neg_bin_pi: Prediction intervals for negative-binomial data

In predint: Prediction Intervals

Prediction intervals for negative-binomial data

Description

neg_bin_pi() calculates bootstrap calibrated prediction intervals for negative-binomial data.

Usage

neg_bin_pi(
  histdat,
  newdat = NULL,
  newoffset = NULL,
  alternative = "both",
  alpha = 0.05,
  nboot = 10000,
  delta_min = 0.01,
  delta_max = 10,
  tolerance = 0.001,
  traceplot = TRUE,
  n_bisec = 30,
  algorithm = "MS22mod"
)

Arguments

histdat	a data.frame with two columns. The first has to contain the historical observations. The second has to contain the number of experimental units per study (offsets).
newdat	data.frame with two columns. The first has to contain the future observations. The second has to contain the number of experimental units per study (offsets).
newoffset	vector with future number of experimental units per historical study.
alternative	either "both", "upper" or "lower". alternative specifies if a prediction interval or an upper or a lower prediction limit should be computed
alpha	defines the level of confidence (1-\alpha)
nboot	number of bootstraps
delta_min	lower start value for bisection
delta_max	upper start value for bisection
tolerance	tolerance for the coverage probability in the bisection
traceplot	if TRUE: Plot for visualization of the bisection process
n_bisec	maximal number of bisection steps
algorithm	either "MS22" or "MS22mod" (see details)

Details

This function returns bootstrap-calibrated prediction intervals as well as lower or upper prediction limits.

If algorithm is set to "MS22", both limits of the prediction interval are calibrated simultaneously using the algorithm described in Menssen and Schaarschmidt (2022), section 3.2.4. The calibrated prediction interval is given as

[l,u]_m = n^*_m \hat{\lambda} \pm q \sqrt{n^*_m \frac{\hat{\lambda} + \hat{\kappa} \bar{n} \hat{\lambda}}{\bar{n} H} + (n^*_m \hat{\lambda} + \hat{\kappa} n^{*2}_m \hat{\lambda}^2) }

with n^*_m as the number of experimental units in the future clusters, \hat{\lambda} as the estimate for the Poisson mean obtained from the historical data, \hat{\kappa} as the estimate for the dispersion parameter, n_h as the number of experimental units per historical cluster and \bar{n}=\sum_h^{n_h} n_h / H.

If algorithm is set to "MS22mod", both limits of the prediction interval are calibrated independently from each other. The resulting prediction interval is given by

[l,u] = \Big[n^*_m \hat{\lambda} - q^{calib}_l \sqrt{n^*_m \frac{\hat{\lambda} + \hat{\kappa} \bar{n} \hat{\lambda}}{\bar{n} H} + (n^*_m \hat{\lambda} + \hat{\kappa} n^{*2}_m \hat{\lambda}^2)}, \quad n^*_m \hat{\lambda} + q^{calib}_u \sqrt{n^*_m \frac{\hat{\lambda} + \hat{\kappa} \bar{n} \hat{\lambda}}{\bar{n} H} + (n^*_m \hat{\lambda} + \hat{\kappa} n^{*2}_m \hat{\lambda}^2) } \Big]

Please note, that this modification does not affect the calibration procedure, if only prediction limits are of interest.

Value

neg_bin_pi() returns an object of class c("predint", "negativeBinomialPI") with prediction intervals or limits in the first entry ($prediction).

References

Menssen and Schaarschmidt (2022): Prediction intervals for all of M future observations based on linear random effects models. Statistica Neerlandica, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/stan.12260")}

Examples

# HCD from the Ames test
ames_HCD

# Prediction interval for one future number of revertant colonies
# obtained in three petridishes
pred_int <- neg_bin_pi(histdat=ames_HCD, newoffset=3, nboot=100)
summary(pred_int)

# Please note that nboot was set to 100 in order to decrease computing time
# of the example. For a valid analysis set nboot=10000.

predint documentation built on May 29, 2024, 12:28 p.m.