normal_pi {predint}

Simple uncalibrated prediction intervals for normal distributed data

Description

normal_pi() is a helper function that is internally called by the lmer_pi_...() functions. It calculates simple uncalibrated prediction intervals for normal distributed observations.

Usage

normal_pi(
  mu,
  pred_se,
  m = 1,
  q = qnorm(1 - 0.05/2),
  alternative = "both",
  futmat_list = NULL,
  futvec = NULL,
  newdat = NULL,
  histdat = NULL,
  algorithm = NULL
)

Arguments

mu

overall mean

pred_se

standard error of the prediction

m

number of future observations

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

futmat_list

used to add the list of future design matrices to the output if called via lmer_pi_futmat()

futvec

used to add the vector of the historical row numbers that define the future experimental design to the output if called via lmer_pi_futmat()

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 lmer_pi_...(). This argument is not of interest for the calculation of simple uncalibrated intervals

Details

This function returns a simple uncalibrated prediction interval as given in Menssen and Schaarschmidt 2022

[l,u] = \hat{\mu} \pm q \sqrt{\widehat{var}(\hat{\mu}) + \sum_{c=1}^{C+1} \hat{\sigma}^2_c}

with \hat{\mu} as the expected future observation (historical mean) and \hat{\sigma}^2_c as the c=1, 2, ..., C variance components and \hat{\sigma}^2_{C+1} as the residual variance and q as the quantile used for interval calculation.

The direct application of this uncalibrated prediction interval to real life data is not recommended. Please use the lmer_pi_...() functions for real life applications.

Value

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

References

Menssen and Schaarschmidt (2022): Prediction intervals for all of M future observations based on linear random effects models. Statistica Neerlandica, doi:10.1111/stan.12260

Examples

# simple PI
norm_pred <- normal_pi(mu=10, pred_se=3, m=1)
summary(norm_pred)