fastglm (version 0.1.0)

fastglm_nb: 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 = 25L,
  outer.tol = 1e-07,
  theta.tol = 1e-08,
  theta.maxit = 100L
)

Value

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

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.

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)
}