Bootstrap intervals for gauge R&R statistics

Parametric bootstrap of the fitted mixed model (lme4::bootMer()): the model is simulated nsim times, refitted and the gauge R&R statistics recomputed. Percentile intervals are returned. With few prompt or model levels the intervals are wide and asymmetric, which is the honest answer; msa_plan() shows how study size changes this.

Usage

msa_boot(fit, nsim = 200, level = 0.95, seed = NULL, ...)

Arguments

fit: An msa_fit of type numeric or binary.
nsim: Number of bootstrap samples.
level: Confidence level.
seed: Optional seed.
...: Passed to lme4::bootMer(), e.g. parallel = "snow" with a caller-supplied cluster cl.

Value

A data.frame with the point estimate and interval for each statistic, plus the bootstrap replicates as attribute boot, the confidence level, and counts n_failed (replicates with at least one non-finite statistic) and n_singular (singular replicates with all statistics finite). An explicitly supplied seed is retained as the seed attribute for reporting; with seed = NULL no seed provenance is claimed.

Details

Available for numeric and binary outcomes (lme4 models). For ordinal outcomes fitted with ordinal::clmm a parametric bootstrap is not yet implemented; as a pragmatic alternative, score the categories numerically and fit type = "numeric", or treat the top category as a binary outcome.

Numeric default fits use ordinary lme4 REML refits with nloptwrap and its usual control settings; the analytical completion of the original fit is not repeated for each bootstrap sample. An explicit fitting control passed to msa_fit() remains the model's refit control.

Singular refits with finite statistics are retained in the percentile intervals. Only non-finite values are removed, separately for each statistic. A replicate with any non-finite statistic counts as failed; it is not also counted as singular. The original fit is not a replicate. Both counts are reported by the print method, including when zero.

The boot_coverage simulation study investigates interval coverage and width by scenario; see its table in vignette("validation", package = "llmsa") (vignettes/validation.Rmd). The full runs report overcoverage of the integer-valued ndc intervals in S-boot-1, S-boot-2, S-boot-3, S-boot-4, S-boot-5, S-boot-6 and S-boot-7 beyond the anchored MCSE report threshold. No other interval estimand exceeds that report threshold in these runs. These are reported findings, not a reason to change the intervals. The vignette tabulates every scenario's coverage, width, bias, empirical standard error and MCSE, with bootstrap diagnostics shown separately.

Examples

# \donttest{
fit <- msa_fit(ic50_demo, type = "numeric")
msa_boot(fit, nsim = 50, seed = 1)
#> Parametric bootstrap, 50 replicates, 95 % percentile intervals
#>                      statistic estimate lower upper
#>              grr_pct_study_var    20.51 13.82 32.02
#>           grr_pct_contribution     4.21  1.91 10.25
#>    repeatability_pct_study_var    11.78 10.17 15.78
#>  reproducibility_pct_study_var    16.79  8.89 28.95
#>                            ndc     6.00  4.00 10.00
#>                      icc_items     0.96  0.90  0.98
#>   0 failed or non-finite replicates (non-finite values dropped)
#>   30 singular replicates retained in the intervals
# }