Simulates new datasets from a fitted model using lme4::bootMer(), refits
the model to each replicate, and computes bootstrap confidence intervals
for the three core hypotheses (H1, H2, H3). This is especially useful when
asymptotic Wald intervals are unreliable due to singular or boundary fits.
Usage
usdt_boot(
object,
nsim = 1000,
ncores = 1L,
max_attempts = 2 * nsim,
seed = NULL,
progress = interactive(),
level = 0.95,
type = c("perc", "norm", "basic")
)Arguments
- object
A frequentist
hsdtobject fitted byhsdt(). A Bayesian fit already carries the posterior of every quantity.- nsim
Target number of successful replicates (at least 500).
- ncores
Number of CPU cores for parallel processing. Values above 1 create a temporary cluster that works across Windows, macOS, and Linux, and automatically stops when finished.
- max_attempts
Maximum number of refits to attempt. Defaults to
2 * nsim.- seed
Random seed for reproducibility. With the default
NULL, no seed is set and the bootstrap continues the current random number stream.- progress
Logical. Display a progress bar during fitting (defaults to
TRUEin interactive sessions).- level
Confidence level for intervals (default is 0.95).
- type
Type of bootstrap interval:
"perc"(percentile),"norm"(normal approximation with bias correction), or"basic"(empirical basic). For correlations,"norm"and"basic"operate on the Fisher-\(z\) scale. If the sample correlation lies on the boundary (-1 or 1), these types returnNA, whereas"perc"remains available.
Value
An updated hsdt object where interval columns in $tests are
replaced by bootstrap estimates. A new $boot element contains:
$t: Matrix of replicates for the three hypotheses.$variance: Replicates of sensitivity variances.$population: Replicates of average criteria and sensitivities.$subjects: Replicates of individual-level parameters.Run diagnostics and convergence counts (
usable,attempted,retained,failures).
Details
Refits are retained if they converge and all four hypothesis estimates are
finite, including singular or boundary refits meeting those conditions.
Inspect $boot$failures and $boot$retained. For dichotomized data, the
bootstrap simulates binary responses, without repeating the median split.
It remains conditional on the fitted model and available information.
When an attempted run finishes with fewer than 500 usable replicates, the
original Wald intervals are preserved, a warning is issued, and raw
attempt diagnostics are stored in $boot.
Point estimates remain identical to the original model fit. Two-sided bootstrap \(p\)-values compare the observed test statistic against the centered bootstrap distribution using standard finite-sample adjustment (\((k + 1) / (B + 1)\)), ensuring \(p\)-values never equal zero.
Examples
# Contextual cuing data from Vadillo et al. (2025)
d <- usdt_data_tasks(
awareness = vadillo_awareness,
influence = vadillo_cuing,
subject_col = "subj",
condition_col = "condition",
condition_levels = c(signal = "old", noise = "new"),
response_col = list(awareness = "judged.old", influence = "rt"),
response_levels = list(awareness = c(signal = 1, noise = 0),
influence = c(signal = "faster",
noise = "slower")),
dichotomize = list(awareness = FALSE, influence = TRUE)
)
m <- hsdt(d)
# \donttest{
# Run parametric bootstrap with 500 replicates. Refitting this model 500
# times takes several minutes
b <- usdt_boot(m, nsim = 500, seed = 1)
# Inspect updated summary with bootstrap intervals and p-values
summary(b)
#> ── Model summary ───────────────────────────────────────────────────────────────
#>
#> Subjects: 104
#> Observations: 416 aggregated rows (46,592 trials)
#> Family: binomial (probit)
#> Coding: deviation
#> Criteria: Awareness estimated, Influence fixed to 0 (Meyen split, mean |c| = 0.0000)
#> Estimation: lme4::glmer (Nelder_Mead), tried bobyqa -> Nelder_Mead
#> Convergence: TRUE
#> Bootstrap: 500 usable replicates (545 attempts; 175 at the boundary)
#>
#> ── Fixed effects ───────────────────────────────────────────────────────────────
#>
#> Parameter Task Estimate SE 95% CI z p-value
#> criterion Awareness -0.0357 0.0289 [ -0.092, 0.021] -1.24 .215
#> d' Awareness 0.2354 0.0335 [ 0.170, 0.301] 7.03 <.001
#> d' Influence 0.1283 0.0153 [ 0.098, 0.158] 8.41 <.001
#>
#> ── Random effects ──────────────────────────────────────────────────────────────
#>
#> Parameter Task Estimate SE 95% CI
#> sd(criterion) Awareness 0.2473 0.0246 [ 0.204, 0.301]
#> sd(d') Awareness 0.1219 0.0666 [ 0.042, 0.356]
#> sd(d') Influence 0.0883 0.0190 [ 0.058, 0.135]
#> cor(d') both 0.4910 0.4949 [ -1.000, 1.000]
#>
#> ── Hypotheses ──────────────────────────────────────────────────────────────────
#>
#> H1: Group-level sensitivity difference (Δd' = Influence d' - Awareness d')
#> Parameter Estimate Boot SE Boot 95% CI (percentile) Boot p-value
#> Δd' (I - A) -0.1071 0.0364 [ -0.179, -0.033] .004
#>
#> H2: Correlation between sensitivities across tasks
#> Parameter Estimate Boot SE Boot 95% CI (percentile) Boot p-value
#> rho 0.4910 0.4949 [ -1.000, 1.000] .459
#>
#> H3: Latent regression of Influence d' on Awareness d'
#> Parameter Estimate Boot SE Boot 95% CI (percentile) Boot p-value
#> Intercept 0.0445 112650529.3249 [ -1.345, 0.341] .677
#> Slope 0.3558 489817354.3244 [ -0.875, 6.049] .425
# Check fit diagnostics across bootstrap replicates
b$boot[c("usable", "attempted", "retained", "failures")]
#> $usable
#> [1] 500
#>
#> $attempted
#> [1] 545
#>
#> $retained
#> singular boundary
#> 162 175
#>
#> $failures
#> non_finite non_converged
#> 2 43
#>
# }