Zero-inflated GEC (Katz-family) regression

A structural-zero mixture with a GEC count component whose dispersion delta is estimated freely. Estimated by direct maximum likelihood from several starts, as in zi_cpb(): the single-equation GEC with a logit of the zero indicator for the inflation, at four dispersions; the zero-inflated Poisson's coefficients; and a low-inflation start. The best is polished, which avoids the degenerate pi -> 0 basin that coordinate-wise EM falls into.

Usage

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

Arguments

formula: Count formula, y ~ x.
data: A data frame.
zero: One-sided formula for the structural-zero logit; defaults to the count formula's right-hand side.
zero_fe: Optional column name for fixed effects in the zero-inflation equation, entered as factor dummies (opt-in). The dummy of a unit with no positive count is not counted in the degrees of freedom (see compare_models(), Degrees of freedom); in new data such a unit gets the structural-zero probability one, and one whose every count is positive zero.
se: Coefficient inference: "none" (default) or "bootstrap".
B: Bootstrap resamples.
cluster: Optional cluster (column name or vector) for the bootstrap.
max.support: Guard on the evaluated support of the count component; NULL (default) sets max(500, 10 * max(y)). See gec().
maxit, tol: Optimizer controls.
offset: Optional exposure offset (log scale) for the count component: a numeric vector or the name of a column in data; the bootstrap carries it through every replicate.
weights: Optional frequency weights (a numeric vector or a column name); see cpb().
cores: Worker processes for the bootstrap; see cpb().

Value

An object of class "zi_gec".

Separation

The fit checks its zero-inflation equation for separation as zi_cpb() does (see its Separation section). It warns when the data put no useful bound on a covariate coefficient, and stores the check in the component separation.

Examples

# \donttest{
set.seed(4); n <- 300; x <- rnorm(n); z <- rnorm(n)
y <- ifelse(rbinom(n, 1, plogis(-0.5 + 0.8 * z)) == 1, 0L, rpois(n, exp(1 + 0.3 * x)))
zi_gec(y ~ x, data.frame(y = y, x = x, z = z), zero = ~ z)
#> Zero-Inflated Generalized Event Count (Katz family)
#> Call:  zi_gec(formula = y ~ x, data = data.frame(y = y, x = x, z = z),     zero = ~z)
#> N: 300   logLik: -494.3
#> 
#> Count (GEC) coefficients:
#> (Intercept)           x 
#>      1.0339      0.2552 
#> Count dispersion delta: 0.914  [underdispersed (point estimate)]
#> 
#> 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 
#>     -0.5617      0.8045 
#> Mean structural-zero probability: 0.371 
# }