Hurdle continuous parameter binomial regression

Fits a participation (hurdle) model joined to a zero-truncated CPB for the positive counts. Because the hurdle log-likelihood factorizes, the two parts are fit separately: a logistic regression of participation on all units, and a zero-truncated CPB (cpb()) on the positive counts. The result is the natural model for a bounded, underdispersed participation process — most units at zero, participants carrying a tight count.

Usage

hurdle_cpb(
  formula,
  data,
  participation = NULL,
  fe = NULL,
  part_fe = NULL,
  link = c("logit", "probit", "cloglog"),
  offset = NULL,
  cluster = NULL,
  se = c("none", "bootstrap"),
  B = 500,
  weights = NULL,
  cores = 1L,
  ...
)

Arguments

formula: Intensity model formula (y ~ x).
data: A data frame.
participation: Optional one-sided formula (~ z) for the participation (hurdle) model; defaults to the intensity model's right-hand side.
fe: Optional column name for unit fixed effects in the intensity model, absorbed by a concentrated likelihood (cpb_fe()). This is how the within-unit underdispersion is recovered.
part_fe: Optional column name for fixed effects in the participation model (added as factors). Units with no within-unit variation in participation are uninformative for a fixed-effects logit.
link: Link for the participation model: "logit" (default), "probit", or "cloglog". Positive participation coefficients raise the probability of a positive count.
offset: Optional offset on the log-mean scale for the intensity (an exposure): a numeric vector or the name of a column in data.
cluster: Optional cluster identifier (a column name in data or a vector) for cluster-robust bootstrap inference on the intensity coefficients; see cpb(). Cluster-robust errors for the participation logit are available directly via sandwich::vcovCL(fit$participation, cluster = ...).
se: Inference for the intensity coefficients: "none" or "bootstrap".
B: Bootstrap replicates when se = "bootstrap".
weights: Optional frequency weights (a numeric vector or a column name), applied to both margins; see cpb().
cores: Worker processes for the intensity bootstrap; see cpb().
...: Passed to cpb() or cpb_fe().

Value

An object of class "hurdle_cpb" with elements participation (a glm), intensity (a cpb or cpb_fe), and bookkeeping.

Examples

set.seed(1)
n <- 800; x <- rnorm(n); z <- rnorm(n)
y <- rhurdle_cpb(n, lambda = exp(1.3 + 0.5 * x), alpha = 0.5,
                 p = plogis(-0.2 + 0.8 * z))
fit <- hurdle_cpb(y ~ x, data = data.frame(y = y, x = x, z = z),
                  participation = ~ z)
fit
#> Hurdle Continuous Parameter Binomial
#> Call:  hurdle_cpb(formula = y ~ x, data = data.frame(y = y, x = x, z = z),     participation = ~z)
#> Units: 800 (392 participate, 49%)
#> 
#> Participation (logit link) -- positive coefficients raise P(Y > 0), i.e. participation:
#> (Intercept)           z 
#>     -0.0437      0.7652 
#> 
#> Intensity (zero-truncated CPB) coefficients:
#> (Intercept)           x 
#>      1.2828      0.5023 
#> Intensity alpha (shape): 0.51