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

[Package spStack version 1.0.1 Index]