lmer_pi_unstruc: Prediction intervals for future observations based on linear...

In predint: Prediction Intervals

Prediction intervals for future observations based on linear random effects models

Description

lmer_pi_unstruc() calculates a bootstrap calibrated prediction interval for one or more future observation(s) based on linear random effects models as described in section 3.2.4. of Menssen and Schaarschmidt (2022). Please note, that the bootstrap calibration used here does not consider the sampling structure of the future data, since the calibration values are drawn randomly from bootstrap data sets that have the same structure as the historical data.

Usage

lmer_pi_unstruc(
  model,
  newdat = NULL,
  m = NULL,
  alternative = "both",
  alpha = 0.05,
  nboot = 10000,
  delta_min = 0.01,
  delta_max = 10,
  tolerance = 0.001,
  traceplot = TRUE,
  n_bisec = 30,
  algorithm = "MS22"
)

Arguments

model	a random effects model of class lmerMod
newdat	a data.frame with the same column names as the historical data on which the model depends
m	number of future observations
alternative	either "both", "upper" or "lower". alternative specifies if a prediction interval or an upper or a lower prediction limit should be computed
alpha	defines the level of confidence (1-alpha)
nboot	number of bootstraps
delta_min	lower start value for bisection
delta_max	upper start value for bisection
tolerance	tolerance for the coverage probability in the bisection
traceplot	if TRUE: Plot for visualization of the bisection process
n_bisec	maximal number of bisection steps
algorithm	either "MS22" or "MS22mod" (see details)

Details

This function returns bootstrap-calibrated prediction intervals as well as lower or upper prediction limits.

If algorithm is set to "MS22", both limits of the prediction interval are calibrated simultaneously using the algorithm described in Menssen and Schaarschmidt (2022), section 3.2.4. The calibrated prediction interval is given as

[l,u] = \hat{\mu} \pm q^{calib} \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 obtained from the random effects model fitted with lme4::lmer() and q^{calib} as the as the bootstrap-calibrated coefficient used for interval calculation.

If algorithm is set to "MS22mod", both limits of the prediction interval are calibrated independently from each other. The resulting prediction interval is given by

[l,u] = \Big[\hat{\mu} - q^{calib}_l \sqrt{\widehat{var}(\hat{\mu}) + \sum_{c=1}^{C+1} \hat{\sigma}^2_c}, \quad \hat{\mu} + q^{calib}_u \sqrt{\widehat{var}(\hat{\mu}) + \sum_{c=1}^{C+1} \hat{\sigma}^2_c} \Big].

Please note, that this modification does not affect the calibration procedure, if only prediction limits are of interest.

This function is an direct implementation of the PI given in Menssen and Schaarschmidt 2022 section 3.2.4.

Value

lmer_pi_futvec() 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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/stan.12260")}

Examples

# loading lme4
library(lme4)

# Fitting a random effects model based on c2_dat1
fit <- lmer(y_ijk~(1|a)+(1|b)+(1|a:b), c2_dat1)
summary(fit)

# Prediction interval using c2_dat2 as future data
pred_int <- lmer_pi_unstruc(model=fit, newdat=c2_dat2, alternative="both", nboot=100)
summary(pred_int)

# Upper prediction limit for m=3 future observations
pred_u <- lmer_pi_unstruc(model=fit, m=3, alternative="upper", nboot=100)
summary(pred_u)

# Please note that nboot was set to 100 in order to decrease computing time
# of the example. For a valid analysis set nboot=10000.

predint documentation built on May 29, 2024, 12:28 p.m.