Non-Randomized Version of the PIT Histogram (for Count Data)

See Czado et al. (2009).

Usage

pit(x, ...)
# Default S3 method
pit(x, pdistr, J = 10, relative = TRUE, ..., plot = list())

Arguments

x

numeric vector representing the observed counts.

pdistr

either a list of predictive cumulative distribution functions for the observations x, or (the name of) a single predictive CDF used for all x (with potentially varying arguments ...). It is checked that the predictive CDF returns 0 at x=-1. The name of its first argument can be different from x, e.g., pdistr="pnbinom" is possible.
If pdistr is a single function and no additional ... arguments are supplied, pdistr is assumed to be vectorized, i.e., it is simply called as pdistr(x) and pdistr(x-1). Otherwise, the predictive CDF is called sequentially and does not need to be vectorized.

J

the number of bins of the histogram.

relative

logical indicating if relative frequency or the density should be plotted. Due to a historical bug, relative=TRUE (the default) actually plots a density histogram while relative=FALSE plots relative frequencies.

...

ignored if pdistr is a list. Otherwise, such additional arguments are used in sequential calls of pdistr via mapply(pdistr, x, ...).

plot

a list of arguments for plot.histogram. Otherwise, no plot will be produced.

Value

an object of class "pit", which inherits from class "histogram" (see hist). It is returned invisibly if a plot is produced.

References

Czado, C., Gneiting, T. and Held, L. (2009): Predictive model assessment for count data. Biometrics, 65 (4), 1254-1261. doi:10.1111/j.1541-0420.2009.01191.x

Author

Michaela Paul and Sebastian Meyer

Examples

## Simulation example of Czado et al. (2009, Section 2.4)
set.seed(100)
x <- rnbinom(200, mu = 5, size = 2)
pdistrs <- list("NB(5,0)"   = function (x) ppois(x, lambda=5),
                "NB(5,1/2)" = function (x) pnbinom(x, mu=5, size=2),
                "NB(5,1)"   = function (x) pnbinom(x, mu=5, size=1))
## Reproduce Figure 1
op <- par(mfrow = c(1,3))
for (i in seq_along(pdistrs)) {
    pit(x, pdistr = pdistrs[[i]], J = 10,
        plot = list(ylim = c(0,2.75), main = names(pdistrs)[i]))
    box()
}
par(op)

## Alternative call using ... arguments for pdistr (less efficient)
stopifnot(identical(pit(x, "pnbinom", mu = 5, size = 2, plot = FALSE),
                    pit(x, pdistrs[[2]], plot = FALSE)))