Simulating Spatial Data in spmodel

Michael Dumelle, Matt Higham, and Jay M. Ver Hoef

Source: vignettes/articles/simulation.Rmd

Introduction

spmodel is an R package used to fit, summarize, and predict for a variety of spatial statistical models. This vignette explores sprnorm(), which simulates spatially correlated normal (Gaussian) random variables, along with its companions for simulating non-Gaussian spatial data. Before proceeding, we load spmodel and ggplot2 by running

If using spmodel in a formal publication or report, please cite it. Citing spmodel lets us devote more resources to it in the future. We view the spmodel citation by running

citation(package = "spmodel")
#> To cite spmodel in publications use:
#> 
#>   Dumelle M, Higham M, Ver Hoef JM (2023). spmodel: Spatial statistical
#>   modeling and prediction in R. PLOS ONE 18(3): e0282524.
#>   https://doi.org/10.1371/journal.pone.0282524
#> 
#> A BibTeX entry for LaTeX users is
#> 
#>   @Article{,
#>     title = {{spmodel}: Spatial statistical modeling and prediction in {R}},
#>     author = {Michael Dumelle and Matt Higham and Jay M. {Ver Hoef}},
#>     journal = {PLOS ONE},
#>     year = {2023},
#>     volume = {18},
#>     number = {3},
#>     pages = {1--32},
#>     doi = {10.1371/journal.pone.0282524},
#>     url = {https://doi.org/10.1371/journal.pone.0282524},
#>   }

Before proceeding, we set a reproducible seed:

Simulating Spatially Correlated Data

sprnorm() is spmodel’s spatial analogue to base-R’s rnorm() for simulating spatially correlated normal (i.e., Gaussian) data. sprnorm() requires an [spcov_params()] object that specifies the (known) spatial covariance parameters and a data argument with the locations to simulate at. We define an exponential spatial covariance with dependent variance (de) of 2, independent variance (ie) of 0.1, and range of 2, and simulate 3,000 locations completely at random on the unit square:

n <- 3000
sim_dat <- data.frame(xc = runif(n), yc = runif(n))

params <- spcov_params(
  spcov_type = "exponential",
  de = 2,
  ie = 0.1,
  range = 2
)

We simulate a single spatially correlated realization by running

sim_dat$val <- sprnorm(params, data = sim_dat, xcoord = xc, ycoord = yc)
ggplot(sim_dat, aes(x = xc, y = yc, color = val)) +
  geom_point(size = 1) +
  scale_color_viridis_c() +
  theme_bw(base_size = 14)

sprnorm() simulates data with mean zero by default; a non-constant mean can be supplied via the mean argument. Multiple independent realizations can be simulated at once via the samples argument, which returns a matrix (one column per sample) instead of a vector. Generating many samples via samples this way costs nearly the same (computationally) as generating a single sample, as the primary cost of factoring an \(n \times n\) covariance matrix occurs only once and is reused for each sample. For technical details regarding simulating data in spmodel, see the Technical Details vignette.

Simulating Non-Gaussian Data

spmodel also provides sprpois(), sprnbinom(), sprbinom(), sprbeta(), sprgamma(), and sprinvgauss() for simulating other spatially correlated random variables (Poisson, negative binomial, binomial, beta, gamma, and inverse Gaussian, respectively). Each works by first simulating a latent process with sprnorm() and then simulating the requested distribution conditional on that latent process.

We simulate a single spatially correlated realization of binomial data by running

n <- 3000
sim_dat <- data.frame(xc = runif(n), yc = runif(n))
sim_dat$val <- as.factor(sprbinom(params, data = sim_dat, xcoord = xc, ycoord = yc))
ggplot(sim_dat, aes(x = xc, y = yc, color = val)) +
  geom_point(size = 1) +
  scale_color_manual(values = c("blue", "orange")) +
  theme_bw(base_size = 14)

References