maternm: Matern spatial covariance structure

In sommer: Solving Mixed Model Equations in R

Matern spatial covariance structure

Description

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.

See Also

metricm, sar, car, vsm.

Examples

## Not run: 
vsm(maternm(cbind(xcoord,ycoord)), ism(genotype))
vsm(maternm(time), ism(id))

## End(Not run)

sommer documentation built on Oct. 24, 2026, 1:08 a.m.