simBinary {spStack} | R Documentation |
Synthetic point-referenced binary data
Description
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(s)
Soumyakanti Pan span18@ucla.edu,
Sudipto Banerjee sudipto@ucla.edu
See Also
simGaussian, simPoisson, simBinom
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)