Matern spatial covariance structure

Matern spatial covariance structure. The returned dimensionless covariance shape is intended for use inside vsm, which supplies the single overall variance scale.

Usage

maternm(x, range = NULL, nu = 0.5, fixed = c(FALSE, FALSE),
        distance = NULL, anisotropy = c("none", "geometric"),
        angle = pi/2, ratio = 1.5)

Arguments

x: Numeric coordinate vector or matrix/data frame whose rows give spatial coordinates.
range: Positive starting range parameter. If NULL, the median positive pairwise distance is used.
nu: Positive starting Matern smoothness parameter.
fixed: Logical of length one or two (range, nu), or four with geometric anisotropy (range, nu, angle, ratio); length one is recycled.
distance: Optional finite symmetric q by q distance matrix with zero diagonal, aligned to the unique spatial locations.
anisotropy: "geometric" rotates two-dimensional coordinates by angle and divides the second rotated axis by ratio before computing distances (ASReml anisotropic Matern).
angle: Starting anisotropy angle in (0, pi).
ratio: Starting positive anisotropy ratio.

Details

For distance $d$, the correlation is $$K(d)=\frac{2^{1-\nu}}{\Gamma(\nu)}z^{\nu}K_{\nu}(z),\qquad z=\frac{\sqrt{2\nu}d}{\phi},$$ where $\phi$ is range. Both range and smoothness are positive and are optimized on log scales. The implementation uses the generic R evaluator and central factor-level numerical derivatives. Repeated coordinate rows are mapped to the same covariance level.

Value

A list containing the incidence/design matrix in Z and a compiled CovarianceFactor v2 descriptor in covFactor, for use inside vsm.

Examples

if (FALSE) { # \dontrun{
vsm(maternm(cbind(xcoord,ycoord)), ism(genotype))
vsm(maternm(time), ism(id))
} # }