Selected-level diagonal covariance structure for mmer and vsr

Creates a diagonal covariance-component selector for specified columns or levels of a covariance dimension. It is intended for the mmer covariance-model interface, typically inside vsr.

Usage

atr(x, levs)

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.

levs

Character vector identifying the columns or levels whose diagonal entries are selected. If omitted, all available column names are selected.

Details

atr() constructs a design matrix \(Z\) together with a diagonal thetaC selector. Let \(q\) be the number of columns of \(Z\), and define $$ a_j = \begin{cases} 1, & \text{if level }j\text{ is included in \code{levs}},\\ 0, & \text{otherwise}. \end{cases} $$ The returned constraint matrix is $$\mathrm{thetaC}=\mathrm{diag}(a_1,\ldots,a_q).$$

Thus atr() is useful when a covariance component is to be associated only with a specified subset of levels or design columns. Levels not selected in levs receive zero on the corresponding diagonal of thetaC.

This function belongs to the mmer/vsr covariance-structure interface. The related atm function belongs to the newer mmes/vsm CovarianceFactor interface and uses a different parameterization.

For a matrix input, its column names define the available levels. For factor or character input, the incidence-matrix column names define the levels. If levs is missing, all available columns are selected.

Value

A list with components:

• Z: the design/incidence representation of x.

• thetaC: a diagonal zero/one matrix selecting the levels specified by levs.

See also

vsr, dsr, usr, csr, atm, mmer

Examples

# Select levels B and C
A <- atr(factor(c("A","B","A","C")), levs = c("B","C"))
A$Z
A$thetaC