bb_pi function

Simple uncalibrated prediction intervals for beta-binomial data

bb_pi() is a helper function that is internally called by beta_bin_pi(). It calculates simple uncalibrated prediction intervals for binary data with overdispersion changing between the clusters (beta-binomial).

bb_pi(
  newsize,
  histsize,
  pi,
  rho,
  q = qnorm(1 - 0.05/2),
  alternative = "both",
  newdat = NULL,
  histdat = NULL,
  algorithm = NULL
)

Arguments

• newsize: number of experimental units in the historical clusters
• histsize: number of experimental units in the future clusters
• pi: binomial proportion
• rho: intra class correlation
• q: quantile used for interval calculation
• alternative: either "both", "upper" or "lower" alternative specifies, if a prediction interval or an upper or a lower prediction limit should be computed
• newdat: additional argument to specify the current data set
• histdat: additional argument to specify the historical data set
• algorithm: used to define the algorithm for calibration if called via beta_bin_pi(). This argument is not of interest for the calculation of simple uncalibrated intervals

Returns

bb_pi() returns an object of class c("predint", "betaBinomialPI")

with prediction intervals or limits in the first entry ($prediction).

Details

This function returns a simple uncalibrated prediction interval

with $n^*_m$ as the number of experimental units in the $m=1, 2, ... , M$ future clusters, $\hat{\pi}$ as the estimate for the binomial proportion obtained from the historical data, $\hat{\rho}$ as the estimate for the intra class correlation and $n_h$ as the number of experimental units per historical cluster.

The direct application of this uncalibrated prediction interval to real life data is not recommended. Please use beta_bin_pi() for real life applications.

Examples

# Pointwise uncalibrated PI
bb_pred <- bb_pi(newsize=c(50), pi=0.3, rho=0.05, histsize=rep(50, 20), q=qnorm(1-0.05/2))
summary(bb_pred)