# generalized additive model
library(ISLR)
library(splines)
library(gam)
model = gam(wage ~ ns(year, 4) + ns(age, 5) + education, data = Wage)
mean((Wage$wage - predict(model, Wage))^2)
model$coefficients


# simple generalized additive model implementation
y = Wage$wage
X = data.frame(Wage$year, Wage$age, Wage$education)
alpha = mean(y)
current.predictions = array(0, c(length(y), 3))
current.model = list()
for (i in 1:30) {
    desired.response = y - (alpha + apply(current.predictions[,-1], 1, sum))
    current.model[[1]] = lm(desired.response ~ ns(X[,1], 4))
    current.predictions[,1] = predict(current.model[[1]], data.frame(X[,1]))

    desired.response = y - (alpha + apply(current.predictions[,-2], 1, sum))
    current.model[[2]] = lm(desired.response ~ ns(X[,2], 5))
    current.predictions[,2] = predict(current.model[[2]], data.frame(X[,2]))

    desired.response = y - (alpha + apply(current.predictions[,-3], 1, sum))
    current.model[[3]] = lm(desired.response ~ X[,3])
    current.predictions[,3] = predict(current.model[[3]], data.frame(X[,3]))
}
mean((y - (alpha + apply(current.predictions, 1, sum)))^2)
c(alpha + current.model[[1]]$coefficients[1] + current.model[[2]]$coefficients[1] + current.model[[3]]$coefficients[1],
  current.model[[1]]$coefficients[2:5],
  current.model[[2]]$coefficients[2:6],
  current.model[[3]]$coefficients[2:5])


# anova
library(ISLR)
library(gam)
m1 = gam(wage ~ year, data = Wage)
summary(m1)
m2 = gam(wage ~ s(year), data = Wage)
summary(m2)
m3 = gam(wage ~ education + s(age) + year, data = Wage)
summary(m3)
par(mfrow = c(1, 3))
plot(m3)