simGaussian {spStack} | R Documentation |
Synthetic point-referenced Gaussian data
Description
Dataset of size 500 with a Gaussian response variable, simulated with spatial coordinates sampled uniformly from the unit square. The model includes one covariate and spatial random effects induced by a Matérn covariogram.
Usage
data(simGaussian)
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
The data is generated using the model
y = X \beta + z + \epsilon,
where the spatial effects z \sim N(0, \sigma^2 R)
is independent of the
measurement error \epsilon \sim N(0, \delta^2 \sigma^2 I_n)
with
\delta^2
being the noise-to-spatial variance ratio and 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, 5)
,
\phi = 2
, \nu = 0.5
, \delta^2 = 1
and
\sigma^2 = 0.4
. This data can be generated with the code as given in
the example.
Author(s)
Soumyakanti Pan span18@ucla.edu
See Also
simPoisson, simBinom, simBinary
Examples
set.seed(1729)
n <- 500
beta <- c(2, 5)
phi0 <- 2
nu0 <- 0.5
spParams <- c(phi0, nu0)
spvar <- 0.4
deltasq <- 1
sim1 <- sim_spData(n = n, beta = beta, cor.fn = "matern",
spParams = spParams, spvar = spvar, deltasq = deltasq,
family = "gaussian")
plot1 <- surfaceplot(sim1, coords_name = c("s1", "s2"), var_name = "z_true",
mark_points = TRUE)
plot1
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)
plot2