Standardise Matern covariance parameters and compute the pairwise correlation from LGCP models

Standardizes Matern covariance parameters across different modeling engines (INLA, spatstat, variofit) and computes the pairwise correlation function for log-Gaussian Cox process (LGCP) models.

Usage

std_matern_corr(model, engine = c("kppm", "inla", "variofit"), r, nu = 1, ...)

Arguments

model: The fitted model object from INLA, spatstat, or geoR
engine: Character string specifying the modeling engine utilised to estimate the covariance parameters: "inla", "kppm", or "variofit".
r: A numeric vector of distances at which to evaluate the covariance function.
nu: The smoothing parameter of the process (it is \(\kappa\) in geoR).
...: Additional arguments to pass on to internal function.

Value

An object of class std_matern_corr (list) containing:

dist_vals: The vector of distances (\(r\)) used for computation.
cov: The computed Matern covariance: \(C(r)\).
sigma2: The standardized marginal variance (\(\sigma^2\)).
rho: The standardized scale parameter (range).
nu: The smoothness parameter.
engine: The original modeling engine used.

For "inla" or "kppm" modeling engines, two additional elements are included:

pair_cor: The pairwise correlation function (PCF) for LGCP, calculated as \(g(r) = \exp(C(r))\).
pair_cor_sc: The standardized pairwise correlation function for cross-model comparison.

Details

The function standardizes Matern covariance parameters and derives the pairwise correlation function across different modeling engines for LGCP models. The engines currently supported include those implemented in INLA/inlabru (and related wrappers), spatstat, and geoR.

Note that the variofit class is included to derive the range and sigma2 parameters for comparison purposes; however, the exponential of the resulting covariance has no interpretation in terms of pairwise correlation. The same applies to covariance functions fitted to geostatistical data in INLA/inlabru, which cannot be interpreted in terms of pairwise correlation.

To facilitate visual comparison across different modeling engines, a scaled version of the pairwise correlation function (pair_cor_sc) is provided. This version applies a min-max normalization to the pairwise correlation, mapping its values to a standardized range (typically [0, 1]). This ensures that the spatial decay and interaction strength can be compared even when models have different marginal variances or measurement scales.

References

Baddeley A, Rubak E, Turner R. Spatial point patterns: Methodology and applications with R. Boca Raton, FL: CHAPMAN & HALL CRC. (2015).
Diggle PJ, Ribeiro PJ. Model-based Geostatistics. 1st ed. New York, NY: Springer. (2007). doi:10.1007/978-0-387-48536-2
Lindgren F, Rue H, Lindström J. An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology) (2011) 73:423–498. doi:10.1111/j.1467-9868.2011.00777.x
Sode AI, Fandohan AB, Krainski ET, et al. Integrating Presence-only and Abundance Data to Predict Baobab (Adansonia digitata L.) Distribution: A Bayesian Data Fusion Framework". doi:10.21203/rs.3.rs-7871875/v1

Examples

if (FALSE) { # \dontrun{
# Example with an INLA model
r_vec <- seq(0, 10, length.out = 100)
matern_results <- std_matern_corr(
  model = fit_inla,
  engine = "inla",
  r = r_vec,
  nu = 1
)

# Access the pair correlation function for LGCP
plot(matern_results$dist_vals, matern_results$cor,
  type = "l",
  ylab = "PCF", xlab = "Distance"
)
} # }