fastFGEE - Fast Functional Generalized Estimating Equations via a One-Step Estimator

Fits functional generalized estimating equations for longitudinal functional outcomes and covariates using a one-step estimator that is fast even for large cluster sizes or large numbers of clusters. The package supports quasi-likelihoods derived from a range of distributions, with substantial simulations run for quasi-likelihoods derived from Gaussian, binomial, Poisson, negative binomial, Gamma and beta families. It supports common link functions and several working correlation structures. An optimized engine constructs cluster score and sensitivity statistics in one pass, provides coefficient-space Gaussian cross-validation, analytic-gradient fast cluster cross-validation, and an experimental sandwich-scaled working restricted quasi-likelihood selector. Internal compiled routines provide symmetric positive-definite Cholesky solves and exact tridiagonal precision operations for irregularly sampled continuous-time AR(1) working correlations. Uncertainty quantification is based on sandwich variance estimators and studentized wild cluster bootstrap procedures for cluster-robust pointwise intervals and optional simultaneous bands. The package implements methods described in Loewinger et al. (2025) <https://pmc.ncbi.nlm.nih.gov/articles/PMC12306803/>.