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Generalized event count (Katz-family) regression

Source: R/gec.R
gec.Rd

Fits King's generalized event count model, a Katz-family count regression whose single dispersion parameter delta (the variance-to-mean ratio) is estimated freely and spans underdispersion (delta < 1, a finite-support member; the continuous parameter binomial is this cell), equidispersion (delta = 1, Poisson), and overdispersion (delta > 1, the negative binomial). Unlike cpb(), which fixes the direction of dispersion to under, gec() lets the data choose. The Katz recursion delivers exact first and second moments—the Winkelmann–Signorino–King correction realized directly on an unbounded support—and the likelihood is evaluated in C++. For delta < 1 the support is finite and the renormalized distribution's mean and variance equal exp(x'b) and delta * exp(x'b) only when exp(x'b)/(1 - delta) is an integer, so exp(x'b) is the rate parameter of the recursion, the fitted mean is computed exactly from the pmf, and delta is the Katz dispersion parameter (the variance-to-mean ratio on an unbounded support). The optimizer works on covariates scaled to unit standard deviation and maps the coefficients back, so the fit does not depend on the covariates' units.

Usage

gec(
  formula,
  data,
  truncated = FALSE,
  se = c("none", "bootstrap"),
  B = 500,
  cluster = NULL,
  offset = NULL,
  weights = NULL,
  cores = 1L,
  max.support = 500,
  maxit = 20000,
  reltol = 1e-08
)

Arguments

formula

A model formula.

data

A data frame.

truncated

Logical; if TRUE, fit the zero-truncated GEC (all Y >= 1), the intensity model of hurdle_gec().

se

Coefficient inference: "none" (default; fast) or "bootstrap".

B

Bootstrap resamples when se = "bootstrap".

cluster

Optional cluster identifier (a column name in data or a vector) for a cluster/block bootstrap; see cpb().

offset

Optional offset on the log-mean scale (an exposure): a numeric vector or the name of a column in data.

weights

Optional frequency weights (a numeric vector or a column name); see cpb().

cores

Worker processes for the bootstrap; see cpb().

max.support

Guard on the maximum evaluated support.

maxit, reltol

Optimizer controls.

Value

An object of class "gec" with coefficients, delta (the estimated dispersion), loglik, bootstrap standard errors, and bookkeeping.

See also

cpb(), compare_dispersion(), dispersion_test()

Examples

set.seed(1); x <- rnorm(400)
y <- rpois(400, exp(1 + 0.5 * x))
gec(y ~ x, data = data.frame(y = y, x = x), se = "none")
#> Generalized event count (Katz family) regression
#> Call:  gec(formula = y ~ x, data = data.frame(y = y, x = x), se = "none")
#> (Intercept)           x 
#>      0.9760      0.4751 
#> 
#> dispersion delta (Katz; Var/Mean on an unbounded support) = 1.131  [equidispersion not rejected (LR p = 0.07)]
#> logLik = -764.34,  n = 400