bb_pi {predint}

Simple uncalibrated prediction intervals for beta-binomial data

Description

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).

Usage

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

Details

This function returns a simple uncalibrated prediction interval

[l,u]_m = n^*_m \hat{\pi} \pm q \sqrt{n^*_m \hat{\pi} (1- \hat{\pi}) [1 + (n^*_m -1) \hat{\rho}] + [\frac{n^{*2}_m \hat{\pi} (1- \hat{\pi})}{\sum_h n_h} + \frac{\sum_h n_h -1}{\sum_h n_h} n^{*2}_m \hat{\pi} (1- \hat{\pi}) \hat{\rho}]}

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.

Value

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

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)