glmmFEL - Generalized Linear Mixed Models via Fully Exponential Laplace in
EM
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.