This vignette reproduces the distribution of kappa under
the no-border, single outer edge and double outer edge scenarios using a
small Monte Carlo loop built from the package’s functions.
fl <- field_layout(nx = 12, ny = 8, ntrt = 3, nblk = 2,
arrangement = "triangular", width = 550, height = 210,
seed = 3000)
W <- border_weights(fl)
X <- model.matrix(~ trt + blk, fl)
iter <- 300 # the paper uses 3000; reduced here for a fast vignette
sim_kappa <- function(mean_fun, sd_fun) {
replicate(iter, {
y <- rnorm(nrow(fl), mean_fun(fl), sd_fun(fl))
kappa_hat(y, W, X)
})
}
k0 <- sim_kappa(function(d) 2.21, function(d) 0.06) # no border
k1 <- sim_kappa(function(d) ifelse(d$outer1 == 1, 2.21, 1.74),
function(d) ifelse(d$outer1 == 1, 0.06, 0.035)) # 1 border
c_no <- "#0072B2"; c_edge <- "#D55E00" # Okabe-Ito blue / vermillion (CVD-safe)
d0 <- density(k0); d1 <- density(k1)
plot(d0, main = "kappa: no border vs single outer edge", xlab = "kappa",
xlim = range(k0, k1, 0), ylim = c(0, max(d0$y, d1$y) * 1.05),
lwd = 2, col = c_no)
lines(d1, lwd = 2, col = c_edge)
abline(v = 0, lty = 3, col = "grey55")
legend("topright", c("no border", "single edge"), col = c(c_no, c_edge),
lwd = 2, bty = "n")
The no-border density is centered at zero; the single-edge density shifts to negative values, matching the paper’s Figure 8.