Held-out ceiling exceedance of a CPB fit

Whether counts respect the CPB's ceiling can be checked, but not in sample: its likelihood is minus infinity for any count above the bound, so every feasible fit respects the bound on the data it was fit to. The check is one-sided: it detects a ceiling that is too low, where held-out counts reach it, and has no power against one that is too high (a fitted ceiling above a true bound is never exceeded), nor where counts stay well below the ceiling (see implied_ceiling()). ceiling_exceedance() takes held-out observations and reports how many of their counts exceed the largest count the fitted model allows at their covariates (max_count of implied_ceiling()); for a two-part model the bound is the count component's, and a fixed-effects unit seen in training enters at its own effect (an unseen one at the mean effect), as in score(). A breached ceiling also zeroes the held-out likelihood, which score() records with its 1e-12 floor.

Usage

ceiling_exceedance(fit, newdata, weights = NULL, offset = NULL)

Arguments

fit

A "cpb", "cpb_fe", "hurdle_cpb", or "zi_cpb" object.

newdata

Held-out observations, including the response.

weights

Optional frequency weights for the rows of newdata: a column name of newdata or a numeric vector with one value per row.

offset

Optional offset (log scale) of the count for the newdata rows; by default a fit made with an offset reads it from the same column of newdata (see predict.cpb()).

Value

A one-row data frame with n (held-out rows, weighted), exceed (rows above the bound, weighted), and share.

See also

implied_ceiling(), score()

Examples

set.seed(7); x <- rnorm(400); y <- rcpb(400, exp(1.4 + 0.3 * x), 0.5)
d <- data.frame(y = y, x = x)
fit <- cpb(y ~ x, d[1:300, ], truncated = FALSE, se = "none")
ceiling_exceedance(fit, d[301:400, ])
#>     n exceed share
#> 1 100      0     0