Radial (Galbraith) Plot for brma Object

radial.brma creates a radial (Galbraith) plot for a fitted brma object. The plot displays each study as a point with precision on the x-axis and the standardized effect size on the z-axis. Without centering, a line from the origin through any point has slope equal to the observed effect size. With centering, slopes are relative to the pooled estimate. An arc on the right side maps standardized values back to the effect size scale.

Usage

# S3 method for class 'brma'
radial(
  x,
  center = FALSE,
  xlim,
  zlim,
  xlab,
  zlab,
  atz,
  aty,
  steps = 7,
  level = 95,
  digits = 2,
  transf,
  targs,
  plot_type = "base",
  ...
)

# S3 method for class 'brma'
galbraith(x, ...)

Arguments

x

a fitted brma object. Must be an intercept-only model (no moderators or scale regression).

center

logical indicating whether to center the plot at the pooled estimate. When TRUE, the pooled estimate is shifted to zero on the z-axis. Defaults to FALSE.

xlim

x-axis limits. If not specified, limits are computed from data.

zlim

z-axis limits. If not specified, limits are computed from data.

xlab

title for the x-axis. If not specified, a default label is used.

zlab

title for the z-axis. If not specified, a default label is used.

atz

numeric vector of positions for tick marks on the z-axis (left vertical axis). If not specified, positions are chosen automatically.

aty

numeric vector of effect size values to mark on the y-axis arc (right side). If not specified, values are chosen automatically.

steps

integer specifying the number of tick marks on the y-axis arc when aty is not specified. Defaults to 7.

level

numeric value between 0 and 100 specifying the confidence level for the confidence band and pooled-effect CI arc. Defaults to 95.

digits

integer specifying the number of decimal places for y-axis arc labels. Defaults to 2.

transf

optional transformation function applied to the y-axis arc labels (e.g., transf = exp when effect sizes are on a log scale).

targs

optional list of additional arguments passed to the transf function.

plot_type

whether to use a base plot "base" or ggplot2 "ggplot" for plotting. Defaults to "base".

...

additional graphical arguments to customize the plot appearance:

pch: point symbol (default: 21, filled circle)
col: point border color (default: "black")
bg: point fill/background color (default: "#A6A6A6")
cex: point size multiplier for base graphics (default: 1)
size: point size for ggplot2 (default: 2)
las: axis-label style for base graphics (default: 1)
back: background color for the confidence band (default: "grey90"). Set to NA to suppress.
arc.res: integer specifying the number of line segments used to draw arcs (default: 100)
main: character string for plot title (default: no title)
as_data: if TRUE, returns plot data instead of creating the plot

Value

radial.brma returns NULL invisibly if plot_type = "base" or a ggplot object if plot_type = "ggplot".

If as_data = TRUE, returns a list with the computed plot data including: points, refline, band, arc, arc_ticks, ci_arc, ci_ticks, xlim, and zlim.

Details

The radial (Galbraith) plot transforms each study's effect size and standard error into a point in precision-standardized space:

x-axis: precision = \(1/\sqrt{v_i + \hat{\tau}^2}\)
z-axis: standardized effect = \(y_i/\sqrt{v_i + \hat{\tau}^2}\)

Under the random-effects model, studies consistent with the pooled effect should fall within the sloped parallelogram confidence band around the pooled-effect line. The arc on the right side allows reading individual effect sizes by projecting from the origin through a point to the arc; when center = TRUE, the plotted slope is relative to the pooled effect.

This function requires an intercept-only model; radial plots are not meaningful for meta-regression or location-scale models where the pooled effect varies across studies.

galbraith() is a same-argument alias for radial().

References

Galbraith, R. F. (1988). Graphical display of estimates having differing standard errors. Technometrics, 30(3), 271-281.

Galbraith, R. F. (1994). Some applications of radial plots. Journal of the American Statistical Association, 89(428), 1232-1242.

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, data = dat, measure = "RR")
  radial(fit)
  radial(fit, center = TRUE)
  radial(fit, plot_type = "ggplot")
  galbraith(fit)
}
} # }