normal_pi function

Simple uncalibrated prediction intervals for normal distributed data

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.

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

Returns

normal_pi() returns an object of class c("predint", "normalPI")

with prediction intervals or limits in the first entry ($prediction).

Details

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

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.

Examples

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

References

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