spStack (version 1.0.1)

simBinary: 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.

Author

Soumyakanti Pan ,
Sudipto Banerjee

Details

With $n=500$, the binary data is simulated using $$\begin{array}{rl}y(s_i)& \sim \mathrm{Bernoulli}(\pi (s_i)),i=1,\dots ,n,\\ \pi (s_i)& =\mathrm{ilogit}(x(s_i{)}^{\mathrm{\top }}\beta +z(s_i))\end{array}$$ 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 $$R(s,s^{\prime })=\frac{(\varphi |s-s^{\prime }|{)}^{\nu }}{\mathrm{\Gamma }(\nu )2^{\nu -1}}{K}_{\nu }(\varphi |s-s^{\prime }|),$$ where $\varphi$ is the spatial decay parameter and $\nu$ the spatial smoothness parameter. We have sampled the data with $\beta =(0.5,-0.5)$, $\varphi =5$, $\nu =0.5$, and ${\sigma }^2=0.4$. This data can be generated with the code as given in the example below.

See Also

simGaussian, 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)