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
)qb_pi returns an object of class c("predint", "quasiBinomailPI").
number of experimental units in the historical clusters.
number of experimental units in the future clusters.
binomial proportion
dispersion parameter
quantile used for interval calculation
either "both", "upper" or "lower"
alternative specifies, if a prediction interval or
an upper or a lower prediction limit should be computed
additional argument to specify the current data set
additional argument to specify the historical data set
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
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.
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)
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