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models.R
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models.R
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####################################################################################
# Basic visualisations of the data
####################################################################################
# Histogram of grant amounts
df %>%
ggplot(aes(x = Amount)) +
geom_histogram()
# Scatterplot of TPP against Grants
df %>%
ggplot(aes(x = LNP_Percent, y = Amount)) +
geom_point()
# Fitting a loess curve to see if there's anything there
df %>%
ggplot(aes(x = LNP_Percent, y = Amount)) +
geom_point() +
geom_smooth(span = 0.5)
####################################################################################
# Building a flexible regression model - GAM
####################################################################################
library(visreg)
library(mgcv)
mod <- gam(Amount ~ s(LNP_Percent) + s(Population) + s(MedianAge) +
s(MedianPersonalIncome) + s(HighSchool) + s(Unemployed) + s(Owned) + s(Swing),
data = df %>%
mutate(Amount_per_Grant = ifelse(Number_Grants == 0, 0, Amount/Number_Grants)))
summary(mod)
visreg(mod, "LNP_Percent")
####################################################################################
# Diagnostics
####################################################################################
# Quantile-quantile plot - Check normality of residuals
ggplot(aes(sample = mod$residuals), data = NULL) +
geom_qq() +
geom_qq_line()
# Checking for influential points
library(broom)
aug <- augment(mod, data = df)
aug %>%
ggplot(aes(x = .hat, y = .cooksd)) +
geom_point() +
geom_label(aes(label = Amount))
##### Robustness #####
# Two electorates have high leverage (hat values) and three have potentially high influence (cooksd > 0.05)
influential_electorates <- aug %>%
filter(.cooksd > 0.05) %>%
select(DivisionNm) %>% unlist %>% unname
# Removing the influential electorates
mod_robust1 <- gam(Amount ~ s(LNP_Percent) + s(Population) + s(MedianAge) +
s(MedianPersonalIncome) + s(HighSchool) + s(Unemployed) + s(Owned) + s(Swing),
data = df %>% filter(!DivisionNm %in% influential_electorates))
visreg(mod_robust1, "LNP_Percent")
# Same effect is observed
# Alternatively remove the outliers in terms of their amount
ggplot(aes(y = Amount), data = df) +
geom_boxplot()
mod_robust2 <- gam(Amount ~ s(LNP_Percent) + s(Population) + s(MedianAge) +
s(MedianPersonalIncome) + s(HighSchool) + s(Unemployed) + s(Owned) + s(Swing),
data = df %>% filter(Amount < 1700000))
visreg(mod_robust2, "LNP_Percent")
# Same effect is observed
####################################################################################
# Scatterplot of TPP against Grants
####################################################################################
df %>%
ggplot(aes(x = LNP_Percent, y = Number_Grants)) +
geom_point() +
geom_smooth()
df %>%
filter(Amount < 1600000) %>%
ggplot(aes(x = LNP_Percent, y = Amount)) +
geom_point() +
geom_smooth()
df %>%
ggplot(aes(x = LNP_Percent, y = Amount)) +
geom_point() +
geom_smooth(method = "lm")
df %>%
mutate(Amount_per_Grant = ifelse(Number_Grants == 0, 0, Amount/Number_Grants)) %>%
ggplot(aes(x = LNP_Percent, y = Amount_per_Grant)) +
geom_point() +
geom_smooth()
p1 <- df %>%
ggplot(aes(x = LNP_Percent, y = Amount)) +
geom_point() +
geom_smooth(span = 0.5) +
ggtitle("0.5")
p2 <- df %>%
ggplot(aes(x = LNP_Percent, y = Amount)) +
geom_point() +
geom_smooth(span = 0.75) +
ggtitle("0.75")
library(gridExtra)
grid.arrange(p1, p2, nrow =1)
library(visreg)
library(mgcv)
mod <- gam(Amount ~ s(LNP_Percent) + s(Population) + s(MedianAge) +
s(MedianPersonalIncome) + s(HighSchool) + s(Unemployed) + s(Owned) + s(Swing),
data = df %>%
mutate(Amount_per_Grant = ifelse(Number_Grants == 0, 0, Amount/Number_Grants)))
visreg(mod, "LNP_Percent")
# Histogram
ggplot(aes(x = mod$residuals), data = NULL) + geom_histogram()
# Quantile-quantile plot
ggplot(aes(sample = mod$residuals), data = NULL) +
geom_qq() +
geom_qq_line()
# Checking for influential points
library(broom)
aug <- augment(mod, data = df)
aug %>%
ggplot(aes(x = .hat, y = .cooksd)) +
geom_point() +
geom_label(aes(label = Amount))
# Two electorates have high leverage (hat values) and three have potentially high influence (cooksd > 0.05)
influential_electorates <- aug %>%
filter(.cooksd > 0.05) %>%
select(DivisionNm) %>% unlist %>% unname
# Removing the influential electorates
mod_robust1 <- gam(Amount ~ s(LNP_Percent) + s(Population) + s(MedianAge) +
s(MedianPersonalIncome) + s(HighSchool) + s(Unemployed) + s(Owned) + s(Swing),
data = df %>% filter(!DivisionNm %in% influential_electorates))
visreg(mod_robust1, "LNP_Percent")
# Same effect is observed
# Alternatively remove the outliers in terms of their amount
ggplot(aes(y = Amount), data = df) +
geom_boxplot()
mod_robust2 <- gam(Amount ~ s(LNP_Percent) + s(Population) + s(MedianAge) +
s(MedianPersonalIncome) + s(HighSchool) + s(Unemployed) + s(Owned) + s(Swing),
data = df %>% filter(Amount < 1700000))
visreg(mod_robust2, "LNP_Percent")
# Same effect is observed