toeplitzm: General positive-definite Toeplitz correlation structure

In sommer: Solving Mixed Model Equations in R

General positive-definite Toeplitz correlation structure

Description

General positive-definite Toeplitz correlation structure. The returned dimensionless covariance shape is intended for use inside vsm, which supplies the single overall variance scale.

Usage

toeplitzm(x, pacf = NULL, fixed = NULL)

Arguments

x	Ordered factor or design defining q covariance levels.
pacf	Optional q-1 starting reflection coefficients / partial autocorrelations. Defaults to 0.10.
fixed	Logical vector of length q-1.

Details

A full q by q Toeplitz correlation matrix is parameterized by q-1 reflection coefficients. Each PACF is mapped from an unconstrained working coordinate with tanh; the reflection coefficients are converted to a stable autoregressive representation and then to the implied Toeplitz correlation sequence. This parameterization preserves positive definiteness while allowing every lag correlation to vary indirectly.

Value

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

See Also

ar1m, ar2m, ar3m, mam, vsm.

Examples

## Not run: 
vsm(toeplitzm(time), ism(id))

## End(Not run)

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