scripts/ch02/f2_9-d1pen.R

In rpkgs/JOPSbook: P-Spline

# First order difference penalty in action with various tuning
# A graph in the book 'Practical Smoothing. The Joys of P-splines'
# Paul Eilers and Brian Marx, 2019

library(ggplot2)
library(gridExtra)
library(JOPS)

# Simulate data
m = 50
set.seed(123)
x = runif(m)
y = sin(2.5 * x) + rnorm(m) * 0.1 + 0.2

# Make basis and penalty
nu = 200
u = seq(0, 1, length = nu)
nseg = 20
Bu = bbase(u, nseg = nseg)
B = bbase(x, nseg = nseg)
nb = ncol(B)
knots = ((1:nb) - 2) / nseg
n = ncol(B)
D = diff(diag(n), diff = 1)
P = t(D) %*% D
BtB = t(B) %*% B
Bty = t(B) %*% y

# Compute coefficients
A = Mu = NULL
lambdas = c(0.1, 1, 10, 100) * 2
for (lambda in lambdas) {
  a = solve(BtB + lambda * P, Bty)
  A = cbind(A, a)
}
Z = Bu %*% A
Mu = cbind(Mu, B %*% A)

# Generate the plots
plts = list()
for (j in 1:4) {
  # Compute roughness
  aj = c(A[, j])
  da = diff(aj)
  r = sqrt(sum(da ^ 2) / (n - 1))
  r = round(r, 2)
  s = sqrt(mean((y - Mu[, j])^2))
  s = round(s, 2)

  # Scaled basis
  Bsc = B %*% diag(aj)
  # Create data frames for ggplot
  Data = data.frame(x, y)
  Zf = data.frame(x = u, y = Z[, j], id  = as.factor(1))
  Bf = data.frame(x = rep(u, n), y = as.vector(Bsc),
                  id = as.factor(rep(1:n, each = nu)))
  Bf$y[Bf$y < 0.0001] = NA
  Bf = na.omit(Bf)
  titl = bquote(lambda==.(lambdas[j])~ "|"~s==.(s)~"|"~r==.(r))

  Fa = data.frame(x = knots, y = aj, id = as.factor(1))

  # Build the graphs
  plt1 = ggplot(Data, aes(x = x, y = y), ylim = c(0, 1.5)) +
    geom_point(color = 'grey40') +
    geom_line(data = Zf, aes(x, y), color = "blue", size = 1)  +
    geom_point(data = Fa, color = "red", size = 2, shape = 1) +
    xlab("") + ylab("") +
    ggtitle(titl) +
    JOPS_theme() +
    theme(plot.title = element_text(size = rel(0.9)))

  # Add to list of plots
  plts[[j]] = plt1
}

# Plot and save
grid.arrange(grobs = plts, nrow = 2, ncol = 2)