_r_0u <- mean(abs(b_r_0u))
mabs_b_r_e_0u <- mean(abs(b_r_e_0u))
mabs_b_r_0h <- mean(abs(b_r_0h))
mabs_b_r_e_0h <-mean(abs(b_r_e_0h))
mabs_b_r_0uh <-mean(abs(b_r_0uh))
mabs_b_r_e_0uh <-mean(abs(b_r_e_0uh))
m_sd_r <- mean(sd_r)
m_SRS_r <- mean(SRS_r)
yearly_mabs_b_r <- rv(Y)
yearly_mabs_b_r_e <-rv(Y)
yearly_mabs_b_r_u <- rv(Y)
yearly_mabs_b_r_h <- rv(Y)
yearly_mabs_b_r_0u <- rv(Y)
yearly_mabs_b_r_e_0u <- rv(Y)
yearly_mabs_b_r_0h <- rv(Y)
yearly_mabs_b_r_e_0h <- rv(Y)
yearly_mabs_b_r_0uh <- rv(Y)
yearly_mabs_b_r_e_0uh <- rv(Y)
yearly_m_sd_r <-rv(Y)
yearly_m_SRS_r <-rv(Y)
# summaries by year
for(i in 1:4){
yearly_mabs_b_r[i] <- mean(abs(b_r[i == vote_data$year_id]))
yearly_mabs_b_r_e[i] <- mean(abs(b_r_e[i == vote_data$year_id]))
yearly_mabs_b_r_u[i] <- mean(abs(b_r_u[i == vote_data$year_id]))
yearly_mabs_b_r_h[i] <- mean(abs(b_r_h[i == vote_data$year_id]))
yearly_mabs_b_r_0u[i] <- mean(abs(b_r_0u[i == vote_data$year_id]))
yearly_mabs_b_r_e_0u[i] <- mean(abs(b_r_e_0u[i == vote_data$year_id]))
yearly_mabs_b_r_0h[i] <- mean(abs(b_r_0h[i == vote_data$year_id]))
yearly_mabs_b_r_e_0h[i] <- mean(abs(b_r_e_0h[i == vote_data$year_id]))
yearly_mabs_b_r_0uh[i] <- mean(abs(b_r_0uh[i == vote_data$year_id]))
yearly_mabs_b_r_e_0uh[i] <- mean(abs(b_r_e_0uh[i == vote_data$year_id]))
yearly_m_sd_r[i] <- mean(sd_r[i == vote_data$year_id])
yearly_m_SRS_r[i] <- mean(SRS_r[i == vote_data$year_id])
}
# pollster bias summary
N_pollsters <- stan_data$H
b_h <- rv(N_pollsters)
hid <- stan_data$house_id
for(i in 1:N_pollsters){
which_polls <- i == hid
which_votes <- stan_data$state_year_id[which_polls]
b_h[i] <- mean(p_i_h[which_polls] - stan_data$vote[which_votes])
}
y_id_ord <- vote_data %>% select(year,year_id) %>%
unique() %>% arrange(year_id) %>% select(year) %>% collect() %>% .[[1]]
# Save more from postrv
alpha_und <- postrv$alpha_und
gamm <- postrv$gamm
kappa <- postrv$kappa
phi_und <- postrv$phi_und
})
}
# remove unwanted rvs calculations
# and save summary rvs
remove_items <- c(remove_items,"p_i_e_0uh","p_i_0uh","p_i_e_0h","p_i_0h","p_i_e_0u","p_i_0u","p_i_h","p_i_u")
models$prop[remove_items] <- NULL
models$even[remove_items] <- NULL
saveRDS(models$prop, file = "fitted_models/extended-SRGG-prop-summary-rvs.rds")
saveRDS(models$even, file = "fitted_models/extended-SRGG-even-summary-rvs.rds")
####