sar: Simultaneous autoregressive spatial covariance structure

In sommer: Solving Mixed Model Equations in R

Simultaneous autoregressive spatial covariance structure

Description

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

Usage

sar(x, W, rho = 0.10, fixed = FALSE)

Arguments

x	Factor or design defining q spatial levels.
W	Square spatial weights matrix aligned to the levels of x. Row/column names are used when available.
rho	Starting SAR dependence parameter.
fixed	Logical indicating whether rho is fixed.

Details

The simultaneous autoregressive covariance is constructed from

B=I-\rho W,\qquad M=B^{-1}B^{-\mathsf T},\qquad K=M/M_{11}.

For a general real weights matrix, rho is restricted to the conservative interval (-1/r(W),1/r(W)), where r(W) is the spectral radius. A bounded-logit working coordinate enforces the interval. The first covariance derivative is supplied analytically to the generic CovarianceFactor engine.

Value

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

See Also

car, maternm, vsm.

Examples

## Not run: 
vsm(sar(location, W), ism(genotype))

## End(Not run)

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