Zero-inflated count regression for the matched count families

Fits a structural-zero mixture whose count component comes from any of the package's count families (see count_reg(), Families), the count analogue of zi_cpb(). The count component uses a log link (on the mean for the mean-parameterized families, on the rate $\lambda$ for "compois") and the inflation probability a link set by link. Returned as a "zi_count" object that compare_models() and score() accept.

Usage

zi_count(
  formula,
  data,
  family = c("poisson", "negbin", "compois", "mpcmp", "genpois", "gammacount",
    "doublepois", "hyperpois", "ewp3", "ewp2"),
  zero = NULL,
  fe = NULL,
  zero_fe = NULL,
  link = c("logit", "probit", "cloglog"),
  offset = NULL,
  weights = NULL,
  se = c("analytic", "robust", "cluster", "none"),
  cluster = NULL
)

Arguments

formula: Count formula (y ~ x).
data: A data frame.
family: The count-component family; see count_reg().
zero: Optional one-sided formula for the inflation (structural-zero) model; defaults to the count right-hand side.
fe: Optional fixed-effects column for the count equation (factor dummies).
zero_fe: Optional fixed-effects column for the inflation equation (factor dummies); zero-equation fixed effects are opt-in. In either equation 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 (with one column each) such a unit gets the structural-zero probability one through zero_fe and a count mean of zero through fe, and a unit whose every count is positive the structural-zero probability zero.
link: Link for the inflation probability: "logit" (default), "probit", or "cloglog". Positive inflation coefficients raise the probability of a structural zero.
offset: Optional offset for the count component, on the linear-predictor (log) scale: a numeric vector or the name of a column in data.
weights: Optional frequency weights (a numeric vector or a column name); see count_reg().
se, cluster: Standard-error type and optional cluster; see count_reg().

Value

An object of class "zi_count"; $fitted.values is the marginal mean (1 - pi) E(Y | count component) that fitted() returns, and $mu the count component's natural parameter.

Separation

The fit checks its zero-inflation equation for separation as zi_cpb() does (see its Separation section), under its own link. It warns when the data put no useful bound on a covariate coefficient, and stores the check in the component separation. Such a coefficient's standard error is not meaningful either.

Examples

set.seed(2); 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_count(y ~ x, data.frame(y = y, x = x, z = z), family = "poisson",
         zero = ~ z, se = "none")
#> Zero-inflated Poisson regression
#> Call:  zi_count(formula = y ~ x, data = data.frame(y = y, x = x, z = z),     family = "poisson", zero = ~z, se = "none")
#> 
#> Count coefficients:
#> (Intercept)           x 
#>      1.0605      0.2989 
#> 
#> 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 
#>     -0.4266      0.5040