fastglm_zi: Zero-inflated Poisson / Negative-Binomial regression

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

Zero-inflated Poisson / Negative-Binomial regression

Description

Fits a zero-inflated count model: a binary inflation component combined with a Poisson or NB count component, where the count component is the *original* (non-truncated) distribution. Excess zeros above what the count model implies are absorbed by the inflation component.

Usage

fastglm_zi(
  formula,
  data,
  subset,
  na.action,
  weights,
  offset,
  dist = c("poisson", "negbin"),
  link = c("logit", "probit", "cloglog", "log"),
  init.theta = NULL,
  em.tol = 1e-08,
  em.maxit = 100L,
  tol = 1e-09,
  maxit = 100L,
  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 inflation design. If '|' is absent, the same RHS is used for both parts.
data	optional data frame / environment.
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"'.
link	character, link for the inflation 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 pilot is used.
em.tol, em.maxit	EM convergence tolerance and iteration cap.
tol, maxit	IRLS-loop convergence tolerance and iteration cap (used inside each M-step).
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

Estimation uses an EM algorithm with all numerical loops in C++. The E-step computes the posterior 'tau_i = P(Z_i = 1 | y_i)' analytically; M-steps fit the inflation logit/probit/cloglog/log and the Poisson/NB count regression via the existing native fastglm IRLS (with weights 'w_i (1 - tau_i)' on the count side). For NB, an inner Brent MLE re-estimates 'theta' after the count-side beta step. Final vcov comes from the numerical Jacobian of the analytical observed score at the EM fixed point (block-structured for '(gamma, beta, theta)').

This is the fastglm analogue of [pscl::zeroinfl()] – coefficients agree to 1e-5 on standard datasets (slightly looser than hurdle to allow for the EM iteration), with all numerical loops in C++.

Value

A list of class 'c("fastglm_zi", "fastglm")' with elements 'coefficients' (a list with 'count' and 'zero'), 'se' (likewise), 'vcov' (full, including theta if NB), 'loglik', 'theta', 'SE.theta', 'tau' (posterior P(Z=1|y)), 'em_iter', 'converged'.

Examples

set.seed(1)
n <- 400
x  <- rnorm(n)
eta_count <- 0.8 + 0.4*x
lam <- exp(eta_count)
eta_zero <- -0.6 + 0.5*x
p_inflate <- plogis(eta_zero)
z <- rbinom(n, 1, p_inflate)
y <- ifelse(z == 1, 0, rpois(n, lam))
df <- data.frame(y = y, x = x)
fit <- fastglm_zi(y ~ x, data = df, dist = "poisson")
coef(fit, model = "count")
coef(fit, model = "zero")

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