rstudent.brma: Externally Standardized (Studentized) Residuals for brma...

In RoBMA: Robust Bayesian Meta-Analyses

Externally Standardized (Studentized) Residuals for brma Objects

Description

Computes externally standardized residuals (also called studentized residuals or standardized deleted residuals) from a fitted brma object using LOO-PIT (Leave-One-Out Probability Integral Transform). Returns a data frame with raw residuals, standard errors, and standardized residuals (z-values).

Usage

## S3 method for class 'brma'
rstudent(model, unit = "estimate", conditioning_depth = "marginal", ...)

Arguments

model	a fitted brma object.
unit	output unit. Only "estimate" is available for LOO-PIT residuals.
conditioning_depth	unused for LOO-PIT residuals. LOO-PIT residuals always use the estimate-unit LOO target.
...	additional arguments (currently ignored)

Details

This function returns a data frame with three columns matching the output of metafor::rstudent:

• resid: LOO predictive residuals (observed - fitted values)

• se: LOO predictive standard errors when available

• z: Externally standardized residuals (LOO-PIT transformed)

LOO-PIT residuals are the Bayesian equivalent of studentized deleted residuals. They are computed via leave-one-out probability integral transformation using Pareto smoothed importance sampling. For each observation, the LOO-weighted CDF is computed and transformed to a standard normal quantile.

Under a correctly specified model, LOO-PIT residuals should follow a standard normal distribution. Large absolute values may indicate outliers or model misspecification.

The z column is the primary standardized diagnostic. The resid and se columns are raw-scale companions computed from LOO predictive moments using the normalized PSIS weights. For selection models, these moments are computed from the fitted selected-normal predictive distribution. For GLMMs, they are computed on the approximate effect-size scale used by the LOO-PIT diagnostic; they are not exact PIT diagnostics for the raw count likelihood.

Unlike rstandard.brma (which uses the hat matrix), LOO-PIT residuals properly account for estimation uncertainty and leverage without requiring explicit hat matrix computation. This makes rstudent.brma suitable for all model types including selection models and GLMMs.

Value

A data frame with columns:

• resid: Raw residuals

• se: Standard errors of the residuals

• z: Externally standardized residuals (LOO-PIT)

See Also

rstandard.brma(), residuals.brma(), loo.brma(), blup.brma()

Examples

## Not run: 
if (requireNamespace("metadat", quietly = TRUE)) {
  data(dat.lehmann2018, package = "metadat")
  fit <- brma(yi = yi, vi = vi, data = dat.lehmann2018, measure = "SMD")
  fit <- add_loo(fit)

  # externally standardized residuals
  rstudent(fit)

  # check Pareto k values
  plot(loo(fit))
}

## End(Not run)

RoBMA documentation built on May 7, 2026, 5:08 p.m.