dfbetas.brma: 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 brma
dfbetas(
  model,
  type = "mods",
  standardized_coefficients = FALSE,
  transform_factors = TRUE,
  return_loo_estimates = FALSE,
  ...
)

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.

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.

Examples

Run this code

if (FALSE) {
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")
}
}