Distance to ROC corner

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".

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).

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 1.4142136, with 0 indicating perfect sensitivity and specificity.

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.

Examples

# Two class
data("two_class_example")
roc_dist(two_class_example, truth, predicted)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 roc_dist binary         0.239

# Multiclass
library(dplyr)
data(hpc_cv)

hpc_cv |>
  filter(Resample == "Fold01") |>
  roc_dist(obs, pred)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 roc_dist macro          0.511

# Groups are respected
hpc_cv |>
  group_by(Resample) |>
  roc_dist(obs, pred)
#> # A tibble: 10 × 4
#>    Resample .metric  .estimator .estimate
#>    <chr>    <chr>    <chr>          <dbl>
#>  1 Fold01   roc_dist macro          0.511
#>  2 Fold02   roc_dist macro          0.518
#>  3 Fold03   roc_dist macro          0.417
#>  4 Fold04   roc_dist macro          0.490
#>  5 Fold05   roc_dist macro          0.505
#>  6 Fold06   roc_dist macro          0.523
#>  7 Fold07   roc_dist macro          0.528
#>  8 Fold08   roc_dist macro          0.473
#>  9 Fold09   roc_dist macro          0.487
#> 10 Fold10   roc_dist macro          0.519

# Weighted macro averaging
hpc_cv |>
  group_by(Resample) |>
  roc_dist(obs, pred, estimator = "macro_weighted")
#> # A tibble: 10 × 4
#>    Resample .metric  .estimator     .estimate
#>    <chr>    <chr>    <chr>              <dbl>
#>  1 Fold01   roc_dist macro_weighted     0.385
#>  2 Fold02   roc_dist macro_weighted     0.400
#>  3 Fold03   roc_dist macro_weighted     0.341
#>  4 Fold04   roc_dist macro_weighted     0.403
#>  5 Fold05   roc_dist macro_weighted     0.392
#>  6 Fold06   roc_dist macro_weighted     0.424
#>  7 Fold07   roc_dist macro_weighted     0.437
#>  8 Fold08   roc_dist macro_weighted     0.389
#>  9 Fold09   roc_dist macro_weighted     0.427
#> 10 Fold10   roc_dist macro_weighted     0.406

# Vector version
roc_dist_vec(
  two_class_example$truth,
  two_class_example$predicted
)
#> [1] 0.2390096

# Making Class2 the "relevant" level
roc_dist_vec(
  two_class_example$truth,
  two_class_example$predicted,
  event_level = "second"
)
#> [1] 0.2390096