Smoothing and piecewise linear data-generating processes

dontsmoothlineardgps.R

### Let's generate some data with a step function
library(mgcv)
set.seed(1116)

nDays <- 200
day <- 1:nDays

y <- rnorm(200, 1, 0.25) + I(day > 100) * -0.5

y <- ifelse(y < 0,
            0,
            y)

dat <- data.frame(y = y,
                  day = day,
                  npi = day > 100)

png(file = "smooth1.png")
plot(day, y,
     xlab = "Day",
     ylab = "Value",
     pch = 19)
abline(v = 100, col = "darkgrey")
dev.off()

piecewise <- lm(y ~ 1 + npi, data = dat)


png(file = "smooth2.png")
plot(day, y,
     xlab = "Day",
     ylab = "Value",
     pch = 19)
abline(v = 100, col = "darkgrey")
yhat <- predict(piecewise)
lines(day, yhat)
dev.off()


smoothed <- gam(y ~ s(day), data = dat)

yhat2 <- predict(smoothed)


png(file = "smooth3.png")
plot(day, y,
     xlab = "Day",
     ylab = "Value",
     pch = 19)
abline(v = 100, col = "darkgrey")
yhat <- predict(piecewise)
lines(day, yhat2)
dev.off()