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, and the dummy logit's coefficients carry the incidental-parameters bias of order 1/T (in short panels the slopes are inflated, roughly toward twice their value at T = 2); the split-panel jackknife (bias_correct) corrects only the intensity. The hurdle's likelihood separates its two parts, so for the logit link a conditional logit on the same data (survival::clogit()) gives participation slopes free of that bias, and an analytical correction (the bife package, for the logit and the probit) reduces it to second order; the hurdle's predictions and quantities of interest use the dummy logit's unit effects. On King's support the dummy of a unit that never participates, at minus infinity, is not counted in the degrees of freedom (see compare_models(), Degrees of freedom). In new data (predict.hurdle_cpb(), score(), cv_score()) such a unit's rows get the participation probability at that limit, zero, and those of a unit whose every count is positive (part_one_units) one; a unit the fit has not seen, or every row of newdata without the part_fe column, enters at the reference unit of the units the data identify. The participation equation is checked for separation by zi_cpb()'s rule (Separation; component part_separation). On the floor support these dummies are counted in the degrees of freedom, new rows of these units are evaluated at the dummies' fitted values, and an unseen unit enters at the mean of all the unit dummies.
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). The participation equation's standard errors are then cluster-robust (the sandwich, with the G/(G - 1) factor), and with se = "bootstrap" the intensity's bootstrap resamples whole clusters; see cpb().
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(), including support (King's CPB, "ceiling", by default; see cpb()).

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 
#>      1.2862      0.5043 
#> Intensity alpha (shape): 0.5093