confint.rlmerMod: Confidence intervals for the fixed-effect coefficients of an rlmer fit.

Description

Two routes.

method = "Wald": the default and the only path implemented in this package. Per-coefficient closed-form CI \(\hat\beta_k \pm z_{1-\alpha/2} \cdot SE_k\) with \(V\) taken from vcov(object, type = vcov_type) -- so the "sandwich" option carries through to the interval.
method = "boot" or "BCa": a thin dispatch to confintROB (Mason, Cantoni & Ghisletta 2021, 2024) with boot.type forwarded. The wrapper subsets the returned matrix to the fixed-effect rows so the shape matches the "Wald" path; variance-component CIs from confintROB are dropped here. vcov_type is not honoured on these paths (confintROB uses its own internal covariance).

Usage

# S3 method for rlmerMod
confint(
  object,
  parm = NULL,
  level = 0.95,
  method = c("Wald", "boot", "BCa"),
  vcov_type = c("default", "sandwich"),
  df = c("none", "satterthwaite"),
  boot.type = c("wild", "parametric"),
  nsim = 1000L,
  seed = NULL,
  ...
)

Value

A 2-column matrix with one row per selected fixed-effect coefficient, columns "<alpha/2> %" /

"<1-alpha/2> %". Attributes "method",

"vcov_type" (and, for the bootstrap paths,

"boot.type") record the options used.

Arguments

object: An rlmerMod object.
parm: Either NULL (all fixed-effect coefficients), an integer vector of coefficient indices, or a character vector of coefficient names.
level: Coverage level; default 0.95.
method: One of "Wald" (default; closed form), "boot" (bootstrap percentile via confintROB), or "BCa" (bias-corrected bootstrap via confintROB).
vcov_type: Covariance to use for \(V\) when method = "Wald": "default" (the linearised lme4 vcov; pre-existing behaviour) or "sandwich" (the robust cluster-sandwich vcov_sandwich; exact for a single nested grouping factor, approximate for crossed designs). Ignored when method = "boot" or "BCa".
df: Critical-value degrees of freedom for method = "Wald". "none" (default) uses the normal quantile \(z_{1-\alpha/2}\) as before; "satterthwaite" uses a per-coefficient Satterthwaite t-quantile (the robust IF-based df), matching summary(object, df = "satterthwaite"). It requires vcov_type = "default" and a single grouping factor; otherwise it warns and falls back to the normal quantile.
boot.type: Bootstrap kind passed to confintROB when method = "boot" or "BCa": one of "wild" (default, the confintROB recommendation) or "parametric".
nsim: Bootstrap replicates; default 1000.
seed: Optional RNG seed for reproducibility of the bootstrap.
...: Additional arguments forwarded to confintROB (e.g. clusterID for the wild bootstrap).

Details

Guidance (Koller 2014; Mason et al. 2024). The chi-sq-p Wald limit is adequate for \(J \gtrsim 20\) groups; the bootstrap earns its (substantial) cost mainly at smaller \(J\). boot.type = "wild" (the default, following confintROB) is robust to misspecification of the response covariance, while "parametric" is exact under the fitted central LMM. method = "BCa" adds the bias-correction-and-acceleration adjustment to the bootstrap percentile (preferred when the bootstrap distribution is skewed).

Small-J caveat for the sandwich. vcov_type = "sandwich" under-covers at \(J < 20\) (in a simulation study: coverage ~0.89 at \(J = 8\) vs. nominal 0.95); the sandwich path emits a warning. For Wald CIs at small \(J\) prefer vcov_type = "default" or use method = "boot" / "BCa".

References

Mason F, Cantoni E, Ghisletta P (2021). Parametric and bootstrap-based inference for linear mixed-effects models in the presence of outliers. Methodology 17(4): 271--293.