J-index

Youden's J statistic is defined as:

sens() + spec() - 1

A related metric is Informedness, see the Details section for the relationship.

j_index(data, ...)

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

j_index_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 j_index_vec(), a single numeric value (or NA).

Details

The value of the J-index ranges from [0, 1] and is 1 when there are no false positives and no false negatives.

The binary version of J-index is equivalent to the binary concept of Informedness. Macro-weighted J-index is equivalent to multiclass informedness as defined in Powers, David M W (2011), equation (42).

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.

References

Youden, W.J. (1950). "Index for rating diagnostic tests". Cancer. 3: 32-35.

Powers, David M W (2011). "Evaluation: From Precision, Recall and F-Score to ROC, Informedness, Markedness and Correlation". Journal of Machine Learning Technologies. 2 (1): 37-63.

Author

Max Kuhn

Examples

# Two class
data("two_class_example")
j_index(two_class_example, truth, predicted)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 j_index binary         0.673

# Multiclass
library(dplyr)
data(hpc_cv)

hpc_cv %>%
  filter(Resample == "Fold01") %>%
  j_index(obs, pred)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 j_index macro          0.434

# Groups are respected
hpc_cv %>%
  group_by(Resample) %>%
  j_index(obs, pred)
#> # A tibble: 10 × 4
#>    Resample .metric .estimator .estimate
#>    <chr>    <chr>   <chr>          <dbl>
#>  1 Fold01   j_index macro          0.434
#>  2 Fold02   j_index macro          0.422
#>  3 Fold03   j_index macro          0.533
#>  4 Fold04   j_index macro          0.449
#>  5 Fold05   j_index macro          0.431
#>  6 Fold06   j_index macro          0.413
#>  7 Fold07   j_index macro          0.398
#>  8 Fold08   j_index macro          0.468
#>  9 Fold09   j_index macro          0.435
#> 10 Fold10   j_index macro          0.412

# Weighted macro averaging
hpc_cv %>%
  group_by(Resample) %>%
  j_index(obs, pred, estimator = "macro_weighted")
#> # A tibble: 10 × 4
#>    Resample .metric .estimator     .estimate
#>    <chr>    <chr>   <chr>              <dbl>
#>  1 Fold01   j_index macro_weighted     0.542
#>  2 Fold02   j_index macro_weighted     0.527
#>  3 Fold03   j_index macro_weighted     0.597
#>  4 Fold04   j_index macro_weighted     0.515
#>  5 Fold05   j_index macro_weighted     0.524
#>  6 Fold06   j_index macro_weighted     0.492
#>  7 Fold07   j_index macro_weighted     0.466
#>  8 Fold08   j_index macro_weighted     0.535
#>  9 Fold09   j_index macro_weighted     0.468
#> 10 Fold10   j_index macro_weighted     0.501

# Vector version
j_index_vec(
  two_class_example$truth,
  two_class_example$predicted
)
#> [1] 0.6732334

# Making Class2 the "relevant" level
j_index_vec(
  two_class_example$truth,
  two_class_example$predicted,
  event_level = "second"
)
#> [1] 0.6732334