qb_pi function

Simple uncalibrated prediction intervals for quasi-binomial data

qb_pi() is a helper function that is internally called by quasi_bin_pi(). It calculates simple uncalibrated prediction intervals for binary data with constant overdispersion (quasi-binomial assumption).

qb_pi(
  newsize,
  histsize,
  pi,
  phi,
  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
• phi: dispersion parameter
• 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 quasi_bin_pi. This argument is not of interest for the calculation of simple uncalibrated intervals

Returns

qb_pi returns an object of class c("predint", "quasiBinomailPI").

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, $\hat{\phi}$ as the estimate for the dispersion parameter 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 the beta_bin_pi() functions for real life applications.

Examples

qb_pred <- qb_pi(newsize=50, pi=0.3, phi=3, histsize=c(50, 50, 30), q=qnorm(1-0.05/2))
summary(qb_pred)