Zero-inflated continuous parameter binomial regression

Fits the zero-inflated CPB. The model mixes a structural-zero process (a logistic model for the probability pi that a unit is a structural zero) with an untruncated CPB for the count, so a zero can arise either structurally or as a sampling zero from the CPB. Unlike hurdle_cpb(), the likelihood does not factorize, so the parameters are estimated by direct joint maximum likelihood, seeded from separate fits (a zero-truncated CPB on the positives and a logit of the zero indicator) and cross-checked against an expectation-maximization climb of the same observed-data likelihood, keeping the better optimum. An EM-only path (method = "em") is retained for comparison.

Usage

zi_cpb(
  formula,
  data,
  zero = NULL,
  fe = NULL,
  zero_fe = NULL,
  method = c("ml", "em"),
  se = c("none", "bootstrap"),
  B = 500,
  cluster = NULL,
  max.support = 500,
  maxit = 200,
  tol = 1e-06,
  offset = NULL,
  weights = NULL,
  cores = 1L
)

Arguments

formula: Intensity (count) model formula (y ~ x).
data: A data frame.
zero: Optional one-sided formula (~ z) for the zero-inflation model; defaults to the intensity model's right-hand side.
fe: Optional column name for unit fixed effects in the intensity (count) component. Under method = "ml" the unit effects enter as plug-in offsets from a first-stage fit; under method = "em" a classification (hard-assignment) step handles the structural zeros.
zero_fe: Optional column name for fixed effects in the zero-inflation equation, entered as factor dummies (opt-in).
method: Estimation method: "ml" (default) is robust direct joint maximum likelihood seeded from separate fits; "em" is expectation- maximization, retained for comparison but prone to a degenerate structural-zero-probability collapse under heavy zero-inflation.
se: Coefficient inference: "none" (default) or "bootstrap".
B: Bootstrap resamples when se = "bootstrap".
cluster: Optional cluster for the bootstrap (a column name or vector); under fixed effects the units are resampled by default. The mixture EM makes the bootstrap costly, so keep B modest.
max.support: Maximum support for the CPB pmf.
maxit: Optimizer iteration budget (scaled internally for the joint maximization; also the EM iteration cap under method = "em").
tol: Relative convergence tolerance on the observed-data log-likelihood.
offset: Optional exposure offset (log scale) for the count component: a numeric vector or the name of a column in data, making the count a rate model. Supported for method = "ml" without fe (the fixed-effects path's plug-in unit effects have no offset handling yet, and errors loudly). The bootstrap carries the offset through every replicate.
weights: Optional frequency weights (a numeric vector or a column name); see cpb(). Supported for method = "ml".
cores: Worker processes for the bootstrap; see cpb().

Value

An object of class "zi_cpb".

Details

The inflation equation uses a logit link. For a probit or cloglog inflation link, use zi_count() (Poisson/NB/COM-Poisson count), whose link argument covers the binary stage.

Examples

# \donttest{
set.seed(1)
n <- 800; x <- rnorm(n); z <- rnorm(n)
y <- rzicpb(n, lambda = exp(1.3 + 0.5 * x), alpha = 0.5, pi = plogis(-0.5 + 0.8 * z))
zi_cpb(y ~ x, data = data.frame(y = y, x = x, z = z), zero = ~ z)
#> Zero-Inflated Continuous Parameter Binomial
#> Call:  zi_cpb(formula = y ~ x, data = data.frame(y = y, x = x, z = z),     zero = ~z)
#> N: 800   EM iterations: 236   logLik: -1239.2
#> 
#> Intensity (CPB) coefficients:
#> (Intercept)           x 
#>      1.2967      0.5011 
#> Intensity alpha (shape): 0.5021 
#> 
#> Zero-inflation (logit link) -- positive coefficients raise P(structural zero), i.e. lower the
#> chance of a positive count (the opposite direction from a hurdle participation model):
#> (Intercept)           z 
#>     -0.3674      0.7065 
#> Mean structural-zero probability: 0.418 
# }