fastglm_nb: Fit a negative-binomial GLM with simultaneous (beta, theta)...

In fastglm: Fast and Stable Fitting of Generalized Linear Models using 'RcppEigen'

Fit a negative-binomial GLM with simultaneous (beta, theta) MLE

Description

'fastglm_nb()' fits a negative-binomial regression model, jointly maximising the likelihood over the regression coefficients 'beta' and the NB2 dispersion 'theta'. It is the fastglm analogue of [MASS::glm.nb()], built on top of the native NB family kernel introduced in 0.0.6 so that all numerical loops – IRLS, the inner theta MLE Brent root-find, and the outer (beta, theta) alternation – run entirely in C++.

Usage

fastglm_nb(
  x,
  y,
  weights = NULL,
  offset = NULL,
  start = NULL,
  init.theta = NULL,
  link = c("log", "sqrt", "identity"),
  method = 2L,
  tol = 1e-08,
  maxit = 100L,
  outer.maxit = 50L,
  outer.tol = 1e-07,
  theta.tol = 1e-08,
  theta.maxit = 100L
)

Arguments

x	design matrix (numeric matrix, dgCMatrix not yet supported here).
y	non-negative integer response vector.
weights	optional prior weights vector of length 'length(y)'.
offset	optional offset vector of length 'length(y)'.
start	optional starting values for 'beta'.
init.theta	optional starting value for 'theta'. If 'NULL', uses the method-of-moments estimator from a Poisson pilot fit.
link	character, one of '"log"' (default), '"sqrt"', '"identity"'.
method	integer; '0..5', see [fastglm()].
tol	convergence tolerance for the IRLS inner loop.
maxit	maximum number of inner-loop IRLS iterations.
outer.maxit	maximum number of '(beta, theta)' outer iterations.
outer.tol	convergence tolerance for the outer loop on the sup-norm of the beta update plus the relative change in 'theta'.
theta.tol	Brent tolerance for the inner theta MLE.
theta.maxit	max iterations for the inner theta MLE.

Value

A list of class 'c("fastglm_nb", "fastglm")' with the usual fastglm components plus 'theta', 'SE.theta', 'iter.theta', and 'twologlik' (twice the maximized NB log-likelihood).

Examples

set.seed(1)
n <- 500
x <- cbind(1, matrix(rnorm(n * 2), n, 2))
eta <- x %*% c(0.3, 0.5, -0.2)
mu  <- exp(eta)
if (requireNamespace("MASS", quietly = TRUE)) {
  y   <- MASS::rnegbin(n, mu = mu, theta = 2)
  fit <- fastglm_nb(x, y)
  c(theta = fit$theta, fit$coefficients)
}

fastglm documentation built on Aug. 27, 2026, 9:07 a.m.