Parametric bootstrap of any statistic of a fitted LMM

mm_bootmer() is mixeff's counterpart of lme4::bootMer(): it simulates nsim responses from the fitted model, refits the model to each, and evaluates FUN on every refit. The result has class c("mm_bootmer", "boot") with the fields boot::boot.ci() reads (t0, t, R, sim, statistic, ...), so boot::boot.ci(b, type = "perc", index = 1) works as it does for a bootMer result.

Usage

mm_bootmer(
  fit,
  FUN,
  nsim = 1L,
  seed = NULL,
  type = c("parametric", "semiparametric"),
  use.u = FALSE,
  verbose = FALSE
)

Arguments

fit

A fitted mm_lmm. GLMM fits are refused (the GLMM parametric bootstrap is confint(fit, method = "bootstrap")).

FUN

A function of a fitted mm_lmm returning a numeric vector (for example fixef, or function(m) c(fixef(m), sigma = sigma(m))).

nsim

Number of bootstrap replicates.

seed

Optional seed; NULL uses the current R RNG state, so set.seed() governs reproducibility.

type

Only "parametric" is available. lme4's "semiparametric" residual bootstrap is refused.

use.u

FALSE (default) draws new random effects for each replicate (lme4's default, the unconditional bootstrap); TRUE conditions on the fitted random effects and resamples only the residual noise.

verbose

Print a progress dot per replicate.

Value

An object of class c("mm_bootmer", "boot"): a list with t0 (FUN(fit)), t (an nsim x length(t0) matrix), R, data, seed, statistic, sim = "parametric", call, and mle, plus attributes bootFail (failed replicates) and boot.fail.msgs.

Details

The function is named mm_bootmer() rather than bootMer() because lme4::bootMer() is not an S3 generic: exporting a bootMer() would mask lme4's for merMod fits.

Replicates use the same model, REML setting, weights, and mm_control() as fit; each refit warm-starts from the fitted covariance parameters (as lme4's refit() does). A replicate whose refit fails, or whose FUN errors, is recorded as an NA row and counted in attr(, "bootFail") (lme4's convention) – never silently dropped.

See also

confint() with method = "bootstrap" for engine-run fixed-effect bootstrap intervals; simulate.mm_lmm(); refit().

Examples

set.seed(1)
d <- data.frame(g = factor(rep(1:8, each = 5)), x = rep(0:4, 8))
d$y <- 1 + 0.5 * d$x + rnorm(8)[d$g] + rnorm(40)
fit <- lmm(y ~ x + (1 | g), d, control = mm_control(verbose = -1))
b <- mm_bootmer(fit, fixef, nsim = 20, seed = 2)
apply(b$t, 2, sd)
#> (Intercept)           x 
#>   0.3896998   0.0944960 
if (requireNamespace("boot", quietly = TRUE)) {
  boot::boot.ci(b, type = "perc", index = 2)
}
#> Warning: extreme order statistics used as endpoints
#> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
#> Based on 20 bootstrap replicates
#> 
#> CALL : 
#> boot::boot.ci(boot.out = b, type = "perc", index = 2)
#> 
#> Intervals : 
#> Level     Percentile     
#> 95%   ( 0.3645,  0.6936 )  
#> Calculations and Intervals on Original Scale
#> Warning : Percentile Intervals used Extreme Quantiles
#> Some percentile intervals may be unstable