Synthetic point-referenced binary data

Dataset of size 500, with a binary response variable indexed by spatial coordinates sampled uniformly from the unit square. The model includes one covariate and spatial random effects induced by a Matérn covariogram.

Usage

data(simBinary)

Format

a data.frame object.

s1, s2: 2-D coordinates; latitude and longitude.
x1: a covariate sampled from the standard normal distribution.
y: response vector (0/1).
z_true: true spatial random effects that generated the data.

Details

With $n = 500$, the binary data is simulated using $$ \begin{aligned} y(s_i) &\sim \mathrm{Bernoulli}(\pi(s_i)), i = 1, \ldots, n,\\ \pi(s_i) &= \mathrm{ilogit}(x(s_i)^\top \beta + z(s_i)) \end{aligned} $$ where the function $\mathrm{ilogit}$ refers to the inverse-logit function, the spatial effects $z \sim N(0, \sigma^2 R)$ with $R$ being a $n \times n$ correlation matrix given by the Matérn covariogram $$ R(s, s') = \frac{(\phi |s-s'|)^\nu}{\Gamma(\nu) 2^{\nu - 1}} K_\nu(\phi |s-s'|), $$ where $\phi$ is the spatial decay parameter and $\nu$ the spatial smoothness parameter. We have sampled the data with $\beta = (0.5, -0.5)$, $\phi = 5$, $\nu = 0.5$, and $\sigma^2 = 0.4$. This data can be generated with the code as given in the example below.

Author

Soumyakanti Pan span18@ucla.edu,
Sudipto Banerjee sudipto@ucla.edu

Examples

set.seed(1729)
n <- 500
beta <- c(0.5, -0.5)
phi0 <- 5
nu0 <- 0.5
spParams <- c(phi0, nu0)
spvar <- 0.4
sim1 <- sim_spData(n = n, beta = beta, cor.fn = "matern",
                   spParams = spParams, spvar = spvar, deltasq = deltasq,
                   family = "binary")
plot1 <- surfaceplot(sim1, coords_name = c("s1", "s2"), var_name = "z_true")

library(ggplot2)
plot2 <- ggplot(sim1, aes(x = s1, y = s2)) +
  geom_point(aes(color = factor(y)), alpha = 0.75) +
  scale_color_manual(values = c("red", "blue"), labels = c("0", "1")) +
  guides(alpha = 'none') +
  theme_bw() +
  theme(axis.ticks = element_line(linewidth = 0.25),
        panel.background = element_blank(),
        panel.grid = element_blank(),
        legend.title = element_text(size = 10, hjust = 0.25),
        legend.box.just = "center", aspect.ratio = 1)