Synthetic point-referenced binomial count data

Dataset of size 500, with a binomial 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. The number of trials at each location is sampled from a Poisson distribution with mean 20.

Usage

data(simBinom)

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.
n_trials: Number of trials at that location.
z_true: true spatial random effects that generated the data.

Details

With $n = 500$, the count data is simulated using $$ \begin{aligned} y(s_i) &\sim \mathrm{Binomial}(m(s_i), \pi(s_i)), i = 1, \ldots, n,\\ \pi(s_i) &= \mathrm{ilogit}(x(s_i)^\top \beta + z(s_i)) \end{aligned} $$ where the function $\mathrm{ilogit}$ refers to the inverse-logit function, the number of trials $m(s_i)$ is sampled from a Poisson distribution with mean 20, 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 $\beta = (0.5, -0.5)$, $\phi = 3$, $\nu = 0.5$, 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 <- 3
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,
                   n_binom = rpois(n, 20),
                   family = "binomial")
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 = 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)