Synthetic point-referenced spatial-temporal data

Dataset of size 500 with spatial coordinates sampled uniformly from the unit square and temporal coordinates sampled uniformly from the unit interval, two covariates, an intercept and a slope of x1 that vary over space and time, and Gaussian and Poisson responses that share them.

Usage

data(simSpaceTime)

Format

a data.frame object with 500 rows and columns

s1, s2: 2-D coordinates in the unit square.
t_coords: temporal coordinates in the unit interval.
x1, x2: covariates sampled from the standard normal distribution.
y_gauss: Gaussian response.
y_pois: Poisson count response.
z1_true: true spatial-temporal effect associated with the intercept.
z2_true: true spatial-temporal effect associated with x1.

Details

With $\ell = (s, t)$, the varying intercept is a wave travelling across space over time and the varying slope of $x_1$ changes with $s_2$ and $t$, $$ z_1(\ell) = \sin(2 \pi s_1 - \pi t), \quad z_2(\ell) = \cos(2 \pi s_2) \cos(\pi t), $$ deterministic surfaces that are not draws from Gaussian processes. The responses are generated as $$ \begin{aligned} y_{\mathrm{gauss}}(\ell) &\sim N(2 + 5 x_1(\ell) - x_2(\ell) + z_1(\ell) + x_1(\ell) z_2(\ell), 0.5^2),\\ y_{\mathrm{pois}}(\ell) &\sim \mathrm{Poisson}(\exp\{2 - 0.5 x_1(\ell) + 0.3 x_2(\ell) + z_1(\ell) + x_1(\ell) z_2(\ell)\}). \end{aligned} $$ This data can be generated with the code given in the example.

Author

Soumyakanti Pan span18@ucla.edu

Examples

set.seed(1726)
n <- 500
s1 <- runif(n)
s2 <- runif(n)
t_coords <- runif(n)
x1 <- rnorm(n)
x2 <- rnorm(n)
z1 <- sin(2 * pi * s1 - pi * t_coords)
z2 <- cos(2 * pi * s2) * cos(pi * t_coords)
dat <- data.frame(
  s1 = s1, s2 = s2, t_coords = t_coords, x1 = x1, x2 = x2,
  y_gauss = rnorm(n, 2 + 5 * x1 - x2 + z1 + x1 * z2, sd = 0.5),
  y_pois = rpois(n, exp(2 - 0.5 * x1 + 0.3 * x2 + z1 + x1 * z2)),
  z1_true = z1, z2_true = z2
)
all.equal(dat, simSpaceTime)
#> [1] TRUE