roc_dist: Distance to ROC corner

In yardstick: Tidy Characterizations of Model Performance

Distance to ROC corner

Description

roc_dist() calculates the Euclidean distance from the observed (sensitivity, specificity) point to the ideal corner (1, 1) in ROC space. This is equivalent to the distance from (FPR, TPR) to (0, 1).

This metric is sometimes called "closest to top-left" in ROC analysis and provides an alternative to j_index() for finding optimal classification thresholds.

Usage

roc_dist(data, ...)

## S3 method for class 'data.frame'
roc_dist(
  data,
  truth,
  estimate,
  estimator = NULL,
  na_rm = TRUE,
  case_weights = NULL,
  event_level = yardstick_event_level(),
  ...
)

roc_dist_vec(
  truth,
  estimate,
  estimator = NULL,
  na_rm = TRUE,
  case_weights = NULL,
  event_level = yardstick_event_level(),
  ...
)

Arguments

data	Either a data.frame containing the columns specified by the truth and estimate arguments, or a table/matrix where the true class results should be in the columns of the table.
...	Not currently used.
truth	The column identifier for the true class results (that is a factor). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For ⁠_vec()⁠ functions, a factor vector.
estimate	The column identifier for the predicted class results (that is also factor). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For ⁠_vec()⁠ functions, a factor vector.
estimator	One of: "binary", "macro", "macro_weighted", or "micro" to specify the type of averaging to be done. "binary" is only relevant for the two class case. The other three are general methods for calculating multiclass metrics. The default will automatically choose "binary" or "macro" based on estimate.
na_rm	A logical value indicating whether NA values should be stripped before the computation proceeds.
case_weights	The optional column identifier for case weights. This should be an unquoted column name that evaluates to a numeric column in data. For ⁠_vec()⁠ functions, a numeric vector, hardhat::importance_weights(), or hardhat::frequency_weights().
event_level	A single string. Either "first" or "second" to specify which level of truth to consider as the "event". This argument is only applicable when estimator = "binary". The default uses an internal helper that defaults to "first".

Details

Suppose a 2x2 table with notation:

	Reference
Predicted	Positive	Negative
Positive	A	B
Negative	C	D

The formulas used here are:

\text{Sensitivity} = \frac{A}{A + C}

\text{Specificity} = \frac{D}{B + D}

\text{roc\_dist} = \sqrt{(1 - \text{Sensitivity})^2 + (1 - \text{Specificity})^2}

roc_dist is a metric that should be minimized. The output ranges from 0 to 1.4142135623731, with 0 indicating perfect sensitivity and specificity.

Value

A tibble with columns .metric, .estimator, and .estimate and 1 row of values.

For grouped data frames, the number of rows returned will be the same as the number of groups.

For roc_dist_vec(), a single numeric value (or NA).

Relevant Level

There is no common convention on which factor level should automatically be considered the "event" or "positive" result when computing binary classification metrics. In yardstick, the default is to use the first level. To alter this, change the argument event_level to "second" to consider the last level of the factor the level of interest. For multiclass extensions involving one-vs-all comparisons (such as macro averaging), this option is ignored and the "one" level is always the relevant result.

Multiclass

Macro, micro, and macro-weighted averaging is available for this metric. The default is to select macro averaging if a truth factor with more than 2 levels is provided. Otherwise, a standard binary calculation is done. See vignette("multiclass", "yardstick") for more information.

See Also

All class metrics

j_index() for Youden's J statistic, another metric for measuring closeness to the ideal classification point.

Other class metrics: accuracy(), bal_accuracy(), detection_prevalence(), f_meas(), fall_out(), j_index(), kap(), markedness(), mcc(), miss_rate(), npv(), ppv(), precision(), recall(), sedi(), sens(), spec()

Examples

# Two class
data("two_class_example")
roc_dist(two_class_example, truth, predicted)

# Multiclass
library(dplyr)
data(hpc_cv)

hpc_cv |>
  filter(Resample == "Fold01") |>
  roc_dist(obs, pred)

# Groups are respected
hpc_cv |>
  group_by(Resample) |>
  roc_dist(obs, pred)

# Weighted macro averaging
hpc_cv |>
  group_by(Resample) |>
  roc_dist(obs, pred, estimator = "macro_weighted")

# Vector version
roc_dist_vec(
  two_class_example$truth,
  two_class_example$predicted
)

# Making Class2 the "relevant" level
roc_dist_vec(
  two_class_example$truth,
  two_class_example$predicted,
  event_level = "second"
)

yardstick documentation built on April 8, 2026, 1:06 a.m.