rxOmegaVarCovDeriv: Variance-covariance (non-Cholesky) Omega parameterization...

In rxode2: Facilities for Simulating from ODE-Based Models

Variance-covariance (non-Cholesky) Omega parameterization derivatives

Description

A non-Cholesky Omega path that differentiates with respect to the variance-covariance entries directly (for reporting SEs on the natural scale or building an analytic covariance over the Omega elements). Returns Omega^{-1}, ⁠log|Omega|⁠, and their first (and optionally second) derivatives with respect to each free lower-triangular element ⁠omega_{ab}⁠, via

Usage

rxOmegaVarCovDeriv(omega, order = 2L)

Arguments

omega	symmetric positive-definite random-effects covariance matrix.
order	integer; 1 for first derivatives only, 2 (default) to also return the second derivatives needed for the covariance Hessian.

Details

\partial \Omega^{-1}/\partial \omega_{ab} = -\Omega^{-1} E_{ab} \Omega^{-1}

\partial \log|\Omega|/\partial \omega_{ab} = \mathrm{tr}(\Omega^{-1} E_{ab})

where E_{ab} is the symmetric single-entry basis matrix.

Value

a list with omegaInv, logDet, the free-element index matrix elements (each row c(a, b), a >= b), first derivatives dOmegaInv / dLogDet, and (when order = 2) second derivatives d2OmegaInv / d2LogDet.

Author(s)

Hidde van de Beek

rxode2 documentation built on July 28, 2026, 5:08 p.m.