dfbetas.brma: DFBETAS for brma Objects

In RoBMA: Robust Bayesian Meta-Analyses

DFBETAS for brma Objects

Description

Computes DFBETAS (Difference in BETAS, standardized) for a fitted brma object. DFBETAS measures the influence of each observation on the estimated model coefficients. Positive values indicate that deleting the observation yields a smaller estimate, negative values indicate that deleting the observation yields a larger estimate.

Usage

## S3 method for class 'brma'
dfbetas(
  model,
  type = "mods",
  standardized_coefficients = FALSE,
  transform_factors = TRUE,
  return_loo_estimates = FALSE,
  ...
)

Arguments

model	a fitted brma object.
type	type of parameters to be summarized. Defaults to "mods" (for the effect size and meta-regression coefficients). The other options are "scale" (for the heterogeneity and scale-regression coefficients) and "bias" (for omega, PET, and PEESE publication-bias parameters).
standardized_coefficients	whether to show standardized meta-regression coefficients. Defaults to FALSE. When set to TRUE, standardized meta-regression coefficients are returned for the intercept and continuous predictors. These coefficients correspond to the standardized scale on which prior distributions are specified by default (i.e., standardize_continuous_predictors = TRUE).
transform_factors	whether to transform factors to their original names. Defaults to TRUE.
return_loo_estimates	whether to return the leave-one-out coefficient estimates used to compute DFBETAS instead of standardized DFBETAS values. Defaults to FALSE.
...	additional arguments (currently ignored).

Details

This function computes DFBETAS values using the Leave-One-Out (LOO) approximation based on Pareto Smoothed Importance Sampling (PSIS) weights. Ideally, DFBETAS is defined as:

DFBETAS_{ij} = \frac{\hat{\beta}_j - \hat{\beta}_{j(-i)}}{SE(\hat{\beta}_{j(-i)})}

where \hat{\beta}_j is the estimate of the j-th coefficient using the full data, \hat{\beta}_{j(-i)} is the estimate when observation i is omitted, and SE(\hat{\beta}_{j(-i)}) is the standard error of the coefficient when observation i is omitted.

In the Bayesian context using LOO approximation:

• \hat{\beta}_{j(-i)} is estimated as the importance sampling weighted mean of the posterior samples, using PSIS weights w_{is}.

• SE(\hat{\beta}_{j(-i)}) is estimated as the importance sampling weighted standard deviation of the posterior samples.

This approximation allows computing influence statistics without refitting the model K times, making it computationally efficient. For type = "bias", fixed identification parameters (e.g., the reference \omega = 1 interval) can have zero LOO posterior standard deviation. These parameters are retained in the output, but their DFBETAS values are reported as NaN because the standardized diagnostic is undefined.

Note: This function requires that LOO-CV has been computed for the model using add_loo.

Value

If return_loo_estimates = FALSE, a data frame with K rows (observations) and P columns (parameters), containing DFBETAS values. If return_loo_estimates = TRUE, returns the corresponding leave-one-out coefficient estimates. Row names correspond to study labels (if available) or indices.

See Also

add_loo, loo_weights.brma

Examples

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

  inf <- dfbetas(fit)
  plot(inf[, 1], type = "h")
}

## End(Not run)

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