# Plot Pearson and deviance residuals for poisson
pearson <- influence(model.best)$pear.res/ sqrt(1 - influence(model.best)$hat)
summary(pearson)
deviance <- influence(model.best)$dev.res/ sqrt(1 - influence(model.best)$hat)
summary(deviance)
xb <- predict(model.best)
plot(pearson~xb) #Over 30
plot(pearson^2~xb) # LArger than 1200 XD This is terrible
abline(4,0, col = "red", lty = 3)
plot(deviance~xb) # Over 20
abline(2,0, col = "red", lty = 3)
abline(-2,0, col = "red", lty = 3)

# Plot Pearson and deviance residuals for negative binomial
pearson <- influence(model.gneg_cars)$pear.res/ sqrt(1 - influence(model.gneg_cars)$hat)
summary(pearson)
deviance <- influence(model.gneg_cars)$dev.res/ sqrt(1 - influence(model.gneg_cars)$hat)
xb <- predict(model.gneg_cars)
plot(pearson~xb) #Over 6
plot(pearson^2~xb) # Larger than 40. Not good, but miles ahead of Poisson
abline(4,0, col = "red", lty = 3)
plot(deviance~xb) #Over 3, not good
abline(2,0, col = "red", lty = 3)
abline(-2,0, col = "red", lty = 3)

# Cooks distance for poisson
cd <- cooks.distance(model.best)
n <- 500
plot(cd~xb) # very weird
abline(h = c(1, 4 / n), col = "red", lty = 3) # Largest 3.5

# Cooks distance for negative binomial
cd <- cooks.distance(model.gneg_cars)
n <- 500
plot(cd~xb) # very weird
abline(h = c(1, 4 / n), col = "red", lty = 3) # smaller than  0.05

# Conclusion: Dont use Poisson in this case