simPoisson {spStack} | R Documentation |
Synthetic point-referenced Poisson count data
Description
Dataset of size 500, with a Poisson distributed 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(simPoisson)
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.
z_true
true spatial random effects that generated the data.
Details
With n = 500
, the count data is simulated using
\begin{aligned}
y(s_i) &\sim \mathrm{Poisson}(\lambda(s_i)),
i = 1, \ldots, n,\\
\log \lambda(s_i) &= x(s_i)^\top \beta + z(s_i)
\end{aligned}
where 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 = (2, -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.
See Also
simGaussian, simBinom, simBinary
Examples
set.seed(1729)
n <- 500
beta <- c(2, -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 = "poisson")
# Plot an interpolated spatial surface of the true random spatial effects
plot1 <- surfaceplot(sim1, coords_name = c("s1", "s2"), var_name = "z_true")
# Plot the simulated count data
library(ggplot2)
plot2 <- ggplot(sim1, aes(x = s1, y = s2)) +
geom_point(aes(color = y), alpha = 0.75) +
scale_color_distiller(palette = "RdYlGn", direction = -1,
label = function(x) sprintf("%.0f", x)) +
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)