Proper conditional autoregressive spatial covariance structure

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

Usage

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

Arguments

x: Factor or design defining q spatial levels.
W: Symmetric nonnegative adjacency/weights matrix with zero diagonal, aligned to the levels of x.
rho: Starting proper-CAR dependence parameter.
fixed: Logical indicating whether rho is fixed.

Details

Let $D=\mathrm{diag}(W\mathbf{1})$. The proper CAR precision and covariance are $$Q=D-\rho W,\qquad M=Q^{-1},\qquad K=M/M_{11}.$$ The constructor requires positive row sums, so isolated levels are not allowed. The admissible open interval for rho is obtained from the eigenvalues of $D^{-1/2}WD^{-1/2}$ and is enforced through a bounded-logit working coordinate. This is a proper, nonsingular CAR model; an intrinsic singular CAR is not used by the current precision-based Henderson implementation. The covariance derivative is analytic.

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(car(location, W), ism(genotype))
} # }