cmod_std function

Standard covariance models for geostatistical data.

Creates a standard covariance model (cmodStd) object for geostatistical data.

cmod_std(
  model,
  psill,
  r,
  evar = 0,
  fvar = 0,
  par3 = 0.5,
  longlat = FALSE,
  angle = 0,
  ratio = 1,
  radians = FALSE,
  invert = TRUE
)

Arguments

• model: A covariance model (e.g., "exponential"). See Details for the complete list of choices.
• psill: The partial sill of the model. Must be a positive number.
• r: The range parameter r. Must be a positive number.
• evar: The variance of the errors. Must be non-negative number. The default is 0.
• fvar: The finescale variance (microscale error). Must be a non-negative number. The default is 0.
• par3: The value of the third parameter for 3 parameter models. Must be a positive number. The default is 0.5.
• longlat: A logical value indicating whether great circle distance should be used. The default is FALSE.
• angle: The major axis of geometric anisotropy (the direction of strongest spatial dependence). Must be between [0, 180) if radians = FALSE, otherwise it must be between [0, $\pi$).
• ratio: The ratio of the minor axis range over the major axis range. The value must be between (0, 1].
• radians: A logical value indicating whether the angles returned should be in degrees or radians. The default is FALSE, indicating that the returned angles are in degrees.
• invert: A logical value indicating whether the axes of the coordinates should be inverted (i.e., the x- and y-axis are switched). The default is TRUE to mimic results from other geostatistical R packages like gstat, geoR, and other software like GSLIB and GeoEAS. Set to FALSE to use the typical x- and y-axes.

Returns

Returns a cmodStd object.

Details

The general, isotropic form of the specified covariance function is psill * $\rho$(d; r) + (evar + fvar) * (d == 0), where $\rho$ is the correlation function of the parametric models and d is the distance between the relevant coordinates.

For the exponential model, $\rho$(d; r) is exp(-d/r).

For the gaussian model, $\rho$(d; r) is exp(-d^2/r^2).

For the matern model, $\rho$(d; r) is 2^(1-par3)/gamma(par3)sd^par3besselK(sd, nu = par3), where sd = d/r.

For the amatern (alternative Matern) model, $\rho$(d; r) is 2^(1-par3)/gamma(par3)*sd^par3*besselK(sd, nu = par3), where sd = 2 * sqrt(par3) * d/r.

For the spherical model, $\rho$(d; r) is 1 - 1.5*sd + 0.5*(sd)^3 if d < r, and 0 otherwise, with sd = d/r.

For the wendland1 model, $\rho$(d; r) is (1 - sd)^4 * (4*sd + 1) if d < r, and 0 otherwise, with sd = d/r.

For the wendland2 model, $\rho$(d; r) is (1 - sd)^6 * (35*sd^2 + 18*sd + 3))/3

if d < r, and 0 otherwise, with sd = d/r.

For the wu1 model, $\rho$(d; r) is (1 - sd)^3 * (1 + 3*sd + sd^2) if d < r, and 0 otherwise, with sd = d/r.

For the wu2 model, $\rho$(d; r) is (1 - sd)^4*(4 + 16*sd + 12*sd^2 + 3*sd^3))/4 if d < r, and 0 otherwise, with sd = d/r.

For the wu3 model, $\rho$(d; r) is (1 - sd)^6 * (1 + 6*sd + 41/3*sd^2 + 12*sd^3 + 5*sd^4 + 5/6*sd^5) if d < r, and 0 otherwise, with sd = d/r.

Examples

cmod_std(model = "exponential", psill = 1, r = 1)

References

Waller, L. A., & Gotway, C. A. (2004). Applied Spatial Statistics for Public Health Data. John Wiley & Sons.

Author(s)

Joshua French