Unstructured covariance structure for mmer and vsr

Creates an unstructured variance-covariance component pattern for use by the mmer covariance-model interface, typically inside vsr.

Usage

usr(x)

Arguments

x

A factor, character vector, numeric vector, or design/incidence matrix defining the covariance dimension. Factor and character inputs are expanded to incidence columns. A matrix is used directly.

Details

usr() is part of the covariance-structure interface used by mmer/vsr; it is distinct from usm, which belongs to the newer mmes/vsm CovarianceFactor interface.

After constructing the design matrix \(Z\), the function calls unsm(q), where \(q\) is the number of columns of \(Z\), to create the thetaC pattern for an unstructured covariance matrix. Thus the associated covariance model permits a separate variance for every level and a separate covariance for every pair of levels: $$ \Sigma = \begin{bmatrix} \sigma_1^2 & \sigma_{12} & \cdots & \sigma_{1q}\\ \sigma_{12} & \sigma_2^2 & \cdots & \sigma_{2q}\\ \vdots & \vdots & \ddots & \vdots\\ \sigma_{1q} & \sigma_{2q} & \cdots & \sigma_q^2 \end{bmatrix}. $$ The exact component coding is stored in the matrix returned by unsm(q) and passed to the vsr machinery through thetaC.

For a factor or character vector, missing observations are retained through the construction of the incidence matrix. For a numeric non-factor input, x is treated as a single design column.

Value

A list with components:

• Z: the design/incidence matrix associated with the covariance dimension.

• thetaC: the unstructured covariance-component pattern produced by unsm().

See also

vsr, dsr, csr, atr, usm, mmer

Examples

# Unstructured covariance pattern across three levels
U <- usr(factor(c("A","B","A","C")))
U$Z
U$thetaC