I want to describe an old project that required some interesting data analysis but first I need to find a way to create some artificial data. I basically need data from a step function, with some noise added. Each step has to have some “measurement” points in the middle. At first I tried to make my own step function in a naïve way, as shown below. I did not realise literally until I started writing this post and wrote a function called step_func that R has a built-in function stats::stepfun, which I need to learn more about.
step_func <- function(n = 100L, m = 10L) {
dat <- sapply(1:n, function(x) rep(x, m))
data.frame(
x = 0:((n * m ) - 1),
y = as.vector(dat)
)
}
step_dat <- step_func(n = 20, m = 4)
ggplot2::ggplot(step_dat, ggplot2::aes(x = x, y = y)) +
ggplot2::geom_point()
This is fine but I also need occasionally lower steps. It turned out one way to do this is to essentially simulate the underlying process that I was studying, by using a cumulative sum, with the step height sometimes decreased according to a probability in rbinom. I also add noise in the function below, and drop some of the “measurement” points randomly.
set.seed(100)
make_data <- function(n = 100L,
m = 10L,
p = 0.15,
rmin = 0.2,
rmax = 0.8,
sd_x = 0.02,
sd_y = 0.02,
del_frac = 0.05) {
sim <- data.frame(
x = seq(m, n * m, by = m),
y = 1 - rbinom(n, 1, p) * runif(n, min = rmin, max = rmax)
)
meas <- data.frame(
x = 0:(n * m),
noise_x = rnorm((n * m) + 1, mean = 0, sd = sd_x),
noise_y = rnorm((n * m) + 1, mean = 0, sd = sd_y)
)
sim_noisy <- merge(sim, meas, all = TRUE)
sim_noisy$y_noisy <- rowSums(sim_noisy[, c("y", "noise_y")], na.rm = TRUE)
sim_noisy$x_noisy <- rowSums(sim_noisy[, c("x", "noise_x")], na.rm = TRUE)
sim_noisy$cumul_noisy <- cumsum(sim_noisy$y_noisy)
del_nrows = as.integer(n * m * del_frac)
del_rows <- sample(n * m, del_nrows, replace = FALSE)
sim_noisy[-del_rows, c("x_noisy", "cumul_noisy")]
}
sim_dat <- make_data(n = 20, m = 4)
ggplot2::ggplot(sim_dat, ggplot2::aes(x = x_noisy, y = cumul_noisy)) +
ggplot2::geom_point()
