Synthetic point-referenced Poisson count data

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)