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
)bb_pi() returns an object of class c("predint", "betaBinomialPI")
with prediction intervals or limits in the first entry ($prediction).
number of experimental units in the historical clusters
number of experimental units in the future clusters
binomial proportion
intra class correlation
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
beta_bin_pi(). This argument is not of interest for the calculation
of simple uncalibrated intervals
This function returns a simple uncalibrated prediction interval $$[l,u]_m = n^*_m \hat{\pi} \pm q \sqrt{n^*_m \hat{\pi} (1- \hat{\pi}) [1 + (n^*_m -1) \hat{\rho}] + [\frac{n^{*2}_m \hat{\pi} (1- \hat{\pi})}{\sum_h n_h} + \frac{\sum_h n_h -1}{\sum_h n_h} n^{*2}_m \hat{\pi} (1- \hat{\pi}) \hat{\rho}]}$$
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.
# 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)
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