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Solve the practical range of a Matérn covariance function

Source: R/matern_helpers.R
solve_practical_range.Rd

Harmonizes spatial range parameters from different R packages (INLA, geoR, spatstat) into a standardized "Practical Range". This is the distance at which the spatial correlation drops to a specific threshold (default is 0.10).

Usage

solve_practical_range(
  param_val,
  nu,
  thresh = 0.1,
  engine = c("inla", "geor", "spatstat")
)

Arguments

param_val

Numeric. The parameter value from the model (\(\rho\) for INLA, \(\phi\) for geoR, or \(\alpha\) for spatstat). It must be positive.

nu

Numeric. The smoothness parameter. It must be positive. For 2D SPDE models in INLA (where alpha = 2), the default is nu = 1. For an exponential covariance, use nu = 0.5.

thresh

Numeric. The target correlation threshold. Defaults to 0.1 (10%).

engine

Character. One of "inla", "geor", or "spatstat".

Value

A numeric value representing the practical range in the same geographic units as the input model parameter.

Details

Different packages use different parameterisations for the Matérn covariance:

  • INLA/inlabru: Estimates a value close to the INLA range parameter (where correlation is ~ 0.139). If thresh = 0.139, the input param_val is returned almost as is. If a 5% threshold (thresh = 0.05) is desired, the function adjusts the INLA range accordingly.

  • geoR: Uses a scale parameter \(\phi\). The practical range is solved numerically based on \(\phi\) and the smoothness \(\nu\).

  • spatstat: Uses a scale parameter \(\alpha\). The function aligns this with the INLA-style practical range.

This harmonization ensures that the rho value used in isdmtools diagnostic functions is consistent, regardless of the modeling engine used for the exploratory analysis.

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, Assogbadjo E, Glèlè Kakaï R. 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

See also

Other Matern covariance helpers: plot.std_matern_corr(), std_matern_corr()

Examples

# Estimated phi = 10 km with exponential covariance in `geoR`
solve_practical_range(param_val = 10, nu = 0.5, thresh = 0.1, engine = "geor")
#> [1] 23.02585

# Estimated alpha = 13.10 km with Matérn covariance in `spatstat`
solve_practical_range(param_val = 13.10, nu = 1.5, thresh = 0.1, engine = "spatstat")
#> [1] 29.41908