fastglm_hurdle: Hurdle (two-part) Poisson / Negative-Binomial regression

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

Hurdle (two-part) Poisson / Negative-Binomial regression

Description

Fits a hurdle model for count data with excess zeros: a binary (zero / non-zero) regression on the full sample combined with a zero- truncated count regression on the positive subset. The two parts have independent likelihoods and are estimated jointly. With 'dist = "negbin"' the negative-binomial dispersion 'theta' is estimated by an inner Brent-1D MLE inside the C++ driver, alternating with the count-side IRLS.

Usage

fastglm_hurdle(
  formula,
  data,
  subset,
  na.action,
  weights,
  offset,
  dist = c("poisson", "negbin"),
  zero.dist = "binomial",
  link = c("logit", "probit", "cloglog", "log"),
  init.theta = NULL,
  tol = 1e-08,
  maxit = 100L,
  outer.tol = 1e-07,
  outer.maxit = 50L,
  theta.tol = 1e-08,
  theta.maxit = 100L,
  model = TRUE,
  y = TRUE,
  x = FALSE
)

Arguments

formula	a [Formula::Formula] of the form 'y ~ x1 + x2 | z1 + z2' where the right-hand side after '|' specifies the zero-model design. If '|' is absent, the same RHS is used for both parts.
data	optional data frame / environment from which to draw model matrix variables.
subset, na.action	standard model-frame arguments.
weights	optional non-negative prior weights.
offset	optional vector or matrix. If a 2-column matrix, columns are taken as '(count_offset, zero_offset)'.
dist	count component distribution: '"poisson"' or '"negbin"'.
zero.dist	zero/non-zero distribution; only '"binomial"' is currently supported.
link	character, link for the zero/non-zero binomial. One of '"logit"' (default), '"probit"', '"cloglog"', '"log"'.
init.theta	optional positive scalar starting value for the NB dispersion. If 'NULL', a method-of-moments initializer is used.
tol, maxit	IRLS-loop convergence tolerance and iteration cap.
outer.tol, outer.maxit	'(beta, theta)' outer-loop convergence tolerance and iteration cap (only used when 'dist = "negbin"').
theta.tol, theta.maxit	Brent-loop tolerance / iteration cap for the inner theta MLE (only used when 'dist = "negbin"').
model	logical; keep the model frame on the result.
y, x	logical; keep the response / design matrices on the result.

Details

This is the fastglm analogue of [pscl::hurdle()] – coefficients agree to 1e-6 on standard datasets, with all numerical loops in C++.

Value

A list of class 'c("fastglm_hurdle", "fastglm")' with elements 'coefficients' (a list with 'count' and 'zero'), 'se' (likewise), 'vcov' (block-diagonal), 'loglik', 'loglik_count', 'loglik_zero', 'theta', 'SE.theta', 'iter_*', and 'converged'.

Examples

set.seed(1)
n <- 300
x1 <- rnorm(n); x2 <- rnorm(n)
eta_count <- 1.0 + 0.4*x1 - 0.2*x2
lam <- exp(eta_count)
y_count <- rpois(n, lam)
eta_zero  <- -0.5 + 0.6*x1
p_pos     <- plogis(eta_zero)
is_pos    <- rbinom(n, 1, p_pos)
# zero-truncated: resample any rare zero from positive Poisson
for (i in seq_len(n)) {
  while (y_count[i] == 0) y_count[i] <- rpois(1, lam[i])
}
y <- ifelse(is_pos == 1, y_count, 0)
df <- data.frame(y = y, x1 = x1, x2 = x2)
fit <- fastglm_hurdle(y ~ x1 + x2, data = df, dist = "poisson")
coef(fit, model = "count")
coef(fit, model = "zero")

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