build_kronecker_precision: Build the Kronecker-structured random-effect precision matrix

In cevcmm: Communication-Efficient Varying Coefficient Mixed-Effects Models

Build the Kronecker-structured random-effect precision matrix

Description

For \Sigma_\alpha = \Sigma_{\mathrm{left}} \otimes \Sigma_{\mathrm{right}} (column-stacking convention), returns

\sigma_\varepsilon^2 \cdot (\Sigma_{\mathrm{left}}^{-1} \otimes \Sigma_{\mathrm{right}}^{-1})

which is added to crossprod(Z) inside the random-effect block of the VCMM Hessian. This is the structured analogue of (sigma_eps^2 / sigma_alpha^2) * I_q used under re_cov = "diag".

Usage

build_kronecker_precision(Sigma_left, Sigma_right, sigma_eps)

Arguments

Sigma_left	A k \times k positive-definite numeric matrix (k = 2 for OD-style; arbitrary k for general separable).
Sigma_right	A G \times G positive-definite numeric matrix.
sigma_eps	Positive numeric. Residual standard deviation.

Value

A kG \times kG numeric matrix.

References

Jalili, L. and Lin, L.-H. (2025). Scalable and Communication-Efficient Varying Coefficient Mixed-Effects Models.

cevcmm documentation built on July 24, 2026, 5:07 p.m.