negbin: Negative binomial family with known dispersion

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

Negative binomial family with known dispersion

Description

A built-in negative-binomial family for use with [fastglm()] and [fastglmPure()] when 'theta' (the NB2 dispersion) is known. Equivalent to 'MASS::negative.binomial(theta, link)' but without taking a hard dependency on the **MASS** package. The variance is 'mu + mu^2 / theta'; as 'theta -> Inf' it reduces to Poisson.

Usage

negbin(theta, link = "log")

Arguments

theta	the (known) dispersion parameter; must be positive.
link	character; one of '"log"' (default), '"sqrt"', or '"identity"'.

Details

For joint estimation of 'theta' together with 'beta', use the dedicated (forthcoming) 'fastglm_nb()' entry point. The 'negbin()' family here is intended for use cases where 'theta' has been pre-specified or estimated separately.

Value

A 'family' object with class '"family"' and 'family$family == "Negative Binomial(theta)"'. The object also carries the slot 'family$theta', which 'family_code()' and the dispatch layer use to detect the native NB fast path.

Examples

set.seed(1)
n <- 500
x  <- cbind(1, matrix(rnorm(n * 2), n, 2))
mu <- exp(x %*% c(0.3, 0.4, -0.2))
y  <- rpois(n, lambda = mu * rgamma(n, shape = 2, rate = 2))   # NB(theta=2)

fit <- fastglm(x, y, family = negbin(theta = 2, link = "log"))
coef(fit)

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