Regression and Other Stories: Congress

Predictive uncertainty for congressional elections. See Chapters 10 and 15 in Regression and Other Stories.

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Load packages

library("rprojroot")
root<-has_file(".ROS-Examples-root")$make_fix_file()
library("rstanarm")

Load data

congress <- read.csv(root("Congress/data","congress.csv"))
inconsistent <- (congress$inc88==(-1) & congress$v86 > 0.5) |  (congress$inc88==1 & congress$v86 < 0.5)
head(congress)

  inc86 inc88 inc90       v86       v88       v90   v86_adj   v88_adj   v90_adj
1     1     1     1 0.7450362 0.7724427 0.7140294 0.7450362 0.7724427 0.7140294
2     1     1     1 0.6738455 0.6361816 0.5970501 0.6738455 0.6361816 0.5970501
3     1     1     0 0.6964566 0.6649283 0.5210433 0.6964566 0.6649283 0.5210433
4    -1    -1    -1 0.4645901 0.2738342 0.2343770 0.4645901 0.2738342 0.2343770
5    -1    -1     0 0.3910945 0.2636131 0.4774393 0.3910945 0.2636131 0.4774393
6    -1    -1    -1 0.3582454 0.3341927 0.2562970 0.3582454 0.3341927 0.2562970

Regression predicting 1988 from 1986

data88 <- data.frame(vote=congress$v88_adj, past_vote=congress$v86_adj, inc=congress$inc88)
fit88 <- stan_glm(vote ~ past_vote + inc, data=data88, refresh=0)
print(fit88, digits=2)

stan_glm
 family:       gaussian [identity]
 formula:      vote ~ past_vote + inc
 observations: 435
 predictors:   3
------
            Median MAD_SD
(Intercept) 0.24   0.02  
past_vote   0.52   0.03  
inc         0.10   0.01  

Auxiliary parameter(s):
      Median MAD_SD
sigma 0.07   0.00  

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* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

Simulation for inferences and predictions of new data points

Predict from 1988 to 1990

data90 <- data.frame(past_vote=congress$v88_adj, inc=congress$inc90)

Simulate predictive simulations of the vector of new outcomes

pred90 <- posterior_predict(fit88, newdata=data90)

Simulate the number of elections predicted to be won by the Democrats in 1990

dems_pred <- rowSums(pred90 > 0.5)

Alternately calculate that sum in a loop

n_sims <- 4000
dems_pred <- rep(NA, n_sims)
for (s in 1:n_sims) {
  dems_pred[s] <- sum(pred90[s,] > 0.5)
}

Our posterior mean and sd of how many districts the Dems will win

print(c(mean(dems_pred), sd(dems_pred)), digits=2)

[1] 260.0   2.5

Histogram of how many districts the Dems will win

hist(dems_pred)

Graphs

par(mar=c(3,0,1,0), mgp=c(1.5, .5, 0), tck=-.01)
v88_hist <- ifelse(congress$v88<.1, .0001, ifelse(congress$v88>.9, .9999, congress$v88))
hist(v88_hist, breaks=seq(0,1,.05),
     xlab="Democratic share of the two-party vote", ylab="", yaxt="n", main="")
mtext("Congressional elections in 1988", 3, 0)

if (savefigs) dev.off()

if (savefigs) pdf("cong.pdf", height=4, width=4, colormodel="gray")
par(pty="s")
par(mar=c(3,0,3,0), mgp=c(1.7, .5, 0), tck=-.01)
plot(0, 0, xlim=c(0,1), ylim=c(0,1), type="n", xaxs="i", yaxs="i",
  xlab="Democratic vote share in 1986", ylab="Democratic vote share in 1988")
abline(0,1, lwd=.5)
jitt <- function(vote){
  n <- length(vote)
  ifelse(vote<0.1, runif(n, 0.01, 0.04), ifelse(vote>0.9, runif(n, 0.96, 0.99), vote))
}
j_v86 <- jitt(congress$v86)
j_v88 <- jitt(congress$v88)
points(j_v86[congress$inc88==0], j_v88[congress$inc88==0], pch=1, cex=1)
points(j_v86[congress$inc88==1], j_v88[congress$inc88==1], pch=16, cex=.8)
points(j_v86[congress$inc88==-1], j_v88[congress$inc88==-1], pch=4, cex=.8)
mtext("Raw data", 3, .7)

par(pty="s")
par(mar=c(3,0,3,0), mgp=c(1.7, .5, 0), tck=-.01)
plot(0, 0, xlim=c(0,1), ylim=c(0,1), type="n", xaxs="i", yaxs="i",
  xlab="Adjusted Dem. vote share in 1986", ylab="Adjusted Dem. vote share in 1988")
abline(0,1, lwd=.5)
points(congress$v86_adj[congress$inc88==0], congress$v88_adj[congress$inc88==0], pch=1, cex=1)
points(congress$v86_adj[congress$inc88==1], congress$v88_adj[congress$inc88==1], pch=16, cex=.8)
points(congress$v86_adj[congress$inc88==-1], congress$v88_adj[congress$inc88==-1], pch=4, cex=.8)
mtext("Adjusted data", 3, .7)