First difference for a CPB fit — first

The effect on a quantity of interest of moving one covariate from one value to another, holding the other covariates at their means (or at the values at gives them).

Usage

first_difference(object, ...)

# S3 method for class 'cpb'
first_difference(
  object,
  variable,
  from,
  to,
  quantity = c("mean", "ceiling", "prob"),
  y = NULL,
  level = 0.95,
  at = NULL,
  ...
)

Arguments

object: A "cpb" object. With se = "bootstrap" at fit time the difference carries a bootstrap percentile interval; otherwise the point estimate is returned with method = "none".
...: Further arguments passed to methods; unknown arguments error.
variable: Name of a model-matrix column to vary.
from, to: The two values of variable to contrast.
quantity: "mean" (E(Y); for a zero-truncated fit the conditional mean E(Y | Y >= 1)), "ceiling" (lambda/(1-alpha)), or "prob" (P(Y = y)).
y: The count value for quantity = "prob".
level: Confidence level (default 0.95).
at: Optional named numeric vector fixing other model-matrix columns at given values instead of their means, e.g. at = c(z = 1, regionB = 0) (a factor's dummies are columns, so a reference level sets them to 0).

Value

A "ud_fd" data frame – the package-wide first-difference contract (columns component, from, to, diff, lower, upper, method) – with one row for the requested quantity and a bootstrap percentile interval on the difference (method = "bootstrap (stored)"). Every first_difference() method in the package returns this same shape.

Details

Every first_difference() method in the package takes its interval by one rule. When the fit carries bootstrap draws (se = "bootstrap" at fit time), the quantity is computed at every draw, jointly over the coefficients and the dispersion parameter (and, for a fixed-effects fit, the reference unit's effect), and the percentile interval is taken; the draws of a fixed-effects fit are first recentered on the reported estimate, because its replicates share the incidental-parameters bias. Otherwise the interval is the delta method's over the fit's full covariance, the dispersion parameter included (the matched count families' analytic, robust or clustered covariance; a hurdle's two margins, which are independent). A fit with neither gets the point estimate with method = "none".

Examples

# \donttest{
set.seed(1); x <- rnorm(250)
N <- pmax(round(exp(1.6 + 0.5 * x) / 0.5), 1); y <- rbinom(250, N, 0.5)
fit <- cpb(y ~ x, data = data.frame(y = y, x = x)[y > 0, ], se = "bootstrap", B = 100)
first_difference(fit, "x", from = -1, to = 1, quantity = "mean")
#>  component  from    to  diff lower upper             method
#>       mean 3.069 8.394 5.325 5.006 5.615 bootstrap (stored)
# }