Variance Inflation Factors for brma Objects

Computes variance inflation factors (VIF) and generalized VIF (GVIF) for a fitted brma meta-regression model. Also optionally returns the posterior correlation matrix of regression coefficients.

Usage

# S3 method for class 'brma'
vif(object, posterior_correlation = TRUE, ...)

Arguments

object: a fitted brma object with moderators
posterior_correlation: logical; whether to also compute and return the posterior correlation matrix of regression coefficients. Defaults to TRUE.
...: additional arguments (currently ignored)

Value

An object of class vif.brma containing:

vif: A data frame with columns term, df, GVIF, and GVIF^(1/(2*df)) (= \(GVIF^{1/(2 \cdot df)}\)). For single-df terms, GVIF equals the standard VIF.
posterior_correlation: A correlation matrix of posterior regression coefficient samples when requested and available; otherwise NULL.

Details

VIF is computed from the correlation matrix derived from the coefficient variance-covariance matrix \((X'WX)^{-1}\). For standard meta-regression models, \(W = \mathrm{diag}(w_i/(v_i + \hat\tau^2))\) with \(\hat\tau\) equal to the posterior mean heterogeneity. For scale and multilevel models, the coefficient covariance is averaged across posterior heterogeneity draws, using observation-specific \(\tau_i\) and block-structured multilevel covariance where applicable.

A VIF of 1 indicates no collinearity; values above 5 or 10 are commonly considered problematic.

For multi-column terms, such as factor contrasts, the Generalized VIF (GVIF) of Fox and Monette (1992) is reported. GVIF captures the joint inflation for all coefficients belonging to the same term. To enable comparison across terms with different degrees of freedom, \(GVIF^{1/(2 \cdot df)}\) is also reported; this value can be compared against the usual VIF thresholds (after squaring).

When posterior_correlation = TRUE, the function also returns the posterior correlation matrix of the regression coefficients. This Bayesian diagnostic complements VIF: while VIF diagnoses the potential for collinearity problems (a data property), the posterior correlation shows the realized identification given the data and priors. Informative priors can mitigate collinearity, reducing posterior correlations even when VIF is high.

References

Fox J, Monette G (1992). “Generalized collinearity diagnostics.” Journal of the American Statistical Association, 87(417), 178–183. doi:10.1080/01621459.1992.10475190 .

Examples

if (FALSE) { # \dontrun{
if (requireNamespace("metadat", quietly = TRUE) &&
    requireNamespace("metafor", quietly = TRUE)) {
  data(dat.bcg, package = "metadat")
  dat <- metafor::escalc(
    measure = "RR",
    ai      = tpos,
    bi      = tneg,
    ci      = cpos,
    di      = cneg,
    data    = dat.bcg
  )
  fit <- brma(
    yi      = yi,
    vi      = vi,
    mods    = ~ ablat + year,
    data    = dat,
    measure = "RR",
    seed    = 1,
    silent  = TRUE
  )

  vif(fit)
}
} # }