glmmfe_trAB

Internal helper to compute $\mathrm{tr}(A B)$ without forming <code>A %*% B</code>:
$$\mathrm{tr}(A B) = \sum (A \circ B^\top).$$
This identity is used repeatedly in the fully exponential (FE) trace
corrections (Karl, Yang, and Lohr, 2014, Appendix B), where a naive
<code>diag(A %*% B)</code> would allocate the full product.

internal

Fit generalized linear mixed models (GLMMs) with normal random
effects using first-order Laplace, fully exponential Laplace (FEL) with
mean-only corrections, and FEL with mean and covariance corrections in
the E-step of an expectation-maximization (EM) algorithm. The current
development version provides a matrix-based interface (y, X, Z) and
supports binary logit and probit, and Poisson log-link models. An EM
framework is used to update fixed effects, random effects, and a single
variance component tau^2 for G = tau^2 I, with staged approximations
(Laplace -> FEL mean-only -> FEL full) for efficiency and stability. A
pseudo-likelihood engine glmmFEL_pl() implements the working-response /
working-weights linearization approach of Wolfinger and O'Connell (1993)
<doi:10.1080/00949659308811554>, and is adapted from the implementation
used in the 'RealVAMS' package (Broatch, Green, and Karl (2018))
<doi:10.32614/RJ-2018-033>. The FEL implementation follows Karl, Yang,
and Lohr (2014) <doi:10.1016/j.csda.2013.11.019> and related work (e.g.,
Tierney, Kass, and Kadane (1989) <doi:10.1080/01621459.1989.10478824>;
Rizopoulos, Verbeke, and Lesaffre (2009)
<doi:10.1111/j.1467-9868.2008.00704.x>; Steele (1996)
<doi:10.2307/2532845>). Package code was drafted with assistance from
generative AI tools.

Andrew T Karl

glmmFEL

Generalized Linear Mixed Models via Fully Exponential Laplace in
EM

Andrew T. Karl

glmmfe_trAB function

<dl><dt>A, B</dt>
<dd>Numeric matrices with identical dimensions.</dd></dl>

Arguments

Fast trace of a matrix product — glmmfe_trAB

<dl>

<dt>A, B</dt>
<dd>Numeric matrices with identical dimensions.</dd>

</dl>

glmmfe_trAB: Fast trace of a matrix product

Description

Usage

Value

Arguments