Predicting Presidential Elections (and other things)
based on Ray Fair's book, Chapter 3
Presidential Data
First grab the data and split it into two subsets if you haven't already
presdata <- read.table('http://fairmodel.econ.yale.edu/vote2012/pres.txt', header=TRUE)
train <- subset(presdata, YEAR<= 1996)
test <- subset(presdata, YEAR>= 2000)
Explanation of Varialbles
VP:: Democratic share of the two-party presidential vote
I: 1 if there is a Democratic presidential incumbent at the time of the
election and −1 if there is a Republican presidential incumbent
DPER: 1 if a Democratic presidential incumbent is running again, −1
if a Republican presidential incumbent is running again, and 0
otherwise.
DUR: 0 if either party has been in the White House for one term, 1 [−1] if
the Democratic [Republican] party has been in the White House for
two consecutive terms, 1.25 [−1.25] if the Democratic [Republican]
party has been in the White House for three consecutive terms, 1.50
[−1.50] if the Democratic [Republican] party
Explanation of Varialbles (continued)
WAR: 1 for the elections of 1918, 1920, 1942, 1944, 1946, and 1948, and
0 otherwise.
G: growth rate of real per capita GDP in the first three quarters of the
on-term election year (annual rate).
P: absolute value of the growth rate of the GDP deflator in the first 15
quarters of the administration (annual rate) except for 1920, 1944,
and 1948, where the values are zero.
Z: number of quarters in the first 15 quarters of the administration in
which the growth rate of real per capita GDP is greater than 3.2
percent at an annual rate except for 1920, 1944, and 1948, where
the values are zero.
Variable Interactions
m_wrong <- lm(VP~G, data=train)
summary(m_wrong)
m_right <- lm(VP~I:G, data=train) #b/c the the sign of this effect should depend on I
summary(m_right)
More Variable Interactions
Some variable need to be crossed with I but some essentially already are crossed with I.
m <- lm(VP~I:G+DPER+DUR+I:P+I:Z+I:WAR+DPER+I:G:Z, data=train)
More Variable Interactions (part 2)
Call:
lm(formula = VP ~ I:G + DPER + DUR + I:P + I:Z + I:WAR + DPER +
I:G:Z, data = train)
Residuals:
Min 1Q Median 3Q Max
-3.214 -1.349 0.280 0.726 4.640
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 47.4614 0.5835 81.34 < 2e-16 ***
DPER 2.4805 1.1637 2.13 0.05270 .
DUR -4.4843 0.8887 -5.05 0.00022 ***
I:G 0.9043 0.1568 5.77 6.5e-05 ***
I:P -0.8191 0.2280 -3.59 0.00328 **
I:Z 0.9923 0.1956 5.07 0.00021 ***
I:WAR 4.9881 2.1553 2.31 0.03765 *
I:G:Z -0.0568 0.0305 -1.86 0.08562 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.23 on 13 degrees of freedom
Multiple R-squared: 0.942, Adjusted R-squared: 0.91
F-statistic: 29.9 on 7 and 13 DF, p-value: 4.91e-07
Plotting the Model
#The last two of these won't make sense yet but we may return to them later.
plot(m)
Making Predictions
predict(m, test)
22 23 24
49.60 44.14 55.37
test$VP
[1] 50.26 48.77 53.69
Compute the RMSE
RMSE <- function(x1, x2){
sqrt(mean((x1-x2)^2))
}
RMSE(predict(m, test), test$VP)
[1] 2.867
RMSE(rep(50,3), test$VP) #predicting 50 for each election
[1] 2.251
Parsimony?
“economy of explanation in conformity with Occam's razor”
Maybe fewer variables would perform better out of sample
More complex models will always perform better in sample even if they over-fit the data.
Try building different (perhaps simpler) models using the training data and then checking how they perform on the test set.