plot.bmm_sdt_roc: Plot a model-implied SDT ROC curve

In bmm: Easy and Accessible Bayesian Measurement Models Using 'brms'

Plot a model-implied SDT ROC curve

Description

Shows the smooth model-implied ROC as a credible-band ribbon, with the model-implied operating points overlaid as colour-coded markers with crosshair error bars (uncertainty in both directions). For binary multi-criteria fits the points are the several criterion levels; for rating models they are the K-1 confidence thresholds (labelled t1..t(K-1)). Pass observed to overlay empirical points from roc_observed().

Usage

## S3 method for class 'bmm_sdt_roc'
plot(
  x,
  observed = NULL,
  condition_col = NULL,
  add_diagonal = TRUE,
  scale = c("probability", "quantile", "z"),
  ribbon_alpha = 0.25,
  point_size = 2.5,
  ...
)

Arguments

x	A "bmm_sdt_roc" object from roc_sdt().
observed	Optional "bmm_sdt_roc_observed" object from roc_observed() to overlay as empirical points.
condition_col	Optional character. Condition column for colour/faceting. If NULL (default), auto-detected.
add_diagonal	Logical. Draw the chance-level diagonal (default TRUE).
scale	Either "probability" (default) for the usual hit vs. false- alarm-rate axes, or "quantile" (alias "z") for the quantile-transformed axes (the inverse CDF of the fitted noise distribution).
ribbon_alpha	Numeric. Transparency of the credible band (default 0.25).
point_size	Numeric. Size of operating-point markers (default 2.5).
...	Ignored.

Details

With scale = "quantile" (or its alias scale = "z") the rates are read on the distribution's quantile axis via the transform -qf(1 - rate), where qf is the inverse CDF of the fitted noise distribution, and the axis label names that transform (z for normal, logit for logistic, loglog/cloglog for the Gumbel distributions). On this axis the binary model ROC is a straight line with slope 1 / exp(sdratio) and intercept d * sqrt((1 + exp(sdratio)^2) / 2) / exp(sdratio) – the separation in noise-SD units over the signal SD, since d is d_a – so a slope below 1 is the unequal-variance signature (signal SD > noise SD), and departures of the observed points from a straight line diagnose misfit. This linearity holds for all four distributions. The (0,0) and (1,1) endpoints map to infinity and are dropped on the transformed scale.

Value

A ggplot2 object. The credible band (ribbon) is the pointwise posterior interval of the hit rate at each criterion value, plotted at that criterion's posterior-mean false-alarm rate; it does not include uncertainty in the false-alarm rate.

See Also

roc_sdt(), roc_observed(), auc_sdt()

bmm documentation built on Oct. 16, 2026, 9:08 a.m.