qb_pi {predint}

Simple uncalibrated prediction intervals for quasi-binomial data

Description

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).

Usage

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

Details

This function returns a simple uncalibrated prediction interval

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

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.

Value

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

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)